tag:blogger.com,1999:blog-44817223997686522252024-02-08T05:14:11.770-08:00Integration toolsUnknownnoreply@blogger.comBlogger33125tag:blogger.com,1999:blog-4481722399768652225.post-49196171321213004152011-08-14T04:52:00.000-07:002011-08-14T04:52:00.505-07:00A look at analog filters <p>There is a large amount of different types of filters that have evolved over the years. Although there are many different filters, all her properties. This for several different points, it looks through the similarity. We'll look at these similarities in analog filters, electronic and digital filters, in an objective manner. If traditional with filters, consideration should not be possible without filters koivori an explosion sound and remove all contacts in the modern era.</p><p>Filters are generally circles indicate processing functions and remove unwanted frequency components of the signal. Analog filters that were described as fundamental building blocks for signal processing, used in electronics are often. There are many applications that occurs with these filters, including main separating audio signals such as bass, mid-range and tweeter loudspeakers. This is sometimes heard often in separate telephone conversations in multiple phone channel one.</p><p>Another major form when discussing analog filters, look at the radio station or signal. In the radio receiver allows selecting a filter inside the box and other signals of refusal to the listener to tune into the frequency of one, although there are many out there. If not, this filter as you may remember the radio may not be present. The user if the receiver is unable to experience other brands to sharpen specific channel in one line, that you do not hear anything but the explosion.</p><p>Analog filters do not end all; there are digital filters in modern times, as well. For digital filters for analog filters, different lies in the way that systems go. Digital filter is simply a system that performs calculations on a separate time and reduce or enhance aspects of the signal. You can send an analog signal and filter through a filter of digital and analog signal reconstructed by using a <a href="http://www.differentiationinfo.com">math</a>ematical formula. However, it is all in the sequence <a href="http://www.differentiationinfo.com">number</a>s, while analog filters directly dealing with electrical circuits, without managing a <a href="http://www.differentiationinfo.com">number</a> such as digital filters.</p><p>Can be a digital filter to analog-digital converter, together with the wizard running software that performs functions of <a href="http://www.differentiationinfo.com">number</a> systems to manipulate <a href="http://www.differentiationinfo.com">math</a>ematics. While sometimes superior to analog filters, digital filters are much more expensive than equivalent analog filter due to the difficulty of the filter. However, digital filters regarding latency response time of input and response that is not a problem with analog counterpart.</p><p>Can be filters, analogue and digital and electronic complex. However, without these filters can be used radios, mobile phones or even stereo receivers. These devices connect depends entirely on these filters to verify that the sound via a signal is possible. Analog filters were standard filters, but it exceeded them digital in daily life, without even raising public opinion.</p><p>More <a href="http://www.differentiationinfo.com">math</a> articles</p><p>Tags: analog, filters,</p>This entry was posted on 18 March 2011 and is filed under "miscellaneous stuff". You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response or Trackback from your site.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-82519504431166457902011-08-10T15:28:00.000-07:002011-08-10T15:28:00.237-07:00A good reason the pension plan of your day! <p>This small off topic, but I'm thinking more about my pension in recent times. I really only 25, so some people say that I am being a bit hasty. But here's something scary <a href="http://www.differentiationinfo.com">math</a> for you:</p><p>A person is 25, and decides to invest $ 2,000 per year for 8 years<br>Person b 34 and decides to invest $ 2,000 per year for 32 years</p><p>All people in any way invest another penny, but just let pensions grow with compound interest in the scheme ... Reasonable health pension</p><p>Has the largest pension fund by the age of 46? It's pretty shocking, but there's really not much in it! That's why I'm starting early!</p><p>Experience of pension<a href="http://www.differentiationinfo.com">calculator</a>.org for some more useful tips and advice, take a look at the premium <a href="http://www.differentiationinfo.com">calculator</a>. They deserve to know what you need to invest to achieve your goals. Personally I want to retire early, so I am <a href="http://www.differentiationinfo.com">plot</a>ting ahead now.</p><p>Tags:</p>This entry was posted on 20 April 2011 and is filed under finance. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-68597041755319779342011-08-07T14:48:00.000-07:002011-08-07T14:48:00.153-07:00Android vs. iPhone – which is better? <p>There is a wide range of mobile phones and smart phones currently on the market, but there are two main contenders when it comes to the best smartphones available. IPhone and Android phones are similar in a <a href="http://www.differentiationinfo.com">number</a> of different areas, but there are certainly some of the main differences between the two countries. Each has pros and cons, so one of the right of the individual may be a very personal option.</p><p>For anyone who uses the Smartphone to time initially, or if you are new to the platform, Android beats iPhone when it comes to ease of use. Programs and functions very intuitive and unadorned to anyone mastering this phone fairly quickly.</p><p>Life is much discussed touch array when it comes to the iPhone, but since Apple's excellent amount of time to improve this; they have superior array of life compared to Android. Depending on the user, and this is still not an array, which will continue for several days at a time and could be replaced.</p><p>When it comes to open Android operating system, is the winner. This system is open source so applications available and a more user-driven and then on the iPhone.</p><p>With regard to notifications via phone, Android much higher. On the iPhone, very limited user types of notifications and how to get an alert. There are 3 fun apps available to help, but don't post on the phone itself to customize these alerts.</p><p>One of the things that Apple would merely pursuing a <a href="http://www.differentiationinfo.com">number</a> of applications that are available on the app store. This is about 4 times the apps on the Android market, but there are a large <a href="http://www.differentiationinfo.com">number</a> of Apple apps store useless. Even with this fact, both platforms provide an excellent set of apps I love good so there's no one better than the other platform in this area.</p><p>People to the joy of gaming, the iPhone much better option. A wide range of game applications available for the iPhone is far superior to that robot.</p><p>Music lovers, the iPhone comes preloaded with the iPod music player is stable and very strong.</p><p>Maybe you'll usually any kind of phones on contract, but it is certainly possible to buy all your handset — in this case Android is definitely going to win, as the price of Iphone remains very high, only package building SIM card seems to be an expensive option.</p><p>There are excellent and awesome points for each phone, so depending on the type of user, it may be a more suitable then others. There is no phone is generally better, as the advertising better left up to the client.</p><p>Tags:</p>This entry was posted on 22 June 2011 and is filed under technology. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-6833399000855955872011-08-03T13:12:00.000-07:002011-08-03T13:12:00.713-07:00How to get value for money when you buy a suit <p>When it comes to buying a suit for men, there are a variety of options available. There are many cases expensive kartisi there, as well as making bad and inexpensive. Find the right fit, and is also affordable and may sometimes be boring task. There are a few things to keep in mind when shopping for men's suits.</p><p>Initially it will consider what the use case l. If one is required for proper event and probably worn in any case you need another such clothing, it may be a better idea to rent one. On the other hand, if this happened to worn day after day as a basis for action, the case should be able to meet straight in a variety of shirts and ties. This will give the wearer flexibility most when it comes to uniforms.</p><p>Specific study cost with this purchase. It is recommended for best fit and service, go to the store for men. Here, one might expect to pay more than one department store. The key is to buy in these stores when there are special offers and promotions that take place. Many times, such as superb discounts all stores where you can buy two suits with the price of one. If they are able to wait for sales, one should do so.</p><p>When you go with a store that specializes in clothing for men, often there is an option for membership in the Club so if any special discounts and promotions. Many times there will be a reward system where the customer buys building is rewarded. If you need to buy multiple suits and shirts and ties, this may be a brilliant idea and would reward savings just buying enough goods.</p><p>Once purchased, proper care will make sure it lasts for a long time. This will vary depending on the clothing and articles, but these are often dry clean only garments. To get a life most of the clothing, need accurate care instructions to be followed.<br>Not purchase claim to be a painful experience a terrible effect on the wallet. With the right to sell and store right and the right attitude, you can buy an economical and enjoyable experience.</p><p>Tags:</p>This entry was posted on 24 June 2011 and is filed under business. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-12452398633906392392011-07-30T19:44:00.000-07:002011-07-30T19:44:00.694-07:00How to crack Iit JEE <p>The right kind of conspiracy is required for students to deal with last minute pressure and deal with people's fears.<br>Should prepare a schedule of study topics Chapter wise and prudent as well.<br>Make notes and vital points of all chapters and study those requiring conclusive.<br>This will help in the revision of chapters before the final exam.</p><p>For students who are preparing for the year<strong> 2010 IIT JEE</strong> alongside twelfth grade examinations, should be just the Board exams focus on the revision of the curriculum XII class11th, class.<br>Student exam time at the outset, it should be borne in mind that consideration should be given from one source and <strong>IIT JEE </strong>archives, workbooks, Biohazard, eats series offered by IITs/ <strong>education kaisons </strong>is an excellent starting point.</p><p>. Initially prepare mentally for IIT JEE yourselves</p><p>"Success in order to achieve", bearing this in mind the aspirants must accept themselves successful deserving candidates during training trust-ing that plays a vital role.</p><p>2. vigorous efforts</p><p>IIT JEE training requires sustained efforts. Each topic must be considered proper and specific time. Instead of one subject for a few days and then other topics, all three subjects (physics, chemistry, (<a href="http://www.differentiationinfo.com">math</a>ematics) must have time every day. it helps bored violation.</p><p>3. good governance</p><p>In the era of competition today, appropriate guidance is required for success. The sample has become completely concept je. So you need clear concepts and without doubt in each topic, to achieve an excellent ranking in ing.</p><p>It is very important to the success of the student should depend entirely on perseverance and hard work rather than luck wekoinsidinsi.</p><p><strong>Attention to detail</strong><br>In physics, chemistry and <a href="http://www.differentiationinfo.com">math</a>ematics all topics that should be selective and to cover the study should be avoided because of objective type questions and generously to a <a href="http://www.differentiationinfo.com">number</a>.<br>Gee<strong> curriculum</strong> class eleventh and twelfth is up to 45 per cent and 55 per cent of the issue ID IIT JEE<br>Topics to be studied extensively in Physics:<br>Fluid sound waves and electromagnetic induction, walictrostatix capacitors, mechanics, optics, modern physics.</p><p>Topics: Chemistry<br>Coordination, balance, physical chemistry chemical quantitative analysis page, thermodynamics, chemical linkage in organic chemistry and inorganic chemistry.</p><p><a href="http://www.differentiationinfo.com">Math</a> topics:<br>Complex <a href="http://www.differentiationinfo.com">number</a>s, a circle, parabola, Hyperbola focal engineering, probability, and limits, vectors matrices in algebra, functions, divirintiabiliti, certain integral in <a href="http://www.differentiationinfo.com">calculus</a> and <a href="http://www.differentiationinfo.com">derivative</a>s.</p><p>And that training is a key factor for success in the exam, but it is very necessary to be comfortable. When we take the stress, the brain tries to deal with things in a different form. Be comfortable while you study and try to decipher this paper cool minded.</p><p><strong>Maintain speed</strong><br>To gain a competitive advantage always aim for 100 per cent rate. Fix speed when you exercise problems. Survival strategy for speed and accuracy because it always gives you time to reconsider later.</p><p><strong>Stay composed and keep your cool</strong><br>No scan and wear yourself before the exam, and instead, take 6-8 hours sleep properly to keep your cool and focus on the exam. It is also desirable to access exam Centre 15 minutes before time. Try the questions that have no negative marks at the beginning. Read the instructions carefully on the Guide. Even if one section heading to remember that relative performance is what counts in the end.</p><p>Related materials in <a href="http://www.differentiationinfo.com">math</a>ematics</p><p>Tags: crack</p>This entry was posted on 18 March 2011 and is filed under "miscellaneous stuff". You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response or Trackback from your site.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-66488604414097853902011-07-26T09:31:00.000-07:002011-07-26T09:31:00.314-07:00Simple math. Do the math: MOS defSorry, I was unable to read the content of this page, romit.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-32486070451645169072011-07-22T02:29:00.000-07:002011-07-22T02:29:00.236-07:00All about engineering <p>In this era of perfect, everything needs to be organized, designed and well-considered fashion show. Design a pencil for a computer system, requires a lot of mind boggling, intelligence and hard work. Many technical aspects involved in stroktorisishn any mechanical developments or chemical or technical or <a href="http://www.differentiationinfo.com">math</a>ematical. Fields related to this, the design and composition and construction of all mechanical or technological called engineering. A very wide field engineering and selection of students for various engineering fields according to their interests. Also, increased appeal to engineers because of developments in the area of equipment.</p><p>The various branches of Engineering:</p><p>V aerospace engineering</p><p>Chemical engineering v</p><p>V civil engineering</p><p>V electrical engineering</p><p>5 mechanical engineering</p><p>V computer and software engineering</p><p>V chemical bioengineering</p><p>Must be called subjects such as physics, chemistry and <a href="http://www.differentiationinfo.com">math</a>ematics in upper secondary study to pursue engineering as his life. There are various colleges and institutes provide diplomas in engineering. Engineers play a key role in the development of the country as a whole. Scholars and computer experts, forensic engineers, software applications and etc from a few fields that contribute to the growth in the country. Ten top <strong>Engineering Colleges</strong> briliantes produced in the field:</p><p>Indian Institute of materials, Kanpur<br>Indian Institute of materials, Chennai<br>Indian Institute of materials, University of Ben<br>Indian Institute of materials, New Delhi<br>Indian Institute of materials, Mumbai<br>Indian Institute of materials, Guwahati<br>Indian Institute of materials, kharagbor<br>IIIT Allahabad<br>Faculty of engineering, Chennai<br>National Institute for equipment, Tamil Nadu</p><p>The entrance to the College of engineering is a lengthy process, involving a series of tests. Each College has its own entrance examination, the reputation and availability of seats. Lower percentage is required to sit the entrance exams <strong>colleges</strong>of various, which chose the College itself, then take the written test, assessing students on topics such as <a href="http://www.differentiationinfo.com">math</a>ematics, physics, chemistry and English. After carrying the written test, group discussion of student appears to be a test of confidence, communication skills and general knowledge, which makes the student eligible for interview round is critical and the last step the student towards the goal of any admission to prestigious Engineering College.