## Wednesday, January 31, 2007

### pure math

modern algebra and real analysis hold a special place within the mathematics curriculum. Between them, these courses encode the bulk of the language and methodology that was discovered and developed in the 19th century. They are the gateway to almost all of modern mathematics. Most careers for mathematics majors need little more mathematics than linear algebra, statistics, perhaps some differential equations, but to be a mathematician with a broad understanding of the field and a recognition of where the powerful tools lie, one must be conversant with both modern algebra and analysis. These courses must be available to mathematics majors, and those with the potential to pursue doctoral-level work in the mathematical sciences should be advised to take them. Undergraduate programs that do not offer modern algebra or real analysis effectively close out the possibility of pursuing graduate work in theoretical as well as many applied fields of mathematics

### Alexandre Grothendieck

Alexandre Grothendieck is arguably the most important mathematician of the 20th century, but he has been willfully missing for the last fourteen years. Unverified accounts have him flitting about the Pyrenees or gardening in southern France, but the inheritors of his groundbreaking work in algebraic geometry can’t be sure that any of these explanations are true.In 1988, after refusing to accept the highly prestigious and lucrative Crafoord prize from the Royal Swedish Academy of Sciences, Grothendieck released a letter to multiple newspapers and scientific journals condemning what he called the politicization of the scientific community. Prizes and awards were changing the spirit and goals of mathematics, sometimes resulting in blatant intellectual theft.

## Tuesday, January 30, 2007

### iim-iit

The Indian Institutes of Management (IIMs)have got competition when it comes to attracting financial companies and consultancies for campus recruitment: the Indian Institutes of Technology (IITs).IIT Bombay will place its students in companies like Mc Kinsey, Boston Consultancy Group and UBS for the first time. IIT Delhi will have recruiters like Barclays Capital, Bain and Company and Opera Solutions on campus this year. The companies will also visit IIT Kharagpur campus for the first time this year.The number of companies visiting IIT campuses have also doubled since last year. So while IIT, Delhi will have more than 300 companies on campus this year, IIT, Bombay is expecting around 225 recruiters.

### news

We all know that IIT + IIM = big money but the new equation, that many don’t know, is IIT + IIM = Formula 69. Formula 69 is a 100-minute sci-fi comic thriller directed by 30-year-old Nitin Das, an alumni of IIM Lucknow.entire cast and crew for the film came from IIT's drama club members. After getting a good response at screenings in the Capital, Formula 69 will be heading for the Sports, Film and TV Festival in Mumbai.

### CBSE introduces a practical finance course

The Central Board of Secondary Education, CBSE, is going to introduce a new course - Financial Markets Management - for Classes XI and XII beginning this academic year from April. This is being done to develop employable skills in financial markets, accounting and business process outsourcing. Financial Markets Management will be taught as an independent stream like humanities, commerce and science in CBSE-affiliated schools across the country.Class XI will have three papers of 100 marks each in the following subjects - accounting, financial market and computer application. Mutual fund will be an optional paper. In class 12, three papers of 100 marks each in accounting, financial market and business process outsourcing skill will be there. Commodities market will be an optional paper.

## Monday, January 29, 2007

### event

A three-day international conference on computational, mathematical and statistical methods is to be jointly hosted by the Department of Mathematics, Indian Institute of Technology Madras, and Stella Maris College from Saturday. The conference would focus on interdisciplinary investigations of the three subjects, which assume significance in view of increasing technology-driven industries outsourcing their units to India. The conference would underline the various techniques used in investigating problems in the three fields by mathematicians, scientists and engineers across the country and abroad. About 300 delegates are expected to participate in the conference in which 16 symposia and seven paper reading sessions, including the one to be awarded the R. S. Varma Best Paper Award, are to be conducted. While IIT Madras will host the conference on Saturday and Monday on its premises Sunday's conference will be held at Stella Maris College. For details, log on to www.cmasm2007.iitm.ac.in. math

### women's poor math performance

A New research may provide insight as to why, despite progress over the last few decades, women remain underrepresented in math-heavy majors and professions.In an article published in the January issue of Psychological Science, psychologists Amy Kiefer of the University of California, San Francisco and Denise Sekaquaptewa of the University of Michigan point to an interaction between women's own underlying "implicit" stereotypes and their gender identification as a source for their underperformance and lowered perseverance in mathematical fields. Studying undergraduates enrolled in an introductory calculus course, the researchers discovered that women who possessed strong implicit gender stereotypes, (for example, automatically associating "male" more than "female" with math ability and math professions) and were likely to identify themselves as feminine performed worse relative to their female counterparts who did not possess such stereotypes and who were less likely to identify with traditionally female characteristics.math

### golden ratio

The Golden Ratio, also called Divine Proportion, is what artists reckon to be the ratio controlling the dimensions of any beautiful figure and which applies to monuments from the Parthenon and the domes of Persia, to the art of the Renaissance.The pyramid exhibits such a high degree of precision in construction and orientation that it is little wonder ill- founded legends have grown up around it. It is said to be the most accurately aligned structure in existence, facing true North with only 3/ 60th of a degree of error (the misalignment in the telescope's sensor axis of the Paris observatory is 7min of arc, or twice the pyramid's error, while the Meridian Building at Greenwich Observatory in London has an inclination of 9min). Moreover, the pyramid's site was selected so as to allow for astronomical observations. It was determined as a site that would be suitable for a building with 61/2 million tons of stone, whose height was 147m and base area 53000 m . So, whereas Egyptologists adopt the view that the ancient Egyptians built the Great Pyramid as a tomb for Khufu, others suggest that their intention was to build a geodesic monument that would demonstrate their knowledge of the earth's shape and size, or perhaps an astronomical observatory.math

## Saturday, January 27, 2007

### Research by IIT students to be available to all

The Creative Commons, an international non-profit organisation that promotes a license that is an alternate to full copyright, will launch its India chapter at the Indian Institute of Technology, Mumbai.The Creative Commons license allows copyright owners to make their work available to others to "share, reuse and remix – legally", while reserving only limited rights.To mark the launch of CC India, the cutting edge projects of final year B Tech students will be made available on the Internet, free of cost.

### MATH NEWS

Are you weak in mathematics? No worries. Just get Perfect Key of Mathematics software developed by a 14-year-old whiz-kid. The programme solves from basic addition and subtraction to complicated algebra formulas at the press of a key.A student of seventh standard, Umair Seddiqi, began developing the software on Visual Basic 6.0 when he was 12. According to Seddiqi, it is not just for solving complicated formulas, but a learning tool to develop mathematics skills for weak students. Seddiqi's interest in computers began when he was ten years old. A self-taught pupil, he soon learnt basic concepts and functions, and became curious to discover secrets of software and various applications.His project aims to build mathematics software for standards one to ten. He has already developed the software for the fifth and sixth standards and expects the entire project to be completed when he is in the 11th standard.

### math in USA

Mathematics education seems to be very subject to passing trends - surprisingly more so than many other subjects. The most notorious are, of course, the rise of New Math in the 60s and 70s, and the corresponding backlash against it in the late 70s and 80s. It turns out that mathematics education, at least in the US, is now subject to a new trend, and it doesn't appear to be a good one.The real tragedy is that, because mathematics is a heavily layered subject, each new topic building upon the previous ones, once students fall behind catching up can be a nightmare. Indeed, students often meet a rude awakening in late high school or at college when their limited mathematical repertoire fails to provide the necessary tools to fully grasp the next topic.

## Thursday, January 25, 2007

### math award

An Indian mathematician has been named the co-winner of the King Faisal International prize for 2006, in recognition of his path-breaking research which has strengthened links between mathematics and physics. India's MS Narasimhan, an honorary fellow at the Tata Institute of Fundamental Research in Mumbai, shares the prize with UK's Simon Kirwan Donaldson, president of the Institute of Mathematical Sciences and professor of mathematics at Imperial College, London for seminal contributions to math which also helped provide a foundation for physical theories. The two mathematicians' work has helped establish strong ties with the formulation of quantum chromodynamics for which the King Faisal Prize in physics was given last year, the Foundation said.