</p><p>Known engineering entrance examinations:</p><p>IIT JEE joint entrance exam ITT<br>No all India engineering entrance examination<br>Pete<br>Acceptance testing ENET-National Institute<br>Webgi Bengal joint entrance examination and the West<br>DCE Delhi College of engineering<br>Manipal Institute of engineering equipment<br>Engineering entrance exam at the University of Barth<br>Exam touched-regular Maharashtra<br>SRM engineering entrance examination<br>Institute majoring science and test equipment<br>Engineering and medical entrance exam karla<br>Institute, Indian Institute of space and equipment<br>Perla Institute for science and equipment bitsat</p><p>Training for this exam is also vital, as these examinations to choose the fate of students admitted to colleges are dependents on the tags that were obtained in this test-entrance. Also many students training courses for this exam, often after choosing engineering as upper secondary theme. Wonderful Institute should meet the educational standards of the Institute and assist in strengthening confidence, speed and many other skills of the student. Time management is a vital factor, which helps students in scoring more and keep track on all subjects. It helps due attention to their respective topics, helping swift and balanced training. Also, since the fake test ID helps the student to practice exam tests and increase their grip even on difficult questions.</p><p>More <a href="http://www.differentiationinfo.com">math</a> articles</p><p>Tags: engineering</p>This entry was posted on 17 March 2011 and is filed under architecture. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-16540168818787879042011-07-17T12:08:00.000-07:002011-07-17T12:08:00.545-07:00Magic tricks revealed: psychological card trick selection <p>This is awesome so close key trick that will quickly straight to convince anyone that you have strong psychic powers. It works great on both strangers, as well as close friends, and you can do so at parties or bars or even people off the street if you're bold enough. Much about this trick is that self working completely, meaning that you don't have to do any one of lightness or anything. This purely <a href="http://www.differentiationinfo.com">math</a>ematical probability, even five years old can do this trick.</p><p>This road would soon be seems to be the trick the audience perplexed. You mention in fast recently learned some of the black arts of psychological "push". You can put your ideas in mind. Of course, don't believe you, and it's a matter for the demonstration, you will happily oblige.</p><p>You can drag fixed deck, the opening of the cards so that only you can see the cards. You spend a great deal of psychic energy in looking, look to your friend. Then you can put your cards to a stack, and tell the person to choose any two cards, without naming the case. Such as ten and three, as well as six, of the form.</p><p>When two cards chosen, look through play, show them two cards chosen right next to each other. They are amazed, and the potential for you to do this trick again. Go through the motions to consider cards, dropping <a href="http://www.differentiationinfo.com">number</a>s in their heads. When you choose two more cards, will be again right next to each other.</p><p>Because this always works because of the possibility of a purely <a href="http://www.differentiationinfo.com">math</a>ematical. Since it's not a label is the card, only the <a href="http://www.differentiationinfo.com">number</a>, there is a 90 per cent would be any two cards they picked up next to each other, since when have chosen two, really selected eight (two cards of the four suits each). Approximately 90 per cent of <a href="http://www.differentiationinfo.com">math</a>ematics only, no two opportunities of any eight cards in the deck are next to each other.</p><p>Of course, whenever talking this trick even better. More demonstration project ideas in mind, and go through the motions do painful psychological projections. If you want you can bet friendly with that you can accurately "project" cards to his head before the trick. Have fun with this.</p><p>For more information see unadorned after an influential force of psychological illusions that make you more sought after guest comfort in the city, and on the head and reveal more of the major tricks today.</p><p><br>Article from articlesbase.com</p><p>Tags: card, magic, psychic, and revealed, selection, trick, tricks</p>This entry was posted on 17 March 2011 and is filed under technology. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-23359478465592507702011-07-12T20:33:00.000-07:002011-07-12T20:33:00.697-07:00Intelligence <p>Sometimes I question if the students could be really intelligent amount smaller 30 seconds within 24 hours. They have no answer to this question. They were also questioning what is intelligence. In fact, students rarely come with any questions and it seems that we teach them what they want. This is one reason why students don't listen to teachers, and why their very poor. We are answering their questions, and even they have no interest in what we say. We are talking to the walls, most of them.<br>In schools, we call these smart students who obtained the highest scores in tests. This measurement of intelligence is not very true because we can measure only part of the intelligence service. When students scores high marks in <a href="http://www.differentiationinfo.com">math</a>, and say that or it's smart and those others who don't do well in this topic is named kghabi. This special student record high marks in <a href="http://www.differentiationinfo.com">math</a> is the only clever in <a href="http://www.differentiationinfo.com">math</a>s, and therefore may not be intelligent in others. This is a partial intelligence. At most, only part of the brain or the left side is the most enlightened part of the brain or in the dark. This gain, this student is less intelligent and more stupid.<br>Also owns intelligence in other things such as music, dance, poetry, etc. are also not much smarter. Only part of the brain which actively keeps approximately 90 per cent of the brain in sleep. We live this way for most of our lives anyway see what kind of life is leading. We have specialties in different things make us proud and vain, and we reckon we know and knows everything. This is an illusion that we live with. Anyway we reckon we don't know. This is the main reason for the inability to learn. There is no learning without humility.<br>Who is responsible for this lack of intelligence in students? More often than not, blamed the teachers currently unable to intelligence reform in their students. The blame is not really incorrect and also not really true. We don't have any programmes in the curriculum to do so, even if we calculate interaction with students in any way for this problem. Are interested only in the implementation of courses, we are satisfied. Our lessons provided no help intelligence reform, even undermining and trying to find ways to do this. How so? The subjects taught in schools and colleges placed on specialization and the outcome of this intelligence reform can only partially. This happens all the time, denied an opportunity for intelligence reform as a whole. Teacher ready to intelligence reform as a whole will fail because he or she would be in two boats at the same time. The conflict may exceed to intelligence reform as a whole.<br>We know that we are promoting this partial intelligence income also encourage stupidity. Has given us the nature of the brain we use only a <a href="http://www.differentiationinfo.com">fraction</a>. But nature does not produce anything of any use. Why men do not use all his brain? This is unnatural, and this has happened because our unnatural. Our unnatural is again a result of our thoughts. Thinking focus. We should focus on a specific point. As long as we reckon, keep only part of the brain active and neglecting the rest of the brain. He goes to sleep.<br>How do I activate the brain as a whole? It is possible to jump from all the brain cells? This is possible only when we free our minds. When it becomes free of ideas one becomes able to see the truth. Once you enter the thought, truth disappears. Surveillance even touch without ideas, taking into account the full intelligence is the key. Self-knowledge and intelligence go together. Either both or no.<br>It's cumbersome to complete and <a href="http://www.differentiationinfo.com">integrate</a>d intelligence because it's boring to avoid thinking. We know that when we try to. How are we going to avoid ideas? We can invent artificial brains more sophisticated but unknowingly becoming more difficult. The invention of computers need only part of your mind, but your brain stimulate another reasonable thing really is, which would be more simple. And keep all the brain cells really active for each time it seems almost impossible. Can we all be without Petro thereby but can be straight just so small periods. For most of the day, we will remain stupid. But if one really determined to keep one awake brain all the time, it could happen, would this person be unstable person now. He or she would in no way the same person as we knew him or her to be. Only a few people in the history of humankind have accomplished this feat.<br>Have you tried to be unknowingly? At the outset cannot stop ideas ahead. First thing we do stick to only one thought as long as you can. It is better to exercise before sleep as beats sleeping, you can go to sleep with only one thought. Then you can practice listening to all the votes to come, with all your senses and your thoughts will be dropped. You are now on your way to a full and <a href="http://www.differentiationinfo.com">integrate</a>d intelligence is the only thing that's worth.</p><p>aresthapa@yahoo.com</p><p>Find more articles in <a href="http://www.differentiationinfo.com">math</a>ematics</p><p>Tags: intelligence</p>This entry was posted on 18 March 2011 and is filed under education. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-77944560346691689352011-07-09T06:14:00.000-07:002011-07-09T06:14:00.778-07:005 top commercial banks for online business <p>And find companies that operate in the world on the Internet that commercial banks are a great way to monitor and operate in the financial aspects of their business. Today, e-commerce sites, and other online businesses need to commercial banks that will allow customers and potential customers to use credit cards with ease. Tech savvy con<a href="http://www.differentiationinfo.com">sum</a>ers want the simplest available payment options available to them, and provide this option from commercial banks.</p><p>There are many commercial banks to choose from, it is unique in the way each one. Should try out Internet business owners that want to make sure they are using the merchant bank account is better than the five listed below:</p><p><strong>Commercial Bank bouirbay</strong> </p><p>Bouirbay is one of the most prominent commercial financial statement for electronic business. The World Bank have grown popular due to the high popularity and simple subscription. Aditionali, there is no cost to owners of ebusiness for account setup. Free setup.</p><p><strong>National banckard</strong></p><p>National banckard credit card processing services, and makes it simple for online business owners to handle transactions. Bank one of the leading credit and debit card processing services. One of the reasons why national is one of the best customer service is brilliant dealer financial statement to deal with the company.</p><p><strong>PayPal</strong></p><p>PayPal many best dealer financial statement and I like the most also among small business owners. And PayPal system provides one of the smallest amount of expensive methods to accept payments online. In addition, you can choose a discount card for business owners to PayPal if the transfer of funds of customers to banking troubles.</p><p><strong>Key merchant services</strong></p><p>Many who best dealer financial statement analysis available always vote "dealer" as a service <a href="http://www.differentiationinfo.com">number</a> one. One special asset of key financial statement Bank dealer equipped with anti-fraud tools. These tools prevent suspicious transactions, and make sure that the details of personal business owners always stored safely.</p><p><strong>One dealer</strong></p><p>One dealer has itself as one of the best available commercial banks due to access to the market's most advanced plants. In addition, FAO programme rewards so that business owners can increase revenue with each transaction.</p><p><strong><a href="http://www.differentiationinfo.com">Sum</a>mary</strong></p><p>When searching for a merchant account, there are some things that should be of small business owners are looking for. At the outset, we must look for allowing them to move fast and simple processing. After that, it helps if the merchant account ready to provide shopping cart for their business on the Internet. Irreversible, small business owners should study fees and choose Bank are affordable and profitable for their businesses. Additionally, it helps to visit sites like merchantaccountforum.com to get valuable information on other good love dealer financial statement.</p><p>Tags:</p>This entry was posted on 29 June 2011 and is filed under business. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-90646440826468114642011-07-05T15:45:00.000-07:002011-07-05T15:46:30.476-07:00How to invest-shares or mutual funds? <p>Hey stock market! So exciting, a lot of fun, even profitable, even risky. It's simple to get swept into the excitement of the stock market bets placed, pitting your brain against the world, money building-with a bit of luck to build money-oh please let me only small funds-Hey what happened to my money?</p><p>Often, many new investors are wondering what the best way to invest in the stock market. Should invest in individual stocks, or should invest in mutual funds or even create solid excellent index fund? This is exactly what I am going to talk about this article today.</p><p>Most new investors diving right in and start using alternative individual stocks in the stock market or stock market Internet account such as e * trade or a touch like that. This might not be a better idea of everyone for two main reasons. First is you have to know or training necessary to select blue chips. The other reason is purely <a href="http://www.differentiationinfo.com">math</a>ematical, that will explain in a moment.</p><p>When it comes to individual stocks there are two things that you should consider. The stock market is all about risk, different risk assessment. For individual stocks there are two main risks. First one is the individual risks that come from a private company and their care. The new product will take off? Competitors come out with a better product? The Executive Chairman will end? Is there fraud? You will make the company's quarterly earnings estimates? This is the kind of things that relate to the individual risk and stocks they focusing most investors.</p><p>The second type of risk is the risk of the market. Like it or not, all the shares to the stock market to varying degrees. What is this your company profits might be a record year, which would make expense shares was about to shoot. Unfortunately may be in recession is dragging the entire market. You can drag this drag down individual stocks such as the one you have invested it. This is what we refer to as market risk.</p><p>Investors more acute problem is to focus on mitigating risk and market risk overlooks and then they get hit by the side. Fortunately, there is a way to eliminate the market risks through diversification.</p><p><a href="http://www.differentiationinfo.com">Math</a>ematically possible to completely eliminate the market risks to diversify widely. The problem, most individual investors cannot buy stocks sufficient to meet the requirements of the sport. You may have to buying 100 or 200 diversify away completely market risks, it is not realistic for most individual investors. Heck transaction costs alone would eat up most of your profits.</p><p>For this reason, starting with the selection of individual investors, especially those just for investing in mutual funds is an excellent hard because those assets, in fact, most mutual diversification away from the market risk. In fact, this is one of the most important reasons why people invest because they are able to buy hundreds of different stocks could not be an individual investor.</p><p>So there you have it; why should invest in assets, and why you should stay away from individual stocks if at all possible.</p><p>Jason Markum writer article online since 14 years. When not writing about investment, has fun running hot store Web site as it reviews the basin ingrond enjoy hot ponds and other reservoirs.</p><p><br>Article from articlesbase.com</p><p>Tags: investing, mutual funds, stocks</p>This entry was posted on 18 March 2011 and is filed under finance. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-54732855229440102012011-06-18T01:22:00.000-07:002011-06-18T01:23:06.683-07:00What we need to solve quadratic equations?Translate Request has too much data<br />Parameter name: request<br />Translate Request has too much data<br />Parameter name: request<br /> <IMG class="size-thumbnail wp-image-4841" title=Galois alt="" src="/Galois-150x150.jpg" width=150 height=150> Evariste Galois</P><P>A former colleague wondered if the <a href="www.differentiationinfo.com">quadratic</a> formula <IMG class=latex title="\frac{-b\pm \sqrt{b^2-4ac}}{2a}" alt="\frac{-b\pm \sqrt{b^2-4ac}}{2a}" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D&bg=ffffff&fg=000000&s=0"> held when <IMG class=latex title="a, b, c" alt="a, b, c" src="http://s.wordpress.com/latex.php?latex=a%2C%20b%2C%20c&bg=ffffff&fg=000000&s=0"> are complex <a href="www.differentiationinfo.com">number</a>s.</P><P>He could, of course, have figured this out by the process of completing the square:</P><P>If <IMG class=latex title="a\neq 0" alt="a\neq 0" src="http://s.wordpress.com/latex.php?latex=a%5Cneq%200&bg=ffffff&fg=000000&s=0"> then <IMG class=latex title="ax^2+bx+c= 0" alt="ax^2+bx+c= 0" src="http://s.wordpress.com/latex.php?latex=ax%5E2%2Bbx%2Bc%3D%200&bg=ffffff&fg=000000&s=0"> exactly when <IMG class=latex title=4a^2x^2+4abx+4ac=0 alt=4a^2x^2+4abx+4ac=0 src="http://s.wordpress.com/latex.php?latex=4a%5E2x%5E2%2B4abx%2B4ac%3D0&bg=ffffff&fg=000000&s=0"> (thanks to James Tanton for this trick).</P><P>This happens exactly when <IMG class=latex title=(2ax)^2+2b(2ax)+4ac=0 alt=(2ax)^2+2b(2ax)+4ac=0 src="http://s.wordpress.com/latex.php?latex=%282ax%29%5E2%2B2b%282ax%29%2B4ac%3D0&bg=ffffff&fg=000000&s=0"> or, equivalently when <IMG class=latex title=[2ax+b]^2+4ac-b^2=0 alt=[2ax+b]^2+4ac-b^2=0 src="http://s.wordpress.com/latex.php?latex=%5B2ax%2Bb%5D%5E2%2B4ac-b%5E2%3D0&bg=ffffff&fg=000000&s=0">.</P><P>This leads us to the equivalent form <IMG class=latex title=[2ax+b]^2=b^2-4ac alt=[2ax+b]^2=b^2-4ac src="http://s.wordpress.com/latex.php?latex=%5B2ax%2Bb%5D%5E2%3Db%5E2-4ac&bg=ffffff&fg=000000&s=0"> from which we deduce the <a href="www.differentiationinfo.com">quadratic</a> formula.</P><P>What did we need to get this line of reasoning to work?</P>We need to know that if <IMG class=latex title="a\neq 0" alt="a\neq 0" src="http://s.wordpress.com/latex.php?latex=a%5Cneq%200&bg=ffffff&fg=000000&s=0"> then <IMG class=latex title="ax^2+bx+c= 0" alt="ax^2+bx+c= 0" src="http://s.wordpress.com/latex.php?latex=ax%5E2%2Bbx%2Bc%3D%200&bg=ffffff&fg=000000&s=0"> exactly when <IMG class=latex title=4a^2x+4abx+4ac=0 alt=4a^2x+4abx+4ac=0 src="http://s.wordpress.com/latex.php?latex=4a%5E2x%2B4abx%2B4ac%3D0&bg=ffffff&fg=000000&s=0">. This means we can multiply and divide by non-zero quantities (as well as add and <a href="http://www.differentiationinfo.com">subtract</a>).In exchanging <IMG class=latex title=2b(2ax) alt=2b(2ax) src="http://s.wordpress.com/latex.php?latex=2b%282ax%29&bg=ffffff&fg=000000&s=0"> for <IMG class=latex title=4abx alt=4abx src="http://s.wordpress.com/latex.php?latex=4abx&bg=ffffff&fg=000000&s=0"> we are using commutativity of multiplication. We use this again in expanding the square <IMG class=latex title=[2ax+b]^2 alt=[2ax+b]^2 src="http://s.wordpress.com/latex.php?latex=%5B2ax%2Bb%5D%5E2&bg=ffffff&fg=000000&s=0"><P>In current <a href="http://www.differentiationinfo.com">math</a>ematical parlance, this means the quantities <IMG class=latex title="a,b,c, x" alt="a,b,c, x" src="http://s.wordpress.com/latex.php?latex=a%2Cb%2Cc%2C%20x&bg=ffffff&fg=000000&s=0"> come from a field</EM>. Examples are the field of rational <a href="www.differentiationinfo.com">number</a>s, the field of real <a href="www.differentiationinfo.com">number</a>s, and the field of complex <a href="www.differentiationinfo.com">number</a>s.</P><P>To take the final step from <IMG class=latex title=[2ax+b]^2=b^2-4ac alt=[2ax+b]^2=b^2-4ac src="http://s.wordpress.com/latex.php?latex=%5B2ax%2Bb%5D%5E2%3Db%5E2-4ac&bg=ffffff&fg=000000&s=0"> to <IMG class=latex title="x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}" alt="x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}" src="http://s.wordpress.com/latex.php?latex=x%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D&bg=ffffff&fg=000000&s=0"> we need to be able to extract square roots. In the field of real <a href="www.differentiationinfo.com">number</a>s we can always do this for non-negative <a href="www.differentiationinfo.com">number</a>s, but already the field of rational <a href="www.differentiationinfo.com">number</a>s presents difficulties. For the complex field we can always <a href="www.differentiationinfo.com">solve</a> <IMG class=latex title=[2ax+b]^2=b^2-4ac alt=[2ax+b]^2=b^2-4ac src="http://s.wordpress.com/latex.php?latex=%5B2ax%2Bb%5D%5E2%3Db%5E2-4ac&bg=ffffff&fg=000000&s=0"> for <IMG class=latex title=2ax+b alt=2ax+b src="http://s.wordpress.com/latex.php?latex=2ax%2Bb&bg=ffffff&fg=000000&s=0"> but the square root function</EM> does not exist as it does for positive real <a href="www.differentiationinfo.com">number</a>s.</P><P>The <a href="www.differentiationinfo.com">number</a>s <IMG class=latex title="0, 1, 2, 3, 4, 5, 6" alt="0, 1, 2, 3, 4, 5, 6" src="http://s.wordpress.com/latex.php?latex=0%2C%201%2C%202%2C%203%2C%204%2C%205%2C%206&bg=ffffff&fg=000000&s=0"> where we add and multiply modulo 7 – keeping only the remainder after division by 7 – form a field, denoted <IMG class=latex title=\mathbf{Z}_7 alt=\mathbf{Z}_7 src="http://s.wordpress.com/latex.php?latex=%5Cmathbf%7BZ%7D_7&bg=ffffff&fg=000000&s=0"></P><P>The only point that might be in doubt is division by a non-zero quantity, but we can see this can always be carried out from the following table of multiplicative <a href="www.differentiationinfo.com">inverse</a>s:</P><P>So to <a href="www.differentiationinfo.com">solve</a> a <a href="www.differentiationinfo.com">quadratic</a> <a href="http://www.differentiationinfo.com">equation</a> <IMG class=latex title="ax^2+bx+c= 0" alt="ax^2+bx+c= 0" src="http://s.wordpress.com/latex.php?latex=ax%5E2%2Bbx%2Bc%3D%200&bg=ffffff&fg=000000&s=0"> where the quantities <IMG class=latex title="a,b,c, x" alt="a,b,c, x" src="http://s.wordpress.com/latex.php?latex=a%2Cb%2Cc%2C%20x&bg=ffffff&fg=000000&s=0"> come from <IMG class=latex title=\mathbf{Z}_7 alt=\mathbf{Z}_7 src="http://s.wordpress.com/latex.php?latex=%5Cmathbf%7BZ%7D_7&bg=ffffff&fg=000000&s=0"> we can reach the step <IMG class=latex title=[2ax+b]^2=b^2-4ac alt=[2ax+b]^2=b^2-4ac src="http://s.wordpress.com/latex.php?latex=%5B2ax%2Bb%5D%5E2%3Db%5E2-4ac&bg=ffffff&fg=000000&s=0"> and then wonder if we can always <a href="www.differentiationinfo.com">solve</a> this <a href="http://www.differentiationinfo.com">equation</a>.</P><P>For example if try to <a href="www.differentiationinfo.com">solve</a> the <a href="www.differentiationinfo.com">quadratic</a> <a href="http://www.differentiationinfo.com">equation</a> <IMG class=latex title="x^2+x+1= 0" alt="x^2+x+1= 0" src="http://s.wordpress.com/latex.php?latex=x%5E2%2Bx%2B1%3D%200&bg=ffffff&fg=000000&s=0"> where <IMG class=latex title=x alt=x src="http://s.wordpress.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0"> come from <IMG class=latex title=\mathbf{Z}_7 alt=\mathbf{Z}_7 src="http://s.wordpress.com/latex.php?latex=%5Cmathbf%7BZ%7D_7&bg=ffffff&fg=000000&s=0"> we reach the step <IMG class=latex title=[2x+1]^2=-3=4 alt=[2x+1]^2=-3=4 src="http://s.wordpress.com/latex.php?latex=%5B2x%2B1%5D%5E2%3D-3%3D4&bg=ffffff&fg=000000&s=0"> mod 7.</P><P>What solutions, if any, are there to <IMG class=latex title=z^2=4 alt=z^2=4 src="http://s.wordpress.com/latex.php?latex=z%5E2%3D4&bg=ffffff&fg=000000&s=0"> mod 7?</P><IMG class=latex title=x^2 alt=x^2 src="http://s.wordpress.com/latex.php?latex=x%5E2&bg=ffffff&fg=000000&s=0"><P>So there are two solutions for <IMG class=latex title=2x+1 alt=2x+1 src="http://s.wordpress.com/latex.php?latex=2x%2B1&bg=ffffff&fg=000000&s=0"> to <IMG class=latex title=[2x+1]^2=-3=4 alt=[2x+1]^2=-3=4 src="http://s.wordpress.com/latex.php?latex=%5B2x%2B1%5D%5E2%3D-3%3D4&bg=ffffff&fg=000000&s=0">: <IMG class=latex title="2x+1=2, 2x+1=5" alt="2x+1=2, 2x+1=5" src="http://s.wordpress.com/latex.php?latex=2x%2B1%3D2%2C%202x%2B1%3D5&bg=ffffff&fg=000000&s=0">.</P><P>This gives <IMG class=latex title=2x=1 alt=2x=1 src="http://s.wordpress.com/latex.php?latex=2x%3D1&bg=ffffff&fg=000000&s=0"> or <IMG class=latex title=2x=4 alt=2x=4 src="http://s.wordpress.com/latex.php?latex=2x%3D4&bg=ffffff&fg=000000&s=0"> so that <IMG class=latex title=x=4 alt=x=4 src="http://s.wordpress.com/latex.php?latex=x%3D4&bg=ffffff&fg=000000&s=0"> or <IMG class=latex title=x=2 alt=x=2 src="http://s.wordpress.com/latex.php?latex=x%3D2&bg=ffffff&fg=000000&s=0"></P><P>We can replace the <a href="www.differentiationinfo.com">number</a> 7, above, by any prime <a href="www.differentiationinfo.com">number</a> <IMG class=latex title=p alt=p src="http://s.wordpress.com/latex.php?latex=p&bg=ffffff&fg=000000&s=0"> to get a field denoted <IMG class=latex title=\mathbf{Z}_p alt=\mathbf{Z}_p src="http://s.wordpress.com/latex.php?latex=%5Cmathbf%7BZ%7D_p&bg=ffffff&fg=000000&s=0">.</P><P>The existence of multiplicative <a href="www.differentiationinfo.com">inverse</a>s follows from Euclid’s algorithm, and when <IMG class=latex title=p alt=p src="http://s.wordpress.com/latex.php?latex=p&bg=ffffff&fg=000000&s=0"> is not a prime <a href="www.differentiationinfo.com">number</a> it’s easy to see that division by non-zero quantities in <IMG class=latex title=\mathbf{Z}_p alt=\mathbf{Z}_p src="http://s.wordpress.com/latex.php?latex=%5Cmathbf%7BZ%7D_p&bg=ffffff&fg=000000&s=0"> is not always possible.</P><P>When the <a href="http://www.differentiationinfo.com">equation</a> <IMG class=latex title=z^2=d alt=z^2=d src="http://s.wordpress.com/latex.php?latex=z%5E2%3Dd&bg=ffffff&fg=000000&s=0"> has a solution in , the <a href="www.differentiationinfo.com">number</a> <IMG class=latex title=d alt=d src="http://s.wordpress.com/latex.php?latex=d&bg=ffffff&fg=000000&s=0"> is called a <a href="www.differentiationinfo.com">quadratic</a> residue mod p.</P><P>Determining which <a href="www.differentiationinfo.com">number</a>s are <a href="www.differentiationinfo.com">quadratic</a> residues mod p is a <a href="www.differentiationinfo.com">solve</a>d, but interesting, problem that is an excellent investigation for students, and it comes simply out of trying to <a href="www.differentiationinfo.com">solve</a> <a href="www.differentiationinfo.com">quadratic</a> <a href="http://www.differentiationinfo.com">equation</a>s over these fields.</P><P>But this does not exhaust the finite fields, and for every prime <a href="www.differentiationinfo.com">number</a> <IMG class=latex title=p alt=p src="http://s.wordpress.com/latex.php?latex=p&bg=ffffff&fg=000000&s=0"> and positive integer <IMG class=latex title=r alt=r src="http://s.wordpress.com/latex.php?latex=r&bg=ffffff&fg=000000&s=0"> there is a field – known as a Galois field – with <IMG class=latex title=p^r alt=p^r src="http://s.wordpress.com/latex.php?latex=p%5Er&bg=ffffff&fg=000000&s=0"> elements.</P><P>So now we want to know under what conditions we can <a href="www.differentiationinfo.com">solve</a> <IMG class=latex title=z^2=d alt=z^2=d src="http://s.wordpress.com/latex.php?latex=z%5E2%3Dd&bg=ffffff&fg=000000&s=0"> where <IMG class=latex title="z, d" alt="z, d" src="http://s.wordpress.com/latex.php?latex=z%2C%20d&bg=ffffff&fg=000000&s=0"> come from a finite field.</P><P>When the quantities <IMG class=latex title="a, b, c ,x" alt="a, b, c ,x" src="http://s.wordpress.com/latex.php?latex=a%2C%20b%2C%20c%20%2Cx&bg=ffffff&fg=000000&s=0"> are rational <a href="www.differentiationinfo.com">number</a>s we again have the question of whether the <a href="http://www.differentiationinfo.com">equation</a> <IMG class=latex title=[2x+1]^2=b^2-4ac alt=[2x+1]^2=b^2-4ac src="http://s.wordpress.com/latex.php?latex=%5B2x%2B1%5D%5E2%3Db%5E2-4ac&bg=ffffff&fg=000000&s=0"> has a rational <a href="www.differentiationinfo.com">number</a> solution for <IMG class=latex title=x alt=x src="http://s.wordpress.com/latex.php?latex=x&bg=ffffff&fg=000000&s=0"><BR>This, of course boils down to when<IMG class=latex title=z^2=d alt=z^2=d src="http://s.wordpress.com/latex.php?latex=z%5E2%3Dd&bg=ffffff&fg=000000&s=0"> has a rational <a href="www.differentiationinfo.com">number</a> solution when <IMG class=latex title=d alt=d src="http://s.wordpress.com/latex.php?latex=d&bg=ffffff&fg=000000&s=0"> is a rational <a href="www.differentiationinfo.com">number</a> – that is, to when square roots of positive rational <a href="www.differentiationinfo.com">number</a>s are again rational <a href="www.differentiationinfo.com">number</a>s.</P><P>Thinking about exactly what we need to <a href="www.differentiationinfo.com">solve</a> a <a href="www.differentiationinfo.com">quadratic</a> <a href="http://www.differentiationinfo.com">equation</a> leads us straightforwardly to solving <a href="www.differentiationinfo.com">quadratic</a> <a href="http://www.differentiationinfo.com">equation</a>s over less often encountered <a href="www.differentiationinfo.com">number</a> fields, which in turn leads us directly to interesting and deep questions of <a href="www.differentiationinfo.com">number</a> theory, which, nevertheless, are capable of being investigated by school students.</P><P>Investigating <a href="www.differentiationinfo.com">quadratic</a> residues mod p, p prime, might also lead to more respect for the subtle intricacies of the square root as a function. The answer to <IMG class=latex title=z^2=d alt=z^2=d src="http://s.wordpress.com/latex.php?latex=z%5E2%3Dd&bg=ffffff&fg=000000&s=0"> is not re<a href="www.differentiationinfo.com">solve</a>d by simply writing <IMG class=latex title=z=\pm\sqrt{d} alt=z=\pm\sqrt{d} src="http://s.wordpress.com/latex.php?latex=z%3D%5Cpm%5Csqrt%7Bd%7D&bg=ffffff&fg=000000&s=0">.</P>Tagged as: completing the square, field, finite field, Galois field, prime <a href="www.differentiationinfo.com">number</a>, <a href="www.differentiationinfo.com">quadratic</a> <a href="http://www.differentiationinfo.com">equation</a>, <a href="www.differentiationinfo.com">quadratic</a> residue </P>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-91311914313752612302011-06-16T03:20:00.000-07:002011-06-16T03:20:00.361-07:00As Arko: cross sums <p>Excess in resto<a href="http://calculustools.wordpress.com/">ratio</a>n and Sudoku puzzles era in 2005, beating other Western game due to the development of Japanese scenery puzzle. Puzzles as Arko, formerly cross sums, is now building newer waves as mad puzzle. Bearing similarities in shape and style to Sudoku is more like a puzzle that Arko more challenging and <a href="http://integrationutilities.blogspot.com/">add</a>ictive than Sudoku.</p><p>We know how the brain and mental exercises strengthen mental functions are included in the list of wesodoko brain boosters. Prosecution, because surely a reasonable challenge Sudoku players. But if you think that just putting <a href="http://mathematictools.blogspot.com/">number</a>s on boxes in the correct sense is challenging enough, try to solve the mystery as Arko. It provides <a href="http://integrationutilities.blogspot.com/">add</a>itional difficulty and challenge of higher because they require knowledge of logic, <a href="http://integrationtool.wordpress.com/">math</a>ematics and process. It sure provide you with a mentally tougher implementation of Sudoku order wegritr. These puzzles are not for the faint-hearted.</p><p>As appalling, Arko puzzles but not impractical. Enthusiasts assert that players need to be exceptional <a href="http://integrationtool.wordpress.com/">math</a>ematical abilities or genius like Einstein decode puzzles. Knowledge calculation often enough decode puzzles as long as players using an effective strategy and logic. The understanding and mastery of the language rules for players like you make it simple to use the correct methods. Puzzles are relatively unadorned rules. "Board game" looks similar to Crossword with squares colorless and dark. However, there is no evidence in the bottom box. Figures on chairs colorless are the only clues. Each <a href="http://mathematictools.blogspot.com/">number</a> represents the total <a href="http://mathematictools.blogspot.com/">number</a> missing cells or referring to boxes. Note that the same <a href="http://mathematictools.blogspot.com/">number</a>s can not be adinds to run itself. Form, if the <a href="http://mathematictools.blogspot.com/">number</a> in box 4, you can use 1 and 3 but not 2 and 2. Though often used method of trial and miscalculation, there are more sophisticated and logical techniques of filling your erasing boxes and pencil marks.</p><p>I love a good tactic to find cells that contain the smallest amount of combinations. These <a href="http://mathematictools.blogspot.com/">number</a>s are usually minimal spectrum <a href="http://mathematictools.blogspot.com/">number</a>s such as 3, 5, 4, and other single-<a href="http://mathematictools.blogspot.com/">digit</a> <a href="http://mathematictools.blogspot.com/">number</a>s. This <a href="http://integrationutilities.blogspot.com/">limit</a>s possible answers or specific cell <a href="http://mathematictools.blogspot.com/">number</a>s. Apply the same method to adjacent cells, giving you the shot properly. Another tactic used to solve puzzles as Arko looking for ordinary <a href="http://mathematictools.blogspot.com/">number</a>s. This occurs when involved in a <a href="http://mathematictools.blogspot.com/">number</a> of cells. A regular <a href="http://mathematictools.blogspot.com/">number</a> lets you choose where to put another <a href="http://mathematictools.blogspot.com/">number</a>. For example, if 3 and 1 your answer to <a href="http://mathematictools.blogspot.com/">number</a> 4 in the vertical column or run, 1, 5, 6 per horizontal line 1 is your normal <a href="http://mathematictools.blogspot.com/">number</a>. Therefore, 1 box intersection 6 and 4. Experienced players decode puzzles to find all possible combinations and convincing plus cross reference to the right. Because like Sudoku, important figures in position as Arko.