### usa higher education

According to a recent National Science Foundation study, there has been a five per cent decline in overall doctoral candidates in the US over the last five years, going down from a peak of 42,652 in 1998 to 39,955 last year. While US citizens continue to dominate in humanities and social sciences, there is a steady decline in the number of Americans getting Ph.Ds in physical sciences (down from 6,679 to 5,715). They are also ditching math (1,123 to 917) and computer sciences (909 to 811). The study points to more and more foreign-born students, particularly Asians, getting doctorates, evidently, at the expense of Americans. In engineering, for instance, the number of US-born doctorates went down from 2,739 in 1997 to 1,890 in 2002. The corresponding rise for foreigner-born doctorates was 2,555 to 2,645. As a result, the share of foreign-born scientists and engineers in US science and engineering occupations stands at 29 per cent at the Master’s level and 38 per centat the doctoral level. At a meeting of graduate school deans held in Washington recently, the sci-tech studies crisis topped the agenda. For the first time, US educationists discussed the prospect of brain drain from USA. Typically, the top three countries of origin of non-US citizens earning doctorates are China, India and Korea. The University of Illinois in Urbana-Champaign (UIUC), whose acronym is sometimes jokingly referred to as the University of Indians and University of Chinese, topped the list of institutions which had the largest number of non-US citizen doctorate recipients. But foreign grads are now conquering even smaller campuses. Last month, Rapid City in sleepy South Dakota celebrated its youngest and fastest Ph.D to graduate from its School of Mines and Technology.It is a familiar story across America’s elite institutions such as MIT, Harvard, UCLA and so on. The gradual decline of Americans going in for Ph.D in science, engineering and math is at the heart of the current crisis of jobs in the US hi-tech sector.

### pi

Gaurav Raja, a 15-year-old Indian American high school student, has memorised 10,980 digits of pi, a mathematical term representing the ratio of a circle's circumference to the diameter, to break a North American record.His math and computer science teacher at Salem High School in Virginia had challenged her students to memorise at least 40 digits of pi, a non-repeating decimal that has no end, more accurately expressed as a fraction: 22/7.But Gaurav decided to go a step further and broke the 27-year-old North American pi memorisation record of 10,625 digits set by David Fiore of Swiftwater, Pennsylvania, to take a place among the top 10 in the world. Hiroyuki Goto of Japan set the world record in 1995 by memorising 42,195 digits of pi.Gaurav, who wants to be a video-game programmer, can't explain how he memorised such a big slice of pi. He just did it. "I don't see anything in my head. It's just kind of there," he was quoted as saying by the Washington Post. "It just flows, I guess."

### Microsoft extends life of Windows XP

Microsoft announced on Wednesday that it was extending technical support for home Windows XP operating systems, a signal that it was not abandoning them for Vista software launching next week.The Redmond, Washington software giant said the "support life cycle" for Windows XP Home Edition and Windows XP Media Center Edition would be stretched to April 2009.Similar support would be provided for users of Windows XP Professional, according to Microsoft.Microsoft's next-generation Vista operating system made its business debut in November and home-computer versions will be launched on January 30. Vista is Microsoft's first revamped operating system in five years

## Wednesday, January 24, 2007

### math teaching

Too many schools are "teaching to the test" in mathematics, stifling genuinely stimulating thinking about the subject, a report suggests. Education watchdog Ofsted looked at 26 schools, sixth forms and other colleges in England and found that about half of lessons failed in this regard.A shortage of qualified maths teachers left some groups taught by non-specialists. In one further education college, a group working on the "application of number" was taught by a tutor whose highest maths qualification was a grade D at GCSE. the Ofsted report follows a government-commissioned review of maths in 2004 by Professor Adrian Smith, principal of Queen Mary, University of London. He said maths was so central to much of the modern economy it should be treated as special, not on a par with other subjects.