</p><p>Probably this trick third smaller amount simpler and more sophisticated. Highlight the edges of the boxes or answers cells with pencil doesn't help you decipher mysteries. But, that helps you keep track of <a href="http://mathematictools.blogspot.com/">number</a>s and your wares. This is especially useful because the puzzles as Arko certain <a href="http://integrationutilities.blogspot.com/">limit</a>s. Do you measure "board game" small k 3 3 or extend to God knows where. Over time, becomes easier with practice. Also, if you inventory combinations in your head that you can use in gameplay. This also indicates the need to abandon the simpler puzzles, and move to more challenging as Arko puzzles.</p><p>Related <a href="http://integrationtool.wordpress.com/">math</a>ematics</p><p>Tags: TRANS, Arko, amounts</p>This entry was posted on 17 March 2011, submit within <a href="http://integrationtool.wordpress.com/">math</a>ematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response or Trackback from your site.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-48045500421186537342011-06-15T04:39:00.000-07:002011-06-15T04:39:00.157-07:00Should we abandon one size fits all curricula mathematics? <p>I will <a href="http://integrationutilities.blogspot.com/">add</a>ress the <a href="http://integrationtool.wordpress.com/">Math</a>ematics Faculty of the University, not-yet-school <a href="http://integrationtool.wordpress.com/">math</a>ematics.</p><p>Nature curriculum <a href="http://integrationtool.wordpress.com/">math</a>ematics, k-16-a key issue in urgent need of rivambing, but today I want to focus on higher education <a href="http://integrationtool.wordpress.com/">math</a>ematics.</p><p>I want to focus on report of extension education times "draw my attention via Twitter of Nalini Joshi (@ monsoon0).</p><img class="size-thumbnail wp-image-4809" title="Nalini_2" alt="" src="/Nalini2-150x150.jpg" width="150" height="150">Nalini Joshi<p>Nalini is Professor of <a href="http://integrationtool.wordpress.com/">math</a>ematics at the University of Sydney, Australia (where "Professor" means "full Professor"), and Chair of applied <a href="http://integrationtool.wordpress.com/">math</a>ematics, computational biology, Director of the Centre ", and former President of the school of <a href="http://integrationtool.wordpress.com/">math</a>ematics and <a href="http://integrationtool.wordpress.com/">statistics</a> (2007-2009), Member of the Australian Academy of science, former President of the Australian <a href="http://integrationtool.wordpress.com/">Math</a>ematical Society" (December 2008-September 2010).</p><p>She is therefore particularly concerned about an article that questions whether <a href="http://integrationtool.wordpress.com/">math</a>ematics for students at colleges and universities throughout the world suitable for students today.</p><p>This is the article "education times":</p><p>________________________________________________________________</p><p>12 May 2011</p><p>The report finds that focus on the content needs of students. Writes Mistress Matthew</p><p>Teaching <a href="http://integrationtool.wordpress.com/">math</a>ematics in universities "may not be fit for purpose", not least because it tends to focus on content without a clear idea of what can be done with it. "</p><p>This is one of the conclusions of the report says universities risk leaving graduates are ill-equipped to apply sports training in "real world".</p><p>Analysis which expands to "<a href="http://integrationtool.wordpress.com/">math</a>" curriculum for <a href="http://integrationtool.wordpress.com/">math</a>ematics and <a href="http://integrationtool.wordpress.com/">statistics</a> f network and its applications to <a href="http://integrationtool.wordpress.com/">math</a>ematics and Institute earlier this year, calling for "a more flexible approach to meet the needs of the employer".</p><p>The Summit brought together heads of <a href="http://integrationtool.wordpress.com/">math</a>ematics University of Birmingham or their representatives from 26 universities offer <a href="http://toolsmathematics.wordpress.com/">degree</a>s in <a href="http://integrationtool.wordpress.com/">math</a>ematics. The resulting report, published last week, challenges and possible solutions.</p><p>One discussion group focusing on knowledge and attributes that must get students <a href="http://integrationtool.wordpress.com/">math</a>ematics allowed out.</p><p>There was "broad consensus" on key areas and Supreme qualities such as problem solving, and flexibility and enthusiasm for the subject — and the ability to communicate <a href="http://integrationtool.wordpress.com/">math</a>ematics.</p><p>The latest came under scrutiny in another discussion group.</p><p>Participants recognized that some students <a href="http://integrationtool.wordpress.com/">Math</a>ematics "social capacity" is low, and chose this topic "specifically to get away after submit through long-form writing and oral communication. However, they also believe that universities should <a href="http://integrationutilities.blogspot.com/">add</a>ress these deficits.</p><p>Institutions that offer <a href="http://toolsmathematics.wordpress.com/">degree</a>s <a href="http://integrationtool.wordpress.com/">math</a>ematics has "a duty and the need to meet the students career aspi<a href="http://calculustools.wordpress.com/">ratio</a>ns", which, says the report, include developing the skills of graduates in display and other forms of communication. The report recommends the need for students to acquire these skills, and that universities help them do so, for example, provide <a href="http://integrationtool.wordpress.com/">math</a> support centers to encourage students to "collective action".</p><p><a href="http://mathematictools.blogspot.com/">Even</a> more controversial is the question of students learning to deal with new problems, is vital because in many areas, graduates will be tackling unfamiliar problems, analysis notes.</p><p>You can <a href="http://integrationutilities.blogspot.com/">add</a> classification and rote learning by encouraging existing assessment methods with the students in new situations.</p><p>It would be more useful to lecturers as a role model in trying to re<a href="www.differentiationinfo.com">solve</a> unfamiliar problems, especially the ' dirty ' problems with substantial risk of failure. "</p><p>The report calls for "coordinated" and less voice concern about the quality assurance agency's demands, saying "if we were clear enough about what we want to do with our students, confidence that happy for us to do what we love".</p><p>The project also warns academics — career ambitions as a <a href="http://integrationtool.wordpress.com/">math</a>ematician at University students and curriculum design to meet "the aspi<a href="http://calculustools.wordpress.com/">ratio</a>ns of those who will study the curriculum".</p><p>The recommendations include more specific "Development Bank of problems based on industry" and further reflection on the difference between strict proof and ways to <a href="http://integrationutilities.blogspot.com/">add</a>ress unusual realism scenarios that might yield useful answers.</p><p>matthew.reisz@tsleducation.com</p><p>________________________________________________________________</p><p>The <a href="http://integrationtool.wordpress.com/">math</a> section where my strengths when developing two: <a href="http://integrationtool.wordpress.com/">math</a>ematics and computational <a href="http://integrationtool.wordpress.com/">math</a>ematics.</p><p><a href="http://integrationtool.wordpress.com/">Math</a>ematics since then grandson in different area at University, and computational <a href="http://integrationtool.wordpress.com/">math</a>ematics from strength to strength.</p><p>It is fair to say that the current Administ<a href="http://calculustools.wordpress.com/">ratio</a>n has a strong national and international reputation in computational <a href="http://integrationtool.wordpress.com/">math</a>ematics, physics and engineering with partners and develop science Biology Chemistry computational science as a discipline.</p><p>No wonder therefore that our graduates are inclined, find work in <a href="www.differentiationinfo.com">arithmetic</a>al application density sports fields.</p><p>Three recent examples: graduate work at Harvard University, majoring in data technician in broad Institute in Cambridge, researcher at the Centre for marine aondirsia war in Newport, RI.</p><p>Students have written, or return, they appreciate that tell us something about their University.</p><p>Things they always remember:</p>Algibrabrograming statistixlinir:<blockquote></blockquote><p>The other thing they mention is an environment where they are encouraged to pursue their own research and Joe, who is expected to talk about their work, and presents at conferences and an environment encouraging the sharing of experience and team work.</p><p>This type of environment was made possible through major grant from the National Science Foundation.</p><p>This funding is scheduled to expire in the next two years.</p><p>Because the academic environment has fundamentally changed how we educate our students, we need to find ways and means to expand this in the future.</p><p>My Administ<a href="http://calculustools.wordpress.com/">ratio</a>n has a real single force pending: computational <a href="http://integrationtool.wordpress.com/">math</a>ematics especially, but not only in terms of <a href="http://toolsmathematics.wordpress.com/">partial</a> differential <a href="www.differentiationinfo.com">equation</a>s.</p><p>We are discussing now how to develop strong scientific data, which will require students skills in <a href="http://integrationtool.wordpress.com/">math</a>ematics and <a href="http://integrationtool.wordpress.com/">statistics</a>, computer science, scientific visualization and communication science.</p><p>As a small management cannot be all things to all students.</p><p>Some great strengths, and seek to develop new partnerships.</p><p>My feeling is that we need to focus on those things that we can do good, be upfront with prospective students about what you do, and redesigning our curricula focus on the skills and habits of mind, we want our graduates to acquire.</p><p>Just "articles", regardless of how well-intentioned, won't cut it anymore.</p><p>Provide students with an environment where it can serve as platoon on research problems of their choice, where the emphasis is on oral and written presentation skills and where to find the global conferences, and is critical to how we proceed in <a href="http://integrationtool.wordpress.com/">math</a>ematics undergraduates now.</p>Tagged: College, curricula, and <a href="http://integrationtool.wordpress.com/">math</a>ematics, UniversityUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-69705270663228466702011-06-14T07:00:00.000-07:002011-06-14T07:00:05.680-07:00All about engineering <p>In this era of perfect, everything perfectly organized and design and then submit a well-considered way. Pen design to your computer's system configu<a href="http://calculustools.wordpress.com/">ratio</a>n requires many mind boggling, intelligence and hard work. Many technical aspects involved in chemical stroktorisishn any mechanical or technical developments. And these related fields is called, is the design and construction of all shape and mechanical or technological engineering. A very wide field engineering and selection of students to various engineering fields according to their interests. Also, increased appeal to engineers because of developments in the area of equipment.</p><p>Various branches of Engineering:</p><p>V aerospace engineering</p><p>5 chemical engineering</p><p>V civil engineering</p><p>V electrical engineering</p><p>5 mechanical engineering</p><p>V computer and software engineering</p><p>V curriculum vitae-chemical engineering</p><p>Must be called subjects such as physics, chemistry and <a href="http://integrationtool.wordpress.com/">math</a>ematics in upper secondary school to pursue engineering as his life. Institutes offering <a href="http://toolsmathematics.wordpress.com/">degree</a>s in engineering and different colleges. Engineers play a key role in the development of the country as a whole. Scientists and experts computer forensic engineers, software applications and etc from a few fields that contribute to growth in the country. The ten highest <strong>Engineering Colleges</strong> briliantes produced in the field:</p><p>Indian Institute of materials, Kanpur<br>Indian Institute of materials, Chennai<br>Indian Institute of materials, Roorkee<br>Indian Institute of materials, New Delhi<br>Indian Institute of materials, Mumbai<br>Indian Institute of materials, Guwahati<br>Indian Institute of materials, kharagbor<br>IIIT Allahabad<br>Faculty of engineering, Chennai<br>National Institute of materials, Tamil Nadu</p><p>Entrance to the College of engineering is a lengthy process, involving a series of tests. Each College has its own entrance examination to the reputation and availability of seats. For a minimum percentage required to sit the entrance exams in various chose <strong>colleges</strong>College, which itself then took the written test to assess students on subjects like <a href="http://integrationtool.wordpress.com/">math</a>ematics, physics, chemistry and English. After providing lodging written test, group discussion of student appears to be general knowledge test confidence and communication skills, provision of room and Board, which makes the student eligible for interview round is critical and another step towards achieving its objective any demanded admission in reputed Engineering College.</p><p>Known engineering entrance examinations:</p><p>IIT JEE joint entrance exam ITT<br>No India engineering entrance examination for all<br>Pete<br>Acceptance testing Annette National Institute<br>Joint entrance examination and West Bengal webgi<br>DCE Delhi College of engineering<br>Manipal Institute of engineering equipment<br>University entrance exam in engineering legacy<br>Regular entrance test level-Maharashtra<br>SRM engineering entrance examination<br>Institute for science and test equipment<br>Engineering and medical entrance exam karla<br>Institute of the Indian Institute of space and equipment<br>Birla Institute of science and equipment bitsat</p><p>Training for this exam is also vital, and choose the fate of students as their admission in colleges are dependents on marks obtained in these experiments walkthrough. Many students of these training courses, examinations after choosing engineering senior secondary theme. Wonderful Institute must satisfy educational standards of the Institute and assist in strengthening confidence, speed and many other skills of the student. Time-management, which helps students in scoring more and keep track on all topics. Helps due attention to their respective topics, helping swift and balanced training. Also, fake caller ID test help in practice exam tests and increase their grip <a href="http://mathematictools.blogspot.com/">even</a> on difficult questions.</p><p>More <a href="http://integrationtool.wordpress.com/">math</a> articles</p><p>Tags: about, engineering</p>This entry was posted on 17 March 2011, submit within <a href="http://integrationtool.wordpress.com/">math</a>ematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response or Trackback from your site.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-85603764895609758622011-06-13T10:28:00.000-07:002011-06-13T10:28:00.350-07:00Obvious choice: can't live without them, can't live with itTranslate Request has too much data<br />Parameter name: request<br />Translate Request has too much data<br />Parameter name: request<br /> <P><IMG class="aligncenter size-large wp-image-4785" title="OLYMPUS DIGITAL CAMERA" alt="" src="/aclandcakes3-1024x768.jpg" width=614 height=461></P><P>Imagine you get to choose one of each type of cake from the cake shop pictured above!</P><P>What a treat!</P><P>With trembling hands you go from one type of cake to another, carefully choosing one of each until you’ve run out of different types of cakes.</P><P>Yum!</P><P>When you’re done you have a collection of cakes, with one cake from each type of cake.</P><P>This is such a natural procedure that <a href="http://integrationtool.wordpress.com/">math</a>ematicians imagined, without really thinking about it, that the same type of choice could be carried out <a href="http://mathematictools.blogspot.com/">even</a> if there were <a href="http://integrationutilities.blogspot.com/">infinite</a>ly many</EM> different types of cakes to choose from.</P><IMG class="size-thumbnail wp-image-4786" title=Zermelo alt="" src="/Zermelo-150x150.jpg" width=150 height=150> Ernst Zermelo (1871 - 1953)</P><P>Until Ernst Zermelo made it clear that it was a foundational axiom, or assumption, of <a href="http://integrationutilities.blogspot.com/">set</a> theory that one could always make such a choice.</P><P>Where in <a href="http://integrationtool.wordpress.com/">math</a>ematics might one need to make a choice from one of <a href="http://integrationutilities.blogspot.com/">infinite</a>ly many different types of collections?</P><P>Here is one simple example:</P><P>The Cartesian <a href="http://differentiationtools.blogspot.com/">plane</a> consists of ordered pairs <IMG class=latex title=(x,y) alt=(x,y) src="http://s.wordpress.com/latex.php?latex=%28x%2Cy%29&bg=ffffff&fg=000000&s=0"> of real <a href="www.differentiationinfo.com">number</a>s <IMG class=latex title="x\textrm{ and } y" alt="x\textrm{ and } y" src="http://s.wordpress.com/latex.php?latex=x%5Ctextrm%7B%20and%20%7D%20y&bg=ffffff&fg=000000&s=0">.</P><P>We can shift points in the Cartesian <a href="http://differentiationtools.blogspot.com/">plane</a> by moving them left or right one unit, or up and down one unit.</P><P>The orbit of a point <IMG class=latex title=(x,y) alt=(x,y) src="http://s.wordpress.com/latex.php?latex=%28x%2Cy%29&bg=ffffff&fg=000000&s=0"> in the Cartesian <a href="http://differentiationtools.blogspot.com/">plane</a> for this group of motions is the collection of all points that <IMG class=latex title=(x,y) alt=(x,y) src="http://s.wordpress.com/latex.php?latex=%28x%2Cy%29&bg=ffffff&fg=000000&s=0"> can be moved to by moving it up, down, left or right one unit, repeatedly.</P><P>In other words the orbit of <IMG class=latex title=(x,y) alt=(x,y) src="http://s.wordpress.com/latex.php?latex=%28x%2Cy%29&bg=ffffff&fg=000000&s=0"> consists exactly of the points <IMG class=latex title="(x\pm m,y\pm n)" alt="(x\pm m,y\pm n)" src="http://s.wordpress.com/latex.php?latex=%28x%5Cpm%20m%2Cy%5Cpm%20n%29&bg=ffffff&fg=000000&s=0"> where <IMG class=latex title=m,n alt=m,n src="http://s.wordpress.com/latex.php?latex=m%2Cn&bg=ffffff&fg=000000&s=0"> range over all possible integers.</P><P>The orbits of points split the Cartesian <a href="http://differentiationtools.blogspot.com/">plane</a> into disjoint <a href="http://integrationutilities.blogspot.com/">set</a>s.</P><P>Is there some way of forming a <a href="http://integrationutilities.blogspot.com/">set</a> that consists of just one point from each possible orbit?</P><P>We can answer this positively by first observing that the orbit of each point on the Cartesian <a href="http://differentiationtools.blogspot.com/">plane</a> passes through the square with corners <IMG class=latex title="(0,0), (1,0), (0,1), (1,1)" alt="(0,0), (1,0), (0,1), (1,1)" src="http://s.wordpress.com/latex.php?latex=%280%2C0%29%2C%20%281%2C0%29%2C%20%280%2C1%29%2C%20%281%2C1%29&bg=ffffff&fg=000000&s=0"> exactly once, except for points on the lines joining <IMG class=latex title=(0,0) alt=(0,0) src="http://s.wordpress.com/latex.php?latex=%280%2C0%29&bg=ffffff&fg=000000&s=0"> to <IMG class=latex title=(1,0) alt=(1,0) src="http://s.wordpress.com/latex.php?latex=%281%2C0%29&bg=ffffff&fg=000000&s=0"> and to <IMG class=latex title=(0,1) alt=(0,1) src="http://s.wordpress.com/latex.php?latex=%280%2C1%29&bg=ffffff&fg=000000&s=0">, and the lines joining <IMG class=latex title=(1,1) alt=(1,1) src="http://s.wordpress.com/latex.php?latex=%281%2C1%29&bg=ffffff&fg=000000&s=0"> to <IMG class=latex title=(1,0) alt=(1,0) src="http://s.wordpress.com/latex.php?latex=%281%2C0%29&bg=ffffff&fg=000000&s=0"> and to <IMG class=latex title=(0,1) alt=(0,1) src="http://s.wordpress.com/latex.php?latex=%280%2C1%29&bg=ffffff&fg=000000&s=0">: for any point on these lines, its orbit passes through the square exactly twice (once on each edge).</P><P><IMG class="aligncenter size-full wp-image-4788" title=flat_torus alt="" src="/flattorus.jpg" width=273 height=253>So, if we identify (= glue together) the edges of the square as indicated, we will have a <a href="http://integrationutilities.blogspot.com/">set</a> of points that (is in one-to-one correspondence with a <a href="http://integrationutilities.blogspot.com/">set</a> that) contains a single point from each and every orbit.</P><P>This identification gives us a torus:</P><P><IMG class="aligncenter size-medium wp-image-4787" title=torus2 alt="" src="/torus2-300x182.jpg" width=300 height=182>So the answer to our question is: “Yes. we can find a <a href="http://integrationutilities.blogspot.com/">set</a> (the torus) consisting of one and only one point from each orbit.”</P><P>If we fancifully imagine the orbits as types of cakes, and points in each orbit as cakes, then we have found a <a href="http://integrationutilities.blogspot.com/">set</a> that consists of one and only one of each of the <a href="http://integrationutilities.blogspot.com/">infinite</a> types of cake.</P><P>Zermelo’s phrasing of the axiom of choice was as follows:</P><P>“If T</EM> is a <a href="http://integrationutilities.blogspot.com/">set</a> whose elements all are <a href="http://integrationutilities.blogspot.com/">set</a>s that are different from Ø and mutually disjoint, its union ?T</EM> includes at least one sub<a href="http://integrationutilities.blogspot.com/">set</a> S</EM>1 having one and only one element in common with each element of T</EM>“.</P><P>Ideas about infinity, and <a href="http://integrationutilities.blogspot.com/">infinite</a> processes, are essential to <a href="http://integrationtool.wordpress.com/">math</a>ematics, so Zermelo’s axiom of choice came to play a central role in the foundations of <a href="http://integrationtool.wordpress.com/">math</a>ematical thought.</P><IMG class="size-thumbnail wp-image-4790 " title=kurt_gödel alt="" src="/kurtgdel-150x150.jpg" width=150 height=150> Kurt Gödel</P><IMG class="size-thumbnail wp-image-4791" title=Cohen alt="" src="/Cohen-150x150.jpg" width=150 height=150> Paul Cohen</P><P>Kurt Godel and Paul Cohen showed that the axiom of choice is independent of the other axioms of Zermelo-Fraenkel (ZF) <a href="http://integrationutilities.blogspot.com/">set</a> theory. Assuming ZF <a href="http://integrationutilities.blogspot.com/">set</a> theory is consistent, Godel constructed a model of <a href="http://integrationutilities.blogspot.com/">set</a> theory in which the the axiom of choice cannot be disproved from the other axioms. Cohen constructed a model of ZF <a href="http://integrationutilities.blogspot.com/">set</a> theory in which the axiom of choice cannot be proved from the other axioms.</P><P>Godel and Cohen’s theorems together tell us that we can take the axiom of choice as an axiom, or take its negation as an axiom – it’s up to us to decide in which <a href="http://integrationutilities.blogspot.com/">set</a>-theoretic world we want to live.</P><P>Now that IS choice!</P><P>1. We say that a <a href="http://integrationutilities.blogspot.com/">set</a> <IMG class=latex title=A alt=A src="http://s.wordpress.com/latex.php?latex=A&bg=ffffff&fg=000000&s=0"> is larger than a <a href="http://integrationutilities.blogspot.com/">set</a> <IMG class=latex title=B alt=B src="http://s.wordpress.com/latex.php?latex=B&bg=ffffff&fg=000000&s=0"> if there is a one-to-one function <IMG class=latex title="f:B\to A" alt="f:B\to A" src="http://s.wordpress.com/latex.php?latex=f%3AB%5Cto%20A&bg=ffffff&fg=000000&s=0">. (“One-to-one” means if <IMG class=latex title="f(b_1)=f(b_2) \textrm{ then } b_1=b_2" alt="f(b_1)=f(b_2) \textrm{ then } b_1=b_2" src="http://s.wordpress.com/latex.php?latex=f%28b_1%29%3Df%28b_2%29%20%5Ctextrm%7B%20then%20%7D%20b_1%3Db_2&bg=ffffff&fg=000000&s=0">)</P><P>The axiom of choice allows us to conclude (indeed, is equivalent with): for any two <a href="http://integrationutilities.blogspot.com/">set</a>s <IMG class=latex title="A, B" alt="A, B" src="http://s.wordpress.com/latex.php?latex=A%2C%20B&bg=ffffff&fg=000000&s=0"> either <IMG class=latex title=A alt=A src="http://s.wordpress.com/latex.php?latex=A&bg=ffffff&fg=000000&s=0"> is larger than <IMG class=latex title=B alt=B src="http://s.wordpress.com/latex.php?latex=B&bg=ffffff&fg=000000&s=0"> or <IMG class=latex title=B alt=B src="http://s.wordpress.com/latex.php?latex=B&bg=ffffff&fg=000000&s=0"> is larger than <IMG class=latex title=A alt=A src="http://s.wordpress.com/latex.php?latex=A&bg=ffffff&fg=000000&s=0">.</P><P>2. A <a href="http://integrationutilities.blogspot.com/">set</a> is countably <a href="http://integrationutilities.blogspot.com/">infinite</a></EM> if it can be put into one-to-one correspondence with the <a href="http://integrationutilities.blogspot.com/">set</a> of natural <a href="www.differentiationinfo.com">number</a>s.</P><P>The axiom of choice allows us to conclude that a countably <a href="http://integrationutilities.blogspot.com/">infinite</a> union of countably <a href="http://integrationutilities.blogspot.com/">infinite</a> <a href="http://integrationutilities.blogspot.com/">set</a>s is again countably <a href="http://integrationutilities.blogspot.com/">infinite</a>.</P><P>1. The axiom of choice allows us to prove the Banach-Tarski theorem:</P><P>A ball of radius 1 in 3-dimensional real space can be dissected into a finite <a href="www.differentiationinfo.com">number</a> of pieces which can be re-arranged by rotations and translations to yield two balls of radius 1.</P><P>As you might suspect, these pieces do not have a rotation and translation invariant volume.</P><P>I was prompted to write this post by someone saying they were puzzled about the reference to the axiom of choice in the following XKCD cartoon:</P><IMG class="size-full wp-image-4789 " title=XKCD alt="" src="/XKCD.jpg" width=666 height=214> Courtsey XKCD</P><P>2. A total order</EM> on a <a href="http://integrationutilities.blogspot.com/">set</a> <IMG class=latex title=A alt=A src="http://s.wordpress.com/latex.php?latex=A&bg=ffffff&fg=000000&s=0"> is a relation between pairs of elements of <IMG class=latex title=A alt=A src="http://s.wordpress.com/latex.php?latex=A&bg=ffffff&fg=000000&s=0"> (a binary relation), denoted <IMG class=latex title=\preceq alt=\preceq src="http://s.wordpress.com/latex.php?latex=%5Cpreceq&bg=ffffff&fg=000000&s=0">, with the following properties:</P><P>A first element</EM> for a sub<a href="http://integrationutilities.blogspot.com/">set</a> <IMG class=latex title="B \subseteq A" alt="B \subseteq A" src="http://s.wordpress.com/latex.php?latex=B%20%5Csubseteq%20A&bg=ffffff&fg=000000&s=0"> for a total order <IMG class=latex title=\preceq alt=\preceq src="http://s.wordpress.com/latex.php?latex=%5Cpreceq&bg=ffffff&fg=000000&s=0"> is a <IMG class=latex title="b_0\in B" alt="b_0\in B" src="http://s.wordpress.com/latex.php?latex=b_0%5Cin%20B&bg=ffffff&fg=000000&s=0"> such that <IMG class=latex title="b_0 \preceq b \textrm{ for all } b \in B" alt="b_0 \preceq b \textrm{ for all } b \in B" src="http://s.wordpress.com/latex.php?latex=b_0%20%5Cpreceq%20b%20%5Ctextrm%7B%20for%20all%20%7D%20b%20%5Cin%20B&bg=ffffff&fg=000000&s=0">.</P><P>The axiom of choice allows us to conclude that there is a total order (not the usual order !) on the <a href="http://integrationutilities.blogspot.com/">set</a> of real <a href="www.differentiationinfo.com">number</a>s such that every non-empty <a href="http://integrationutilities.blogspot.com/">set</a> of real <a href="www.differentiationinfo.com">number</a>s has a first element.</P><P>Indeed there is nothing special about the <a href="http://integrationutilities.blogspot.com/">set</a> of real <a href="www.differentiationinfo.com">number</a>s in this respect: we can replace it by any <a href="http://integrationutilities.blogspot.com/">set</a> whatsoever.</P><P>No Banach-Tarski paradox.</P><P>There is a model for ZF <a href="http://integrationutilities.blogspot.com/">set</a> theory with the negation of the axiom of choice in which the <a href="http://integrationutilities.blogspot.com/">set</a> of real <a href="www.differentiationinfo.com">number</a>s is a countable union of countable sub<a href="http://integrationutilities.blogspot.com/">set</a>s (but, of course, is not itself countable).</P><P>To paraphrase Horst Herrlich:</P><P><a href="http://integrationtool.wordpress.com/">Math</a>ematics with “choice” may be as unreal as a soap-bubble dream, but <a href="http://integrationtool.wordpress.com/">math</a>ematics without “choice” is as horrible as nightmare.</EM></P><P>We might also say that you have to know if you can choose your cake before you can eat it. </EM></P><P>And we couldn’t pass up the old, but golden, riddle: “What’s yellow and equivalent to the axiom of choice?”</P><P><IMG class="alignleft size-full wp-image-4795" title=Zorns_lemon alt="" src="/Zornslemon.jpg" width=437 height=295></P>Tagged as: axiom of choice, Banach-Tarski paradox, countable <a href="http://integrationutilities.blogspot.com/">set</a>, infinity, Kurt Godel, Paul Cohen </P>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-23487189599462481402011-06-12T11:45:00.000-07:002011-06-12T11:45:00.512-07:00Experimental sciences, mathematics <p><img class="aligncenter size-full wp-image-4778" title="shocked_kitten" alt="" src="/shockedkitten.jpg" width="485" height="493"></p><p>Many people-including some of my colleagues--like say that <a href="http://integrationtool.wordpress.com/">math</a>ematics is the art, science, and <a href="http://mathematictools.blogspot.com/">even</a> aware it's not like physics or chemistry or biology because deductive, experimental science.</p><p>Zilberger Doron says five videos below of viewpoint.</p><p><embed height="390" type="application/x-shockwave-flash" width="640" src="http://www.youtube.com/v/8zhXZO1J2ac?fs=1&hl=en_US" allowfullscreen="true" allowscriptaccess="always"></p><p><embed height="390" type="application/x-shockwave-flash" width="640" src="http://www.youtube.com/v/D59zua4YUrw?fs=1&hl=en_US" allowfullscreen="true" allowscriptaccess="always"></p><p><embed height="390" type="application/x-shockwave-flash" width="640" src="http://www.youtube.com/v/VS35mZm6qxQ?fs=1&hl=en_US" allowfullscreen="true" allowscriptaccess="always"></p><p><embed height="390" type="application/x-shockwave-flash" width="640" src="http://www.youtube.com/v/DkoXDFFppj0?fs=1&hl=en_US" allowfullscreen="true" allowscriptaccess="always"></p><p><embed height="390" type="application/x-shockwave-flash" width="640" src="http://www.youtube.com/v/yy1wELl2Z6U?fs=1&hl=en_US" allowfullscreen="true" allowscriptaccess="always"></p>Tagged: experience, trial account, and <a href="http://integrationtool.wordpress.com/">math</a>ematics, and science, zilbergerUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-87367519765966454072011-06-11T13:48:00.000-07:002011-06-11T13:48:00.873-07:00Important instructions: learning to help Mpower fifth grade students at deal with mathematic better assignments <p><strong>You get stumped</strong> when you are given the "assignment of <a href="http://integrationtool.wordpress.com/">Math</a>ematics"? Do <a href="http://integrationtool.wordpress.com/">math</a> problems pose enormous challenges for you?</p><p>Well, <strong><a href="http://integrationtool.wordpress.com/">math</a> problems <a href="http://integrationtool.wordpress.com/">math</a> functions</strong> causes concern to most students. The majority of students feel that <a href="http://integrationtool.wordpress.com/">math</a> assignments from fields such as algebra and <a href="http://integrationtool.wordpress.com/">trigonometry</a>, <a href="http://differentiationtools.blogspot.com/">geometry</a>, calculus, and so boring to do without the assistance of some experts.</p><p>This is where we must promote. We have guides in MPowerLearning.com be secondment of experts has helped hundreds of students provide quality assignments. Not only help students with training assignments, teachers mbouirlerning also help students learn basic concepts in a clear form. They provide students with accurate and logical solutions to <a href="http://integrationtool.wordpress.com/">math</a> problems to help them learn better. <strong>Guides in MpowerLearning.com</strong> professionals with advanced <a href="http://toolsmathematics.wordpress.com/">degree</a>s and doctorates with a passion for teaching, but is still available and very easy.</p><p><strong>What is <a href="http://integrationtool.wordpress.com/">math</a>ematics?</strong> According to Wikipedia, <a href="http://integrationtool.wordpress.com/">math</a>ematics can be generally divided redress to study and quantitative structure-changing space, arithmetic and <a href="http://differentiationtools.blogspot.com/">geometry</a>. <a href="http://integrationutilities.blogspot.com/">Add</a>itionally, there are also subdivisions dedicated to exploring links from the heart of <a href="http://integrationtool.wordpress.com/">math</a>ematics to other fields: to logic, to <a href="http://integrationutilities.blogspot.com/">set</a> schema (institutions), experimental <a href="http://integrationtool.wordpress.com/">math</a>ematics of the various Sciences (applied <a href="http://integrationtool.wordpress.com/">math</a>ematics), and careful conside<a href="http://calculustools.wordpress.com/">ratio</a>n of uncertainty in recent times.</p><p><a href="http://integrationtool.wordpress.com/">Math</a>ematics is also a study on space structure and change many other topics of the sample. <a href="http://integrationtool.wordpress.com/">Math</a>ematics as an essential and vital in most fields, including engineering, social sciences, medicine, natural sciences, etc.</p><p><strong><a href="http://integrationtool.wordpress.com/">Math</a>ematics subject fantastic</strong>. And ubiquitous, and you can only avoid <a href="http://integrationtool.wordpress.com/">math</a>. When we look at building and wondering how tall, doing <a href="http://integrationtool.wordpress.com/">math</a>. When you tell your friend how much you will take to cover a distance of 120 kilometres in the car, do the <a href="http://integrationtool.wordpress.com/">math</a>. When you admire the beauty of sunflower or greenhouse buzzing, which is marviling in <a href="http://integrationtool.wordpress.com/">math</a>ematics itself.</p><p>To help you learn and see the beauty of <a href="http://integrationtool.wordpress.com/">math</a>ematics have tutors available 24 x 7. Guides in MpowerLearning.com are there to back you all the way from school until he graduated from College in triumph.</p><p><strong>MpowerLearning.com one of the few companies</strong> you may understand the intricacies of the equipment and content developers.</p><p>They are leaders in the field, it will motivate you to learn from the leaders!</p><p>For more information about appointments, please visit: http://www.mpowerlearning.com</p><p>Madhu Naryan consultant with MPowerLearning.com and enthusiastically participate in spreading education through equipment. and she also speaks at various educational institutions <a href="http://integrationutilities.blogspot.com/">add</a>ressing teachers on how to use modern teaching methods to help students learn better. She also blogs regularly at: http://www.mpowerlearning.com/</p><p><br>Article from articlesbase.com</p><p>Tags: recruitment, appointments, faculty, students, learning assistance, handle and level <a href="http://integrationtool.wordpress.com/">math</a>ematics, mbouer,</p>This entry was posted on 18 March 2011, submit within <a href="http://integrationtool.wordpress.com/">math</a>ematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response or Trackback from your site.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-81009033144165790722011-06-10T17:19:00.000-07:002011-06-10T17:19:00.891-07:00Rationalizing rational?Translate Request has too much data<br />Parameter name: request<br />Translate Request has too much data<br />Parameter name: request<br /> <P>Text books and test <a href="http://integrationutilities.blogspot.com/">set</a>ters regularly mark students wrong if they give an answer of <IMG class=latex title=\frac{1}{\sqrt{2}} alt=\frac{1}{\sqrt{2}} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D&bg=ffffff&fg=000000&s=0"> to a problem.</P><P>A student is supposed to know, as part of <a href="http://integrationtool.wordpress.com/">math</a>ematical convention, that <IMG class=latex title=\frac{1}{\sqrt{2}} alt=\frac{1}{\sqrt{2}} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D&bg=ffffff&fg=000000&s=0"> should be <a href="http://calculustools.wordpress.com/">ratio</a>nalized to <IMG class=latex title=\frac{\sqrt{2}}{2} alt=\frac{\sqrt{2}}{2} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D&bg=ffffff&fg=000000&s=0">.</P><P>This issue has been discussed before by @suburbanlion at SuburbanLion’s Blog and @jamestanton at <a href="http://calculustools.wordpress.com/">Ratio</a>nalising the Denominator, among others.</P><P>Marking a student wrong for not carrying out a <a href="http://calculustools.wordpress.com/">ratio</a>nalization like this is just BS (and I don’t mean “Bachelor of Science”).</P><P>And there is no such <a href="http://integrationtool.wordpress.com/">math</a>ematical convention – it’s made up by people who write text books and <a href="http://integrationutilities.blogspot.com/">set</a> tests.</P><P>This issue came up again recently in #<a href="http://integrationtool.wordpress.com/">math</a>chat when @davidwees wrote: “I tell my students that people used to <a href="http://calculustools.wordpress.com/">ratio</a>nalize denominators b/c it made calculations easier” and “1.414…/2 is much easier to do than 1/1.414… without a calculator.”</P><P>My issue with what David wrote (and indeed with part of what James Tanton says in his video) is how, without a calculator, do we know that <IMG class=latex title="\sqrt{2}\approx 1.414" alt="\sqrt{2}\approx 1.414" src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D%5Capprox%201.414&bg=ffffff&fg=000000&s=0">?</P><P>Of course if someone told</EM> us that <IMG class=latex title="\sqrt{2}\approx 1.414" alt="\sqrt{2}\approx 1.414" src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D%5Capprox%201.414&bg=ffffff&fg=000000&s=0"> and we figured that <IMG class=latex title=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2} alt=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D&bg=ffffff&fg=000000&s=0"> then we could probably be adept enough to calculate <IMG class=latex title="\frac{1}{\sqrt{2}}\approx 1.414/2=0.707" alt="\frac{1}{\sqrt{2}}\approx 1.414/2=0.707" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5Capprox%201.414%2F2%3D0.707&bg=ffffff&fg=000000&s=0"> by hand.</P><P><a href="www.differentiationinfo.com">Number</a>s of the form <IMG class=latex title=a+b\sqrt{2} alt=a+b\sqrt{2} src="http://s.wordpress.com/latex.php?latex=a%2Bb%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> where <IMG class=latex title="a \textrm{ and }b" alt="a \textrm{ and }b" src="http://s.wordpress.com/latex.php?latex=a%20%5Ctextrm%7B%20and%20%7Db&bg=ffffff&fg=000000&s=0"> are <a href="http://calculustools.wordpress.com/">ratio</a>nal <a href="www.differentiationinfo.com">number</a>s (<a href="www.differentiationinfo.com">fraction</a>s) collectively have a remarkable structural property:</P><P>not only can we <a href="http://integrationutilities.blogspot.com/">add</a>, <a href="http://mathematictools.blogspot.com/">subtract</a> and multiply such <a href="www.differentiationinfo.com">number</a>s and still get <a href="www.differentiationinfo.com">number</a>s of the same form (e.g. <IMG class=latex title="(1+2\sqrt{2})\times (2-3\sqrt{2})=-10+\sqrt{2}" alt="(1+2\sqrt{2})\times (2-3\sqrt{2})=-10+\sqrt{2}" src="http://s.wordpress.com/latex.php?latex=%281%2B2%5Csqrt%7B2%7D%29%5Ctimes%20%282-3%5Csqrt%7B2%7D%29%3D-10%2B%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0">), we can also divide such <a href="www.differentiationinfo.com">number</a>s and still get a <a href="www.differentiationinfo.com">number</a> of the same form:</P><P>e.g. <IMG class=latex title="\frac{1+\sqrt{2}}{2-3\sqrt{2}}= \frac{1+\sqrt{2}}{2-3\sqrt{2}}\times \frac{2+3\sqrt{2}}{2+3\sqrt{2}}=\frac{14+7\sqrt{2}}{-14}=-1-\frac{1}{2}\sqrt{2}" alt="\frac{1+\sqrt{2}}{2-3\sqrt{2}}= \frac{1+\sqrt{2}}{2-3\sqrt{2}}\times \frac{2+3\sqrt{2}}{2+3\sqrt{2}}=\frac{14+7\sqrt{2}}{-14}=-1-\frac{1}{2}\sqrt{2}" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%2B%5Csqrt%7B2%7D%7D%7B2-3%5Csqrt%7B2%7D%7D%3D%20%5Cfrac%7B1%2B%5Csqrt%7B2%7D%7D%7B2-3%5Csqrt%7B2%7D%7D%5Ctimes%20%5Cfrac%7B2%2B3%5Csqrt%7B2%7D%7D%7B2%2B3%5Csqrt%7B2%7D%7D%3D%5Cfrac%7B14%2B7%5Csqrt%7B2%7D%7D%7B-14%7D%3D-1-%5Cfrac%7B1%7D%7B2%7D%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"></P><P>Collectively, <a href="www.differentiationinfo.com">number</a>s of the form <IMG class=latex title=a+b\sqrt{2} alt=a+b\sqrt{2} src="http://s.wordpress.com/latex.php?latex=a%2Bb%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> constitute a <a href="http://integrationtool.wordpress.com/">math</a>ematical field, denoted by <IMG class=latex title=\mathbb{Q}[\sqrt{2}] alt=\mathbb{Q}[\sqrt{2}] src="http://s.wordpress.com/latex.php?latex=%5Cmathbb%7BQ%7D%5B%5Csqrt%7B2%7D%5D&bg=ffffff&fg=000000&s=0"> – a structure in which <a href="http://integrationutilities.blogspot.com/">add</a>ition, <a href="http://mathematictools.blogspot.com/">subtract</a>ion, multiplication and division (by non-zero <a href="www.differentiationinfo.com">number</a>s) is always possible.</P><P>From this perspective, <a href="http://calculustools.wordpress.com/">ratio</a>nalizing <IMG class=latex title=\frac{1}{\sqrt{2}}=\frac{1}{2}\sqrt{2} alt=\frac{1}{\sqrt{2}}=\frac{1}{2}\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> is just expressing the fact that the reciprocal of <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> is again in the field <IMG class=latex title=\mathbb{Q}[\sqrt{2}] alt=\mathbb{Q}[\sqrt{2}] src="http://s.wordpress.com/latex.php?latex=%5Cmathbb%7BQ%7D%5B%5Csqrt%7B2%7D%5D&bg=ffffff&fg=000000&s=0">.</P><P>There are technical senses in which the continued <a href="www.differentiationinfo.com">fraction</a> of a real <a href="www.differentiationinfo.com">number</a> gives the “best” <a href="http://calculustools.wordpress.com/">ratio</a>nal approximation to that <a href="www.differentiationinfo.com">number</a>.</P><P>So how do we find the continued <a href="www.differentiationinfo.com">fraction</a> for <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0">?</P><P>We are looking for an (<a href="http://integrationutilities.blogspot.com/">infinite</a>) expression of the form :</P><P><IMG class=latex title=\sqrt{2}=a_0+\frac{1}{a_1+\frac{1}{a_2+\ldots}} alt=\sqrt{2}=a_0+\frac{1}{a_1+\frac{1}{a_2+\ldots}} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D%3Da_0%2B%5Cfrac%7B1%7D%7Ba_1%2B%5Cfrac%7B1%7D%7Ba_2%2B%5Cldots%7D%7D&bg=ffffff&fg=000000&s=0"></P><P>where the <IMG class=latex title=a_n alt=a_n src="http://s.wordpress.com/latex.php?latex=a_n&bg=ffffff&fg=000000&s=0"> are whole <a href="www.differentiationinfo.com">number</a>s.</P><P>Because the piece <IMG class=latex title=\frac{1}{a_1+\frac{1}{a_2+\ldots}} alt=\frac{1}{a_1+\frac{1}{a_2+\ldots}} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7Ba_1%2B%5Cfrac%7B1%7D%7Ba_2%2B%5Cldots%7D%7D&bg=ffffff&fg=000000&s=0"> after <IMG class=latex title=a_0 alt=a_0 src="http://s.wordpress.com/latex.php?latex=a_0&bg=ffffff&fg=000000&s=0"> is less than 1, we see that <IMG class=latex title=a_0 alt=a_0 src="http://s.wordpress.com/latex.php?latex=a_0&bg=ffffff&fg=000000&s=0"> is the largest integer less than <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0">, which is 1 (we know <IMG class=latex title="1 because <IMG class=latex title="1=1^2 ).</P><P>This leaves <IMG class=latex title="\frac{1}{a_1+\frac{1}{a_2+\ldots}}= \sqrt{2}-1" alt="\frac{1}{a_1+\frac{1}{a_2+\ldots}}= \sqrt{2}-1" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7Ba_1%2B%5Cfrac%7B1%7D%7Ba_2%2B%5Cldots%7D%7D%3D%20%5Csqrt%7B2%7D-1&bg=ffffff&fg=000000&s=0"> so taking reciprocals we see that <IMG class=latex title="a_1+\frac{1}{a_2+\ldots} =\frac{1}{\sqrt{2}-1}" alt="a_1+\frac{1}{a_2+\ldots} =\frac{1}{\sqrt{2}-1}" src="http://s.wordpress.com/latex.php?latex=a_1%2B%5Cfrac%7B1%7D%7Ba_2%2B%5Cldots%7D%20%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D-1%7D&bg=ffffff&fg=000000&s=0">.</P><P>This means that <IMG class=latex title=a_1 alt=a_1 src="http://s.wordpress.com/latex.php?latex=a_1&bg=ffffff&fg=000000&s=0"> is the largest integer less than <IMG class=latex title=\frac{1}{\sqrt{2}-1} alt=\frac{1}{\sqrt{2}-1} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D-1%7D&bg=ffffff&fg=000000&s=0">.</P><P>In other words, <IMG class=latex title="a_1, which means that <IMG class=latex title="1+\frac{1}{a_1+1}.</P><P>We know <IMG class=latex title="1+\frac{1}{3} because <IMG class=latex title="(1+\frac{1}{3})^2=\frac{16}{9} , so <IMG class=latex title="a_1=2 " alt="a_1=2 " src="http://s.wordpress.com/latex.php?latex=a_1%3D2%20&bg=ffffff&fg=000000&s=0">.</P><P>Continuing in this vein gets trickier, because next we have to find the largest integer less than <IMG class=latex title=\frac{1}{\frac{1}{\sqrt{2}-1}-2} alt=\frac{1}{\frac{1}{\sqrt{2}-1}-2} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D-1%7D-2%7D&bg=ffffff&fg=000000&s=0">.</P><P>Because <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> satisfies a <a href="www.differentiationinfo.com">quadratic</a> <a href="www.differentiationinfo.com">equation</a> we can use a cute trick to find the continued <a href="www.differentiationinfo.com">fraction</a> for <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0">.</P><P>Let’s write <IMG class=latex title="\alpha = \sqrt{2}+1" alt="\alpha = \sqrt{2}+1" src="http://s.wordpress.com/latex.php?latex=%5Calpha%20%3D%20%5Csqrt%7B2%7D%2B1&bg=ffffff&fg=000000&s=0"> so that <IMG class=latex title=\alpha^2=(\sqrt{2}+1)^2=2+2\sqrt{2}+1=2\alpha+1 alt=\alpha^2=(\sqrt{2}+1)^2=2+2\sqrt{2}+1=2\alpha+1 src="http://s.wordpress.com/latex.php?latex=%5Calpha%5E2%3D%28%5Csqrt%7B2%7D%2B1%29%5E2%3D2%2B2%5Csqrt%7B2%7D%2B1%3D2%5Calpha%2B1&bg=ffffff&fg=000000&s=0">.</P><P>Dividing by <IMG class=latex title=\alpha alt=\alpha src="http://s.wordpress.com/latex.php?latex=%5Calpha&bg=ffffff&fg=000000&s=0"> gives:</P><IMG class=latex title="\alpha = 2+\frac{1}{\alpha} = 2+\frac{1}{2+\frac{1}{\alpha}}=2+\frac{1}{2+\frac{1}{2+\frac{1}{\alpha}}}" alt="\alpha = 2+\frac{1}{\alpha} = 2+\frac{1}{2+\frac{1}{\alpha}}=2+\frac{1}{2+\frac{1}{2+\frac{1}{\alpha}}}" src="http://s.wordpress.com/latex.php?latex=%5Calpha%20%3D%202%2B%5Cfrac%7B1%7D%7B%5Calpha%7D%20%3D%202%2B%5Cfrac%7B1%7D%7B2%2B%5Cfrac%7B1%7D%7B%5Calpha%7D%7D%3D2%2B%5Cfrac%7B1%7D%7B2%2B%5Cfrac%7B1%7D%7B2%2B%5Cfrac%7B1%7D%7B%5Calpha%7D%7D%7D&bg=ffffff&fg=000000&s=0"> <P>Taking this to a <a href="http://integrationutilities.blogspot.com/">limit</a> we get <IMG class=latex title="\alpha = 2+\frac{1}{2+\frac{1}{2+\ldots}}" alt="\alpha = 2+\frac{1}{2+\frac{1}{2+\ldots}}" src="http://s.wordpress.com/latex.php?latex=%5Calpha%20%3D%202%2B%5Cfrac%7B1%7D%7B2%2B%5Cfrac%7B1%7D%7B2%2B%5Cldots%7D%7D&bg=ffffff&fg=000000&s=0">.</P><P>Since <IMG class=latex title="\sqrt{2}=\alpha - 1" alt="\sqrt{2}=\alpha - 1" src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D%3D%5Calpha%20-%201&bg=ffffff&fg=000000&s=0"> we get <IMG class=latex title="\alpha = 1+\frac{1}{2+\frac{1}{2+\ldots}}" alt="\alpha = 1+\frac{1}{2+\frac{1}{2+\ldots}}" src="http://s.wordpress.com/latex.php?latex=%5Calpha%20%3D%201%2B%5Cfrac%7B1%7D%7B2%2B%5Cfrac%7B1%7D%7B2%2B%5Cldots%7D%7D&bg=ffffff&fg=000000&s=0">.</P><P>By successively terminating this continued <a href="www.differentiationinfo.com">fraction</a> we get the following <a href="http://calculustools.wordpress.com/">ratio</a>nal approximations to <IMG class=latex title="\sqrt{2}: 1, \frac{3}{2}, \frac{7}{5}, \frac{17}{12},\frac{41}{29}" alt="\sqrt{2}: 1, \frac{3}{2}, \frac{7}{5}, \frac{17}{12},\frac{41}{29}" src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D%3A%201%2C%20%5Cfrac%7B3%7D%7B2%7D%2C%20%5Cfrac%7B7%7D%7B5%7D%2C%20%5Cfrac%7B17%7D%7B12%7D%2C%5Cfrac%7B41%7D%7B29%7D&bg=ffffff&fg=000000&s=0">.</P><P>This immediately gives us the following <a href="http://calculustools.wordpress.com/">ratio</a>nal approximations to <IMG class=latex title="\frac{1}{\sqrt{2}}: \frac{2}{3}, \frac{5}{7}, \frac{12}{17},\frac{29}{41}" alt="\frac{1}{\sqrt{2}}: \frac{2}{3}, \frac{5}{7}, \frac{12}{17},\frac{29}{41}" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%3A%20%5Cfrac%7B2%7D%7B3%7D%2C%20%5Cfrac%7B5%7D%7B7%7D%2C%20%5Cfrac%7B12%7D%7B17%7D%2C%5Cfrac%7B29%7D%7B41%7D&bg=ffffff&fg=000000&s=0">.</P><IMG class="size-thumbnail wp-image-4783 " title=Ybc7289-bw alt="" src="/Ybc7289-bw-150x150.jpg" width=150 height=150> Image courtesy Bill Casselman</P><P> leads directly to a method for approximating <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> known to the Babylonians.</P><P>Using this method we start with an approximation <IMG class=latex title=x_0 alt=x_0 src="http://s.wordpress.com/latex.php?latex=x_0&bg=ffffff&fg=000000&s=0"> – let’s start with <IMG class=latex title=x_0=1 alt=x_0=1 src="http://s.wordpress.com/latex.php?latex=x_0%3D1&bg=ffffff&fg=000000&s=0"> because its the first approximation from the continued <a href="www.differentiationinfo.com">fraction</a> for <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0">: it’s the integer part of <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0">.</P><P>We then average <IMG class=latex title="x_0 \textrm{ and } \frac{2}{x_0}" alt="x_0 \textrm{ and } \frac{2}{x_0}" src="http://s.wordpress.com/latex.php?latex=x_0%20%5Ctextrm%7B%20and%20%7D%20%5Cfrac%7B2%7D%7Bx_0%7D&bg=ffffff&fg=000000&s=0"> to get the next approximation <IMG class=latex title=x_1 alt=x_1 src="http://s.wordpress.com/latex.php?latex=x_1&bg=ffffff&fg=000000&s=0">.</P><P>We generate a sequence of <a href="http://calculustools.wordpress.com/">ratio</a>nal <a href="www.differentiationinfo.com">number</a> approximations <IMG class=latex title=x_n alt=x_n src="http://s.wordpress.com/latex.php?latex=x_n&bg=ffffff&fg=000000&s=0"> to <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> where. at each step, <IMG class=latex title=x_{n+1}=\frac{1}{2}(x_n+\frac{2}{x_n}) alt=x_{n+1}=\frac{1}{2}(x_n+\frac{2}{x_n}) src="http://s.wordpress.com/latex.php?latex=x_%7Bn%2B1%7D%3D%5Cfrac%7B1%7D%7B2%7D%28x_n%2B%5Cfrac%7B2%7D%7Bx_n%7D%29&bg=ffffff&fg=000000&s=0">.</P><P>This gives us the following <a href="http://calculustools.wordpress.com/">ratio</a>nal <a href="www.differentiationinfo.com">number</a> approximations to <IMG class=latex title="\sqrt{2}: 1, \frac{3}{2}, \frac{17}{12},\frac{577}{408}" alt="\sqrt{2}: 1, \frac{3}{2}, \frac{17}{12},\frac{577}{408}" src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D%3A%201%2C%20%5Cfrac%7B3%7D%7B2%7D%2C%20%5Cfrac%7B17%7D%7B12%7D%2C%5Cfrac%7B577%7D%7B408%7D&bg=ffffff&fg=000000&s=0">.