## Tuesday, January 23, 2007

### new state of matter

Conventional matter exists in three familiar forms—solid, liquid and gas. But under special circumstances, quantum theory predicts exotic states of matter, such as superconductors in which electrons flow with no resistance and Bose-Einstein condensates in which atoms move as a collective whole. Now, in the Dec. 15 issue of the journal Science, three Stanford physicists theorize a new state of matter that may pave the way for electronic devices that dissipate less energy and generate less heat."Searching for new states of matter has become the holy grail of condensed matter physics, just as the quest for new elements dominated chemistry and the pursuit of new subatomic particles dominates particle physics," says physics Professor Shoucheng Zhang, who also holds courtesy appointments in the Applied Physics and Electrical Engineering departments. With graduate student Taylor Hughes and former graduate student and current Princeton University postdoctoral fellow Andrei Bernevig, Zhang proposed the existence of the so-called "quantum spin Hall state," which has extraordinary properties. The U.S. Department of Energy and National Science Foundation funded their work.

### knowledge industry

If BPO was the first wave of offshoring and has now matured as a business model, then knowledge process outsourcing (KPO) is rapidly emerging as the sequel success that’s keeping the outsourcing story firmly in corporate radar screens. The figures are impressive indeed.Estimates are that the global KPO industry is likely to be annually worth almost $17 billion and India is once again poised to capture more than 70% of this pie. Almost 2.5 lakh professionals are expected to be working in India’s KPO industry. India expects KPO to clock a compounded annual growth rate (CAGR) of around 45% as against 26% for non-KPO outsourcing business. And once again, lower costs and a high quality knowledge pool are proving to be invaluable advantages for the country. The project management experience gained in BPO is adding immeasurable value in delivering KPO offerings.Individuals who choose to live in one place but provide their inputs to a process somewhere else. For example, a mathematics tutor in India could be providing tuitions to American children over the internet, or a specialised professional may be employed by a global corporation to be a part of a global team, but the market being addressed by the team could well exclude the market in which the individual lives.Therefore, KPO will not be a distinct industry, as is BPO. Consequently, the accepted management paradigms and principles that apply to BPO will not apply to KPO. BPO is about size and volume and efficiency. In contrast, KPO will not be about size but depth of knowledge, experience and judgment.We would like to conclude by saying that KPO is a huge opportunity for companies around the world to include professional talent from around the world in meeting their business objectives. However, it is not an extension of BPO. While costs in India for highly qualified knowledge professionals are far lower than in the US and in Europe, this would not be the key driver in including Indians in the global economy. The key driver of KPO would be access to the vast professional talent in India.math

### Fermat's Last Theorem

A retired professor has claimed to have given two solutions to Fermat's Last Theorem (FLT), the nearly 400-year old problem that has puzzled mathematicians the world over.Prof V K Gurtu, the former Head of the Mathematics Department at the Laxminarayan Institute of Technology offered two solutions -- one based on the techniques prevalent during the 17th Century French judge and mathematician Pierre de Fermat's time and another using modern methods.The 66-year-old professor presented the solutions to the mind-boggling 370-year-old problem at the International Congress of Mathematicians in Madrid, Spain last month, which was attended by leading lights from the world of math.In his 28-page paper "On Fermat's Historic Marginal Note: Some Left Out Grains of Truth Leading to New Proof of FLT", Gurtu claims to have revealed facts which were left out by earliest researchers including Euler, Gauss, Dirichlet and Legendre who have proved the FLT to to the fifth power any number.FLT has its origin in the Historic Marginal Note (HMN) Fermat (1601-1665) had written against the backdrop of Pythagoras Theorem in its arithmetic form in the book "Arithmetica" of Diophantus in 1637.In the first proof, Gurtu uses identities known in Fermat's time and his well known method of infinite descent while in the second, non-natural numbers have been used for a very limited purpose.Gurtu claims that his techniques are the closest to Fermat's thought process and has sent the paper to an American peer review journal for publication which is considering the solution.The retired professor said he had been working on the problem since 1989 and had given a solution in 1998 to the Indian Mathematical Society, which had raised certain queries.Gurtu claims to have found satisfactory answers to the queries in the last eight years

### Robert Langlands

In 1995, British mathematician Andrew Wiles cracked open Fermat’s last theorem, a problem that had vexed the best of mathematicians for more than 350 years. There was another man, though, who had made an important contribution in this matter: Canada-born mathematician Robert Langlands, whose functoriality conjecture became the starting point in the solution of Fermat’s last theorem. Sixty-nine-year-old Langlands was in Mumbai recently to deliver a lecture at the Tata Institute of Fundamental Research. The Wolf Prize recipient seemed modest about his contribution. “It was one of the many elements in finding the proof for Fermat’s theorem,” he says, admitting it would have been difficult to start off without the functoriality conjecture.Was Fermat’s theorem the final frontier for mathematicians? “It certainly was the most famous and fascinating of all theorems because it is a difficult problem of elementary mathematics. The next challenge could be the proof of Riemann hypothesis. But it won’t attract the same attention,” he says.

### Gauss prize for Japanese math wizard

Japan’s Kiyoshi Ito shared with fellow mathematical genius Grigory Perelman by winning Gauss prize for mathematics.90-year-old Ito received the inaugural prize worth 10,000 euros (11,500 dollars) in person at the 25th annual International Congress of Mathematicians presided by Spanish King Juan Carlos. Ito had made a major contribution to 20th Century applied mathematics and credited him with laying the foundations of the theory of stochastic differential equations and stochastic analysis.Stochastics involves creating models of study around random events which can happen at any time. Their practical application is highly diverse, ranging from population dynamics to engineering filtering and, of particular interest to financial analysts, probabilities of financial risk.The idea underpins market instruments such as options and futures, whereby prices are calculated according to stochastic analysis. In biology, the theory allows biologists to assess the probability of a gene dominating a species.Ito, born on September 7, 1915 in Hokusei-cho, Mie prefecture, central southern Japan, was professor at the University of Kyoto until his retirement in 1979.He also held a string of lectureships at institutions as august as Cornell and Princeton, where he began his US career in 1954.After graduating from the Imperial University, Tokyo, Ito went on to work for the national statistical office, publishing seminal works on theories of probability and stochastics. He was awarded a PhD in 1945.The Gauss prize, awarded by the International Mathematical Union and the German Mathematical Union, is named after Carl Friedrich Gauss (1777-1855), who was known as the “prince of mathematicians” owing to contributions across a wide range of fields from number theory and differential geometry to astronomy

### Robert Tompson

Robert Tompson, a longtime Nevada university math professor who led the development of the first computer science curriculum on campus, passed away on Jan. 6 in Reno following complications from pneumonia. Tompson was 86.

Tompson, a native of Adrian, Mich., taught at the Nevada University from 1956-91, including 10 years as chairman of the mathematics department. In addition to his leadership role in establishing the computer science curriculum which later became the Department of Computer Science, Tompson was also credited with playing an instrumental role in the formation of The Desert Research Institute. In 1967-68, Tompson taught in India as part of a United States and Indian exchange program.

Tompson, a native of Adrian, Mich., taught at the Nevada University from 1956-91, including 10 years as chairman of the mathematics department. In addition to his leadership role in establishing the computer science curriculum which later became the Department of Computer Science, Tompson was also credited with playing an instrumental role in the formation of The Desert Research Institute. In 1967-68, Tompson taught in India as part of a United States and Indian exchange program.

### Bethel Young Alumnus Award for 2007

The Awards Committee of the Bethel College Alumni Association has named Susan Loepp, Williamstown, Mass., as the winner of the 2007 Young Alumnus Award. Loepp is an associate professor of mathematics at Williams College, where she has been since 1996. Her field of research is commutative algebra and she often teaches courses in abstract algebra at Williams.Loepp is a 1989 graduate of Bethel College with a B.A. in mathematics and a B.S. in physics. She earned her Ph.D. in mathematics from the University of Texas at Austin in 1994, where her dissertation topic was “Making the generic formal fiber local.” She was a visiting professor at the University of Nebraska from 1994-96.Loepp is the author of a number of articles published in the Journal of Algebra, the Journal of Pure and Applied Algebra and the Rocky Mountain Journal of Algebra, among others. In 2006, she published her first book, a collaborative effort with fellow Williams College professor William Wootters, a physicist.

## Monday, January 22, 2007

### Tributes to maths giant

A FORMER maths teacher at St Albans School who was reputed to have been the inspiration for Stephen Hawking, the famous theoretical physicist and author of A Brief History of Time, died recently aged 78.

Dick Tahta, who was born in Manchester, taught at St Albans School for six years between 1956 and 1962.In a national advertising campaign to attract recruits to science, Stephen Hawking was among famous people asked to name one teacher who had inspired them. "Mr Tahta", was Hawking's response.During his time at the school he met and married his wife Hilary, who died in 2000. He later lectured at Exeter University and taught in America and South Africa. He also wrote and co-authored several text books. Mr Tahta is survived by three daughters and a son.

Dick Tahta, who was born in Manchester, taught at St Albans School for six years between 1956 and 1962.In a national advertising campaign to attract recruits to science, Stephen Hawking was among famous people asked to name one teacher who had inspired them. "Mr Tahta", was Hawking's response.During his time at the school he met and married his wife Hilary, who died in 2000. He later lectured at Exeter University and taught in America and South Africa. He also wrote and co-authored several text books. Mr Tahta is survived by three daughters and a son.

### math teaching

Teaching math seems like it should be so much simpler than teaching reading. In math there are algorithms and formulas that are used to get answers. Want to know the square root of a number? There's a formula. Want to know the diameter of a circle? There's a formula for that, too.In math the answer is either right or wrong. Two plus two equals four. There's no gray areaWell, not necessarily. A problem might have only one answer, but there could be many ways to get to the answer; that's the gray area. And teaching students how to get to the answer has been a topic of much debate -- so much that it's been dubbed "math wars" -- pitting reform math against traditional math. Traditional, also known as the basics, is what most parents think of as math.

### Good reading culture is key to career development

The role science and technology has assumed in the career prospects of students has effectively undermined the relevance of literature in society. Mathematics and science teachers express their contempt for the arts, saying serious students looking forward to getting an attractive career do not give their attention to literature. Instead, they should concentrate more on mathematics and science. As a result, many students who would have developed competence to understand and appreciate literature have ignored it, making them to score poorly in the English Language. This jeopardises their chances of getting enrolled to study medicine, engineering and other science based courses, which need excellent grades in English to qualify.

## Sunday, January 21, 2007

### iit-jee math

1..Find the nature of roots of f(x)=e*x-x-1 =0.

2..the value of the parameter a for which the fuction f(x)=1+ax,where (a is nonzero), is inverse of itself is...

3..find the number of spherical balls in a complete pyramidal pile, whose base is an equilateral triangle each side of which contains n balls.

2..the value of the parameter a for which the fuction f(x)=1+ax,where (a is nonzero), is inverse of itself is...

3..find the number of spherical balls in a complete pyramidal pile, whose base is an equilateral triangle each side of which contains n balls.

### Prof. Chandrashekhar Khare and Fermat's last theorem

An Indian mathematician, Chandrashekhar Khare, is poised to make a significant breakthrough in the field of number theory: with his solution of part of a major outstanding problem in algebraic number theory. In a paper posted on the Mathematics Arxiv on the web in April 2005 and subsequently sent for publication to a leading mathematics journal, the 37-year-old mathematician based at the University of Utah has proved what is known to specialists in the field as the `level-1 case of the Serre conjecture.' In earlier work done with the French mathematician, J.P. Wintenberger, in December 2004, Dr. Khare outlined a two-part general strategy to prove the Serre conjecture fully. The present result is a first key step. Experts in the field emphasise that the attempt to prove the Serre conjecture — named after the eminent French mathematician, Jean-Pierre Serre, who originally formulated it in the early 1970s — has been the driving force behind many recent developments in number theory. As Professor Serre himself noted many years ago, his conjecture, if proved in generality, would imply the proof of Fermat's last theorem.Dr. Khare's work reaps the harvest of seeds sown by Andrew Wiles and his co-worker, Richard Taylor, en route to proving Fermat's last theorem. Speaking to this correspondent after outlining his results at a TIFR seminar, Dr. Khare recounted that little progress had been made towards the proof of the conjecture till Professor Wiles' great work, and the realisation by Dr. Taylor that their methods could be used to tackle the solution of this outstanding problem.

### Fractals and electronics

FRACTALS ADD a new dimension to electronics. People most often see fractals in the familiar, irregular branching shapes of nature — leaf, or tree, or snowflake. Fractal, in mathematics, is a geometric shape that is complex and detailed in structure at any level of magnification. Often fractals are self-similar — that is, they have the property that each small portion of the fractal can be viewed as a reduced-scale replica of the whole. A repeating pattern of ever-smaller branches gives these structures a unique profile that defies classical geometry. Now a study suggests that magnetic fields can take the form of fractals too if a magnet is made of plastic molecules that are stacked in parallel chains.Mathematically, fractals are considered to exist in partial, or fractional, dimensions. That means if a device produces a magnetic field that exhibits fractal behaviour, the magnetic field would not posses dimension equal to a whole number — such as one, two, or three dimensions — but rather a fractional value such as 0.8 or 1.6 dimensions.

### string theory

String theory, which considers that the fundamental building blocks of nature are strings rather than point-like objects or particles as has been believed hitherto, has become a major theme of research in the discipline of theoretical high-energy physics. Hailed by its practitioners as the `Theory of Everything' because of its ability to provide a framework to unify all the fundamental forces of nature, the string theory has both fascinated and mystified physicists. string theory is a very promising, exciting and interesting proposal for developing our understanding of the laws of nature beyond where they currently stand. What happened is that we discovered that string theory contains within it particles and forces that look very, very much like the particles and forces that we see in the world around us. The door was opened to the possibility that string theory really is a theory of nature. The initial progress in 1984 and 1985 was so rapid and dramatic that many people had the feeling that we would push it all the way to the finish line within a few years or even months.There are two major problems that have arisen in theoretical physics in the last half of the 20th century. The first is the very basic problem that the laws of physics as we know them are not self-consistent. Quantum mechanics is not consistent with Einstein's theory of general relativity. So we don't have any choice but to go on. We have a theory where we can ignore various inconsistencies and make some predictions but ultimately if we were to try and make detailed enough predictions, those inconsistencies would prevent us from getting correct results.Then there's another problem. The laws of physics as we currently understand are kind of a laundry list of equations and masses for various particles and strengths of various forces and there doesn't seem to be any unifying theme or any order behind this list.

## Saturday, January 20, 2007

### Geoffrey Matthews

A rare combination of mathematical talent, humour, strategic vision and energy enabled Geoffrey Matthews, who has died aged 85, to pioneer much-needed changes in the teaching of maths in the 1960s and 70s.As the first British professor of mathematics education, at London University's Chelsea College (1968-77), Matthews established a research and development tradition much copied in Britain and abroad.His ideas were influenced by his London University PhD work on infinite matrices, completed part-time while teaching; and by attendance at international seminars. The distinctive feature of his curriculum was the introduction of topics such as matrices, sets and logic, computing and statistics.Matthews was subversive, creative, strategic and tactical. He had ambitious plans to benefit children and teachers, especially those in deprived areas and developing countries, but was never ambitious for himself.

## Friday, January 19, 2007

### Ecstasy of mathematics

The ecstasy of mathematics can be experienced not only by an Euler or Ramanujan but also by an aspirant to a career in creative research.Sir C. V. Raman told frankly with his customary emphasis that the greatest deterrent to creative work is fame! By that he meant that all creative work is spontaneous which results in fame, but once a scientist becomes famous he tries to match his new work with the standard of his old work. This removes the spontaneity and therefore affects the quality of research, since no two discoveries are identical in their origin. But this assertion of Sir C. V. Raman should bother only famous scientists but should not deter a fresh entrant who takes up the challenge of creative work. The first level of achievement consists in proving the same result by a different method. In this case since the result is known, the discovery of a new method is just the first step toward creative research. But this helps the young scientists to choose the field of research in which he has demonstrated his originality. The second source of inspiration is to study the papers announcing the first discovery. Such papers reveal the `insurrection in the mind' of the discoverer and the reason he chose the new assumptions that led to the discovery. It is more purposeful to read the first papers of Einstein on Special Relativity than reading his biography eulogising his genius. In other words the first paper is an autobiography of the `discovery'.

It is a historical fact that Nobel prize work resulted from observing the properties of 2 x 2 matrices and interpreting them to suit the physical problem. The discoverer sees more than meets the eye and has the courage to assert his conclusions.Pauli matrices are the roots of the unit matrix which any student