</P><P>So now we know how to approximate <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> by <a href="http://calculustools.wordpress.com/">ratio</a>nal <a href="www.differentiationinfo.com">number</a>s, we can use the <a href="http://calculustools.wordpress.com/">ratio</a>nalization <IMG class=latex title=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2} alt=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D&bg=ffffff&fg=000000&s=0"> to get <a href="http://calculustools.wordpress.com/">ratio</a>nal approximations to <IMG class=latex title=\frac{1}{\sqrt{2}} alt=\frac{1}{\sqrt{2}} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D&bg=ffffff&fg=000000&s=0">, but you see the absurdity – why bother? Just invert the <a href="http://calculustools.wordpress.com/">ratio</a>nal approximations to <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0">.</P><P>How about the decimal expansion of <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> – where does that come from?</P><P>Decimal approximations to <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> are usually obtained from the <a href="http://calculustools.wordpress.com/">ratio</a>nal approximation from the continued <a href="www.differentiationinfo.com">fraction</a>, of from the more rapidly convergent Newton’s (= Babylonian) method.</P><P>The record at the time of writing this post is is 1,000,000,000,000 decimal places due to S. Kondo & A.J. Yee in 2010.</P><P>The empirical evidence is that <IMG class=latex title=\sqrt{2} alt=\sqrt{2} src="http://s.wordpress.com/latex.php?latex=%5Csqrt%7B2%7D&bg=ffffff&fg=000000&s=0"> is normal in base 10, meaning that, to date, each of the <a href="http://mathematictools.blogspot.com/">digit</a>s appears with proprtion <IMG class=latex title=\frac{1}{10} alt=\frac{1}{10} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B10%7D&bg=ffffff&fg=000000&s=0">, each pair of <a href="http://mathematictools.blogspot.com/">digit</a>s with proportion <IMG class=latex title=\frac{1}{100} alt=\frac{1}{100} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B100%7D&bg=ffffff&fg=000000&s=0">, each triple of <a href="http://mathematictools.blogspot.com/">digit</a>s with proportion <IMG class=latex title=\frac{1}{1000} alt=\frac{1}{1000} src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B1%7D%7B1000%7D&bg=ffffff&fg=000000&s=0"> and so on.</P><P>However no one yet has a proof of this.</P>Tagged as: Babylonian, decimals, <a href="www.differentiationinfo.com">fraction</a>s, Newton's method, <a href="http://calculustools.wordpress.com/">ratio</a>nalize, square root of 2 </P>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-48054309936885537822011-06-09T20:55:00.000-07:002011-06-09T20:55:00.138-07:00Explore a number of strange <p>Tweeted Benjamin Vitale (@ binvitali) to follow people, 203 <img class="latex" title="203^2 + 203^0 + 203^3 = 8406637" alt="203^2 + 203^0 + 203^3 = 8406637" src="http://s.wordpress.com/latex.php?latex=203%5E2%20%2B%20203%5E0%20%2B%20203%5E3%20%3D%208406637&bg=ffffff&fg=000000&s=0"> to Twitter and Nr.</p><p>Alex bogomolni (@ kotthiknot<a href="http://integrationtool.wordpress.com/">math</a>) and note that <img class="latex" title="n=abc" alt="n=abc" src="http://s.wordpress.com/latex.php?latex=n%3Dabc&bg=ffffff&fg=000000&s=0"> if (s) and then <img class="latex" title="abc^a+abc^b+abc^c" alt="abc^a+abc^b+abc^c" src="http://s.wordpress.com/latex.php?latex=abc%5Ea%2Babc%5Eb%2Babc%5Ec&bg=ffffff&fg=000000&s=0"> may <img class="latex" title="abc" alt="abc" src="http://s.wordpress.com/latex.php?latex=abc&bg=ffffff&fg=000000&s=0"> agents of the <img class="latex" title="a, b, c =0" alt="a, b, c =0" src="http://s.wordpress.com/latex.php?latex=a%2C%20b%2C%20c%20%3D0&bg=ffffff&fg=000000&s=0">not one.</p><p>Search quick calculation (using ™ <a href="http://integrationtool.wordpress.com/">math</a>) <img class="latex" title="n=d_k\ldots d_0 \leq 10000" alt="n=d_k\ldots d_0 \leq 10000" src="http://s.wordpress.com/latex.php?latex=n%3Dd_k%5Cldots%20d_0%20%5Cleq%2010000&bg=ffffff&fg=000000&s=0"> gives the following <a href="www.differentiationinfo.com">number</a>s (base 10 <a href="www.differentiationinfo.com">number</a>s) that <img class="latex" title="n^{d_k}+\ldots +n^{d_0}" alt="n^{d_k}+\ldots +n^{d_0}" src="http://s.wordpress.com/latex.php?latex=n%5E%7Bd_k%7D%2B%5Cldots%20%2Bn%5E%7Bd_0%7D&bg=ffffff&fg=000000&s=0"> is Prime:</p><p>10, 20, 230, 203, 308, 309, 330, 350, 503, 550, 650, 960, 1068, 1110, 1206, 1350, 1404, 1480, 5.30, 1802, 1860, 1910, 2032, 2038, 2044, 2054, 2250, and, 2502, 3044, 3082, 3541, 3,974, 4032, 4046, 4072, 4120, 4340, 4450th, 4540, 4650, 4908, 5174, 5310, 5402, 5231, 5770, 5820, 6038, 6100, 6120, 6206, 7039, 6520, 6830, 8065, 8074, 7110 State trading, 8120, 8333, 8446, 8610, 8690, 8902, 8,960, 9064, 9330, 9402, 9408, 9950</p><p>How to increase these <a href="www.differentiationinfo.com">number</a>s?</p><p>They become relatively rare?</p><p>Let's <img class="latex" title="V(p)" alt="V(p)" src="http://s.wordpress.com/latex.php?latex=V%28p%29&bg=ffffff&fg=000000&s=0"> denote the <a href="www.differentiationinfo.com">number</a> <img class="latex" title="n=d_k \ldots d_0 \textrm{ (base 10 digits) } \leq p" alt="n=d_k \ldots d_0 \textrm{ (base 10 digits) } \leq p" src="http://s.wordpress.com/latex.php?latex=n%3Dd_k%20%5Cldots%20d_0%20%5Ctextrm%7B%20%28base%2010%20%20digits%29%20%7D%20%5Cleq%20p&bg=ffffff&fg=000000&s=0"> to <img class="latex" title="n^{d_k}+\ldots + n^{d_0}" alt="n^{d_k}+\ldots + n^{d_0}" src="http://s.wordpress.com/latex.php?latex=n%5E%7Bd_k%7D%2B%5Cldots%20%2B%20n%5E%7Bd_0%7D&bg=ffffff&fg=000000&s=0"> is prime.</p><p>How <img class="latex" title="\frac{V (p)}{p}" alt="\frac{V (p)}{p}" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7BV%20%28p%29%7D%7Bp%7D&bg=ffffff&fg=000000&s=0"> can break with increasing <img class="latex" title="p" alt="p" src="http://s.wordpress.com/latex.php?latex=p&bg=ffffff&fg=000000&s=0">differ?</p><p>Here is a <a href="www.differentiationinfo.com">plot</a> to break this <img class="latex" title="p=200000" alt="p=200000" src="http://s.wordpress.com/latex.php?latex=p%3D200000&bg=ffffff&fg=000000&s=0">: up to</p><p><img class="aligncenter size-full wp-image-4799" title="digits_pic" alt="" src="/digitspic.jpg" width="518" height="324"></p><p><img class="latex" title="\frac{V(p)}{p} \to 0" alt="\frac{V(p)}{p} \to 0" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7BV%28p%29%7D%7Bp%7D%20%5Cto%200&bg=ffffff&fg=000000&s=0"> Seems as <img class="latex" title="p" alt="p" src="http://s.wordpress.com/latex.php?latex=p&bg=ffffff&fg=000000&s=0"> increases, although the decline exaggerated highly forishortinade <a href="www.differentiationinfo.com">plot</a>.</p><p>Do <img class="latex" title="\frac{V(p)}{p} \to 0" alt="\frac{V(p)}{p} \to 0" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7BV%28p%29%7D%7Bp%7D%20%5Cto%200&bg=ffffff&fg=000000&s=0"> k <img class="latex" title="p" alt="p" src="http://s.wordpress.com/latex.php?latex=p&bg=ffffff&fg=000000&s=0"> over?</p><p>Matt Henderson (@ mattthen2) gave the following comment useful:</p><p>Let <img class="latex" title="Z(p)" alt="Z(p)" src="http://s.wordpress.com/latex.php?latex=Z%28p%29&bg=ffffff&fg=000000&s=0"> indicates <img class="latex" title="n\leq p" alt="n\leq p" src="http://s.wordpress.com/latex.php?latex=n%5Cleq%20p&bg=ffffff&fg=000000&s=0"> <a href="www.differentiationinfo.com">number</a> of containing <img class="latex" title="0" alt="0" src="http://s.wordpress.com/latex.php?latex=0&bg=ffffff&fg=000000&s=0"> figures.</p><p>Then <img class="latex" title="Z(10^n) so <IMG class=latex title=" \frac{z(10^n)}{10^{nk}}\to="" 0\textrm{="" as="" }="" n\to="" \infty"="" alt="\frac{Z(10^n)}{10^{nk}}\to 0\textrm{ as } n\to \infty" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7BZ%2810%5En%29%7D%7B10%5E%7Bnk%7D%7D%5Cto%200%5Ctextrm%7B%20as%20%7D%20n%5Cto%20%5Cinfty&bg=ffffff&fg=000000&s=0"> <img class="latex" title="k>1" alt="k>1" src="http://s.wordpress.com/latex.php?latex=k%3E1&bg=ffffff&fg=000000&s=0">for everyone.</p><p>Because <img class="latex" title="V(p)\leq Z(p)" alt="V(p)\leq Z(p)" src="http://s.wordpress.com/latex.php?latex=V%28p%29%5Cleq%20Z%28p%29&bg=ffffff&fg=000000&s=0"> <img class="latex" title="p" alt="p" src="http://s.wordpress.com/latex.php?latex=p&bg=ffffff&fg=000000&s=0"> view for all that:</p><p><img class="latex" title="\frac{V(10^n)}{10^{nk}}\to 0\textrm{ as } n\to \infty" alt="\frac{V(10^n)}{10^{nk}}\to 0\textrm{ as } n\to \infty" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7BV%2810%5En%29%7D%7B10%5E%7Bnk%7D%7D%5Cto%200%5Ctextrm%7B%20as%20%7D%20n%5Cto%20%5Cinfty&bg=ffffff&fg=000000&s=0"><img class="latex" title="k>1" alt="k>1" src="http://s.wordpress.com/latex.php?latex=k%3E1&bg=ffffff&fg=000000&s=0">To all.</p>Tagged as: initial <a href="http://integrationutilities.blogspot.com/">Set</a>upUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-24806064495241042052011-06-09T18:11:00.001-07:002011-06-09T18:11:38.566-07:00Who is kidding who? What test testing? <p>Worldwide, at all levels of education, and <a href="http://www.differentiationinfo.com">math</a>ematics teachers assign tests to students, grading on the basis of those experiences.</p><p>Tests usually believed to be reliable indicators (if not measures) of how to involve students in the material being taught them, and often thought to be related to a korilashonal with their sports.</p><p>Prestige class-test where students in rows — might indicate both these things.</p><p>I would say, however, that what really tested is the teacher. Test, in my opinion and experience, testing the teacher to assign a test to "correct".</p><p>Usually students will be awarded points for testing and recalls part points available student obtained as a result of correct answers.</p><p>Criteria for classifying responses vary widely. Some teachers give <a href="http://toolsmathematics.wordpress.com/">partial</a> credit, others are not. Some teachers lenient regarding answers that require interpretation, and others don't.</p><p>Taking a certain <a href="www.differentiationinfo.com">number</a> of percentage points to pass. Following those critical is called "failed", it "passed" student.</p><p>In many cultures, especially to North America, just a "corridor" students and their parents as a disgrace. In my experience the vast majority of North American students see themselves as a or b students, and certainly not as students.</p><p>Classification criteria vary widely in the United States.</p><p>One variable, common in my experience converting percentages to letter grades as follows:</p><p>A = 90% or higher</p><p>B = 80%-89%</p><p>C = 70%-79%</p><p>D = 60%-69%</p><p>F = 0%, 59%</p><p>These grades vary very little message.</p><p>For example, University students often have no longer row below c "major success" for, but could count "as" pass "if placed outside the home, for example, can carry many engineering students in <a href="www.differentiationinfo.com">differentiation</a> as a sign of success.</p><p>Standard model institutes pass percentage in Australia is 50 per cent, and in the United Kingdom is 40 per cent.</p><p>Curiously, academic standards in these countries generally seem counterproductive for passing percentage. United Kingdom academic standards generally higher than Australia, which, in turn, generally higher academic standards of the United States. What does it mean "the highest academic standards" is one you will find a certain level of academic attainment United Kingdom students are generally more advanced in knowledge, skills and achievements of Australian students who in turn is generally more able students in the United States, on the same grade level.</p><p>Fellow, change the order of questions on the test for a course taught every year and disastrous results. Typically his students would study tests from previous years in prepa<a href="http://calculustools.wordpress.com/">ratio</a>n for the test this year. It was just changing the order of questions is enough to send the <a href="www.differentiationinfo.com">number</a> of students in a tail spin.</p><p>Teachers easily to a test for all but the best and brightest students will fail to pass. This requires identifying articles that have seen students: just push standards a little logic and accuracy generally do that. Or just change the order of the questions from the experiences of previous years.</p><p>Teachers who do so regularly show their colleagues as very difficult and unrealistic, and uninterrupted.</p><p>Meanwhile, it's easy to <a href="http://integrationutilities.blogspot.com/">set</a> a test for everyone but will pass the least diligent students, most students will do well: just focus on alaisodin routine, which exercised much earlier.</p><p>Teachers who this see colleagues very easy, and very weak, and not fulfilling its obligations to evaluate students correctly.</p><p>So he wants to guide conscientious teacher between being too demanding, and are very weak.</p><p>Using different skills and previous experience, therefore, teachers generally will test the potential outcome of a reasonable <a href="www.differentiationinfo.com">number</a> of students passing the highest marks, not much and a few failures, but not much.</p><p>In other words, what is being tested when tagged builds a test is in fact, the ability to <a href="http://integrationutilities.blogspot.com/">set</a> test "occasion" or satisfactory.</p><p>Many people, and particularly administrators and test scores as they appeared "objective".</p><p>This perception is illusory objective for several reasons.</p><p>We already <a href="http://integrationutilities.blogspot.com/">add</a>ressed how the teacher need to build test carefully so that not every failure and not all promising exceptional like colleagues convinced they were appropriate and sufficient work for evaluation.</p><p>There is no objective standard for this: it's just a matter of practice is an integral part of culture.</p><p><a href="http://mathematictools.blogspot.com/">Even</a> within a given culture there is the problem, test in the test of <a href="http://www.differentiationinfo.com">math</a>ematics, <a href="http://toolsmathematics.wordpress.com/">partial</a> credit for deciding what to do if a student makes a mistake alaisodin simple but then completed more or less correctly in application logic.</p><p>The final percentage or grade-point average message received as a result of many such decisions.</p><p>There is very little of this objective on this process.</p><p>To see only one reason, to give the same test papers to a colleague, with the same classification code, and see how different scores. More for teachers rigrd test papers a week or so later and see how consistent the rows.</p><p>Believed students who fail to pass tests of <a href="http://www.differentiationinfo.com">math</a>ematics usually is failure.</p><p>It is not.</p><p>You may not have examined all the articles on depth will pass or higher level possible, perhaps sick of some or all season, and they may have family problems, and have seriously misunderstood the teacher's intentions and help. Can be <a href="http://integrationutilities.blogspot.com/">add</a>, very be careful, or medicines that affect their ability to focus.</p><p>These factors are real and should be understood as mitigating factors.</p><p>Believing objective tests and the consequent high opinion of himself as a failure. Lowers self-esteem and hinder future efforts.</p><p>On the other hand, students who study conscientiously who relatively stress-free, and a high <a href="http://toolsmathematics.wordpress.com/">degree</a> of experience is very likely to see success as a self-enforcing: they began to see themselves as "students. It may be for such students high or <a href="http://mathematictools.blogspot.com/">even</a> exceptional, but the test class is to provide evidence. What experiments provide evidence that some factors, or a combination of factors, leads students to good results. These factors can include high capacity, but almost certainly will include time spent in study, effective study habits, belonging to a group of peers, ask questions for the teacher, noting, listen carefully, in a low stress environment, good luck. Substantive tests belief to attribute their success leads students to test only one of the factors: capacity.</p><p>I do not know.</p><p>I don't know any more because I see tests as test my ability to <a href="http://integrationutilities.blogspot.com/">set</a> them appropriately, and not subjective test for students.</p><p>You can get an estimate of student work habits, but frankly I'm not interested in experiments that tell me that when I see them regularly in the category of workers. I can see how much work they put: I don't need to tell me that the overall test.</p><p>Frankie I put too much emphasis on tests and examinations. My preference for a more collaborative project in which students can exercise their ability to think, reason, plan and work towards the goal, take advantage of the skills and talents with others.</p><p>Education, to me, should be actively win, nothing we determine-through false means in my opinion-which is a success and failure.</p>Tagged: exam, <a href="http://www.differentiationinfo.com">math</a>ematics, and experiencesUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-75196463678583183992011-06-09T00:00:00.000-07:002011-06-09T00:00:09.042-07:00Answer پاي ^ 2/6: what is the question? <p><img class="size-large wp-image-4802" title="zeta2" alt="" src="/zeta2-1024x292.jpg" width="614" height="175"></p><img class="size-thumbnail wp-image-4803" title="Pietro_Mengoli" alt="" src="/PietroMengoli-150x150.gif" width="150" height="150">Pietro mingoli<img class="size-thumbnail wp-image-4804" title="Leonhard_Euler" alt="" src="/LeonhardEuler-150x150.jpg" width="150" height="150"> Leonhard Euler<p>One question <img class="latex" title="\frac{\pi^2}{6}" alt="\frac{\pi^2}{6}" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B%5Cpi%5E2%7D%7B6%7D&bg=ffffff&fg=000000&s=0"> contains, put mingoli Pietro answer in 1644:</p><p>" <img class="latex" title="1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\ldots" alt="1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\ldots" src="http://s.wordpress.com/latex.php?latex=1%2B%5Cfrac%7B1%7D%7B2%5E2%7D%2B%5Cfrac%7B1%7D%7B3%5E2%7D%2B%5Cfrac%7B1%7D%7B4%5E2%7D%2B%5Cldots&bg=ffffff&fg=000000&s=0">What is value?"</p><p>This became known as "Basel problem" welionhard Euler <a href="www.differentiationinfo.com">solve</a>d, and announced his solution in 1735 when he as 28 years.</p><p>Euler showed-not entirely accurate — the first</p><p><img class="latex" title="1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\ldots =\frac{\pi^2}{6}" alt="1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\ldots =\frac{\pi^2}{6}" src="http://s.wordpress.com/latex.php?latex=1%2B%5Cfrac%7B1%7D%7B2%5E2%7D%2B%5Cfrac%7B1%7D%7B3%5E2%7D%2B%5Cfrac%7B1%7D%7B4%5E2%7D%2B%5Cldots%20%3D%5Cfrac%7B%5Cpi%5E2%7D%7B6%7D&bg=ffffff&fg=000000&s=0"></p><p>x</p><p>Point-point slide in the <a href="http://differentiationtools.blogspot.com/">plane</a>: integer</p><p><img class="size-full wp-image-4805 aligncenter" title="lattice-points" alt="" src="/lattice-points.jpg" width="339" height="335"></p><p>And say <img class="latex" title="(m,n)" alt="(m,n)" src="http://s.wordpress.com/latex.php?latex=%28m%2Cn%29&bg=ffffff&fg=000000&s=0"> chip point of origin <img class="latex" title="(0,0)" alt="(0,0)" src="http://s.wordpress.com/latex.php?latex=%280%2C0%29&bg=ffffff&fg=000000&s=0"> visible upon accession to the <img class="latex" title="(0,0)" alt="(0,0)" src="http://s.wordpress.com/latex.php?latex=%280%2C0%29&bg=ffffff&fg=000000&s=0"> line to <img class="latex" title="(m,n)" alt="(m,n)" src="http://s.wordpress.com/latex.php?latex=%28m%2Cn%29&bg=ffffff&fg=000000&s=0"> contains no other points of slides.</p><p>Question <img class="latex" title="\frac{\pi^2}{6}" alt="\frac{\pi^2}{6}" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B%5Cpi%5E2%7D%7B6%7D&bg=ffffff&fg=000000&s=0"> also has the answer: "how many times you expect to choose a random slides until we get the point is visible from the parent?"</p><p>The reason that the <a href="http://integrationtool.wordpress.com/">probability</a> that a randomly selected <img class="latex" title="\frac{6}{\pi^2}" alt="\frac{6}{\pi^2}" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B6%7D%7B%5Cpi%5E2%7D&bg=ffffff&fg=000000&s=0">is visible from the origin, and <a href="http://mathematictools.blogspot.com/">even</a> choose a random slides such as flipping a weighted currency that comes <img class="latex" title="\frac{6}{\pi^2}" alt="\frac{6}{\pi^2}" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B6%7D%7B%5Cpi%5E2%7D&bg=ffffff&fg=000000&s=0"> "visible" from reflection and <img class="latex" title="1-\frac{6}{\pi^2}" alt="1-\frac{6}{\pi^2}" src="http://s.wordpress.com/latex.php?latex=1-%5Cfrac%7B6%7D%7B%5Cpi%5E2%7D&bg=ffffff&fg=000000&s=0"> "invisible from reflection. Time wait point visible that gives a geometric distribution, which is just the <a href="www.differentiationinfo.com">inverse</a> of the <a href="http://integrationtool.wordpress.com/">probability</a> of choosing point visible.</p><p>Points <img class="latex" title="(m,n)" alt="(m,n)" src="http://s.wordpress.com/latex.php?latex=%28m%2Cn%29&bg=ffffff&fg=000000&s=0"> slides that are visible from the origin <img class="latex" title="m \textrm{ and } n" alt="m \textrm{ and } n" src="http://s.wordpress.com/latex.php?latex=m%20%5Ctextrm%7B%20and%20%7D%20n&bg=ffffff&fg=000000&s=0"> are completely with no common factors (being, master).</p><p><a href="http://mathematictools.blogspot.com/">Even</a> <img class="latex" title="\frac{\pi^2}{6}" alt="\frac{\pi^2}{6}" src="http://s.wordpress.com/latex.php?latex=%5Cfrac%7B%5Cpi%5E2%7D%7B6%7D&bg=ffffff&fg=000000&s=0"> is also the time to wait until their integers chosen at random.</p><p>Why ask the question, as a result, is that such questions to stimulate a creative solutions, answer a question that leads to the desired result being.</p><p>For example, watch a teacher <a href="http://integrationtool.wordpress.com/">math</a>ematics relatively easily related how he knows the question of this kind.</p><p>Here is a simple but revealing ask people at all levels of sports: "the answer is 10. What is the question? "</p><p>Try on a few people, preferably in the collections: answers may amaze you.</p><p>I guarantee people will try, and you and they will be amused with various answers given.</p>Tagged as: Basel, Euler problem, mingoliUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-46299531650921834462011-06-08T00:50:00.000-07:002011-06-08T00:50:00.342-07:00How to crack Iit JEE <p>The right kind of conspiracy is required for students to deal with last minute pressure and deal with people's fears.<br>Timetable should be prepared to study topics Chapter wise and subject wise also.<br>Make notes and critical points of all chapters and study those requiring conclusive.<br>This will help in revising the chapters before the final exam.</p><p>For students who are preparing for the year<strong> 2010 IIT JEE</strong> together with 12th grade examinations, should be just the Board exams focus on curriculum revision and class XII class11th.<br>For students taking the exam time at the out<a href="http://integrationutilities.blogspot.com/">set</a> it should be borne in mind that they should be taught from one source and <strong>IIT JEE </strong>archives, workbooks, Biohazard, eats series offered by IITs/ <strong>education kaisons </strong>is an excellent starting point.</p><p>. Initially prepare yourself mentally for IIT JEE</p><p>"Success in achieving", bearing this in mind aspirants must accept themselves as deserving candidates during the successful ING Trust training plays a vital role.</p><p>2. vigorous efforts</p><p>IIT JEE training requires sustained efforts. Each topic must give proper and stable time. Instead of preparing a subject for a few days and other topics, all three subjects (physics, chemistry, (<a href="http://integrationtool.wordpress.com/">math</a>ematics) must have time every day as they assist in boredom.</p><p>3. good governance</p><p>This afternoon, competitive needs to appropriate guidance to success. The sample is based on fully-concept. So you need clear concepts and without doubt in each topic, to achieve an excellent ranking in ing.</p><p>It is very important to successful student should depend entirely on perseverance and hard work rather than luck wekoinsidinsi.</p><p><strong>Attention to detail</strong><br>In physics, chemistry and <a href="http://integrationtool.wordpress.com/">math</a>ematics all topics that should be selective and cover examination should be avoided because of objective type questions and generously in <a href="http://mathematictools.blogspot.com/">number</a>.<br>Gee<strong> curriculum</strong> of class 11 and 12 are up to 45 per cent and 55 per cent of the issue ID IIT JEE<br>Topics to be studied extensively in Physics:<br>Fluid sound waves, and electromagnetic induction, walictrostatix capacitors, mechanics, optics, modern physics.</p><p>Chemistry topics:<br>Coordination in chemical equilibrium in physical chemistry, quantitative analysis in chemical thermodynamics page, feeding in organic chemistry and inorganic chemistry.</p><p><a href="http://integrationtool.wordpress.com/">Math</a> topics:<br><a href="http://toolsmathematics.wordpress.com/">Complex</a> <a href="http://mathematictools.blogspot.com/">number</a>s, brabola, haibrbola service, in coordination <a href="http://differentiationtools.blogspot.com/">geometry</a>, <a href="http://integrationtool.wordpress.com/">probability</a>, <a href="http://integrationutilities.blogspot.com/">limit</a>s, vectors of <a href="http://differentiationtools.blogspot.com/">matrix</a> algebra, functions, divirintiabiliti, certain integral in calculus and interest derivatives.</p><p>And training is a key factor for success in the exam, but it's essential to be comfortable. When we take the stress, the brain tries to deal with things differently. Be comfortable during the scan and try to decode a cool mind.</p><p><strong>Maintain speed</strong><br>To gain a competitive advantage always aim for 100 per cent rate. Fix speed when exercise problems. Survival strategy for speed and accuracy always because it gives you time to reconsider later.</p><p><strong>Stay composed and keep your cool</strong><br>Not scanned and wear yourself by exam, and instead, take appropriate 6-8 hours of sleep to keep your cool and focus on the exam. It is also advisable to arrive at the exam 15 minutes before time. Try the questions that have any negative marks. Read the instructions carefully on the Guide. <a href="http://mathematictools.blogspot.com/">Even</a> if you go to one section is very good to remember that relative performance is what counts in the end.</p><p>Related <a href="http://integrationtool.wordpress.com/">math</a>ematics</p><p>Tags: crack</p>This entry was posted on 18 March 2011, submit within <a href="http://integrationtool.wordpress.com/">math</a>ematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response or Trackback from your site.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-21975684291837847702011-06-07T02:50:00.000-07:002011-06-07T02:50:02.052-07:00Class X Cbse sample papers? 2010 Hi <p>Www.cbse.nic.in.All website of class x students Board present each issue ID site themes that will take school examination Board CBSE class X 2010. School based assessment Weightage will be in accordance with past practice, i.e. 20 per cent each in science subjects, social sciences and <a href="http://integrationtool.wordpress.com/">math</a>ematics.</p><p>The new Grading System was introduced in secondary schools (& classes for ninth X) as of 2009-10 academic courses. Details of the scheme have been circulated to school grades through no 39 & 40 available on the website www.cbse.nic.in.</p><p><strong>CBSE Class –X sample 2010 ID</strong></p><p>Hi</p><p>Www.cbse.nic.in.All website of class x students Board present each issue ID site themes that will take school examination Board CBSE class X 2010. School based assessment Weightage will be in accordance with past practice, i.e. 20 per cent each in science subjects, social sciences and <a href="http://integrationtool.wordpress.com/">math</a>ematics.</p><p><strong>CBSE Class –X sample 2010 ID</strong></p><p>Hi</p><p>Www.cbse.nic.in.All website of class x students Board present each issue ID site themes that will take school examination Board CBSE class X 2010. School based assessment Weightage will be in accordance with past practice, i.e. 20 per cent each in science subjects, social sciences and <a href="http://integrationtool.wordpress.com/">math</a>ematics.</p><p>The new Grading System was introduced in secondary schools (& classes for ninth X) as of 2009-10 academic courses. Details of the scheme have been circulated to school grades through no 39 & 40 available on the website www.cbse.nic.in.</p><p><strong>You enter a new rating system "with the aim to:</strong></p><p>Minimizes misclassification to students based on tags.<br>It would eliminate unhealthy competition among high achievers.<br>Reducing societal pressures, learner and provide more flexibility.<br>Will focus on a better educational environment</p><p><strong>And modalities of work</strong><br>-Assess the performance of students using the traditional method of marking.<br>Awarded in grades nine <a href="http://toolsmathematics.wordpress.com/">degree</a>s to indicate performance wise.</p><p>The new Grading System was introduced in secondary schools (& classes for ninth X) as of 2009-10 academic courses. Details of the scheme have been circulated to school grades through no 39 & 40 available on the website www.cbse.nic.in.</p><p><strong>You enter a new rating system "with the aim to:</strong></p><p>Minimizes misclassification to students based on tags.<br>It would eliminate unhealthy competition among high achievers.<br>Reducing societal pressures, learner and provide more flexibility.<br>Will focus on a better educational environment</p><p><strong>And modalities of work</strong><br>-Assess the performance of students using the traditional method of marking.<br>Awarded in grades nine <a href="http://toolsmathematics.wordpress.com/">degree</a>s to indicate performance wise.</p><p><strong>You enter a new rating system "with the aim to:</strong></p><p>Minimizes misclassification to students based on tags.<br>It would eliminate unhealthy competition among high achievers.<br>Reducing societal pressures, learner and provide more flexibility.<br>Will focus on a better educational environment</p><p><strong>And modalities of work</strong><br>-Assess the performance of students using the traditional method of marking.<br>Awarded in grades nine <a href="http://toolsmathematics.wordpress.com/">degree</a>s to indicate performance wise.</p><p><embed height="355" type="application/x-shockwave-flash" width="425" src="http://www.youtube.com/v/vMClXppUdro?fs=1&rel=0" allowfullscreen="true"></p><p>Method man, stritlivi, DJ <a href="http://integrationtool.wordpress.com/">math</a>ematics, celvarings, Mr. ghastman, home of hip hop, huh, Tang clan, Karl Kani European tour, ainsbikth deck, the ins rebels, Paris, France</p><p>Tags: 2010, Cbse, class papers, sample</p>This entry was posted on 18 March 2011, submit within <a href="http://integrationtool.wordpress.com/">math</a>ematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response or Trackback from your site.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-4481722399768652225.post-89520585601488150402011-06-06T04:10:00.000-07:002011-06-06T04:10:01.000-07:00Magic tricks revealed: psychological card trick pick <p>This is awesome so close to the main trick to speed straight to convince anyone that you have strong psychic powers. It works great on strangers, as well as close friends, and you can do so at parties or bars or <a href="http://mathematictools.blogspot.com/">even</a> people off the street if you're bold enough. More about this trick is that totally self working, meaning that you don't have to do with anyone's lightness or anything. This purely <a href="http://integrationtool.wordpress.com/">math</a>ematical <a href="http://integrationtool.wordpress.com/">probability</a>, or <a href="http://mathematictools.blogspot.com/">even</a> five years old can do the trick.</p><p>This road would seem to be resourceful in confusion of the public soon. You mention in fast recently learned some black arts to psychological "push". You can develop ideas in mind. Of course, they don't believe, as a matter of manifestations, which obligates you to good luck.</p><p>Dragging fixed deck, cards that only you can see these cards. Spend a considerable amount of psychic energy looking at papers and given to a friend. Then put the cards into a stack, and tell the person to choose two cards, without naming it. Such as ten and three, or six, to form.</p><p>When two cards chosen, deck, and found that two cards chosen right, side by side. They are amazed and possibilities you can do this trick again. Go through the motions look at cards, and dropping <a href="http://mathematictools.blogspot.com/">number</a>s in their heads. When you choose two more cards, again will be right next to each other.</p><p>Why this always works because of the possibility of a purely <a href="http://integrationtool.wordpress.com/">math</a>ematical. Since it's not a suit of the card <a href="http://mathematictools.blogspot.com/">number</a> only, there are about 90 per cent chance will any cards they picked up next to each other, since when they chose their eight cards really (two cards of the four suits each). Approximately 90 per cent of <a href="http://integrationtool.wordpress.com/">math</a>ematics just chances any two eight cards in a deck are side by side.</p><p>Of course, whenever talking this trick is better. Project ideas whenever pretending in mind, and go through the motions do painful psychological projections for the better. If you want you can bet friendly with them you can do "project" cards to his head before the trick. Have fun with this.</p><p>For more information see unadorned after strong influential psychological illusions will make you more sought after guest comfort in the city, head to the main tricks revealed today.</p><p><br>Article from articlesbase.com</p><p>Tags: card, magic, psychic, and detecting selection, trick, tricks</p>This entry was posted on 17 March 2011, submit within <a href="http://integrationtool.wordpress.com/">math</a>ematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response or Trackback from your site.Unknownnoreply@blogger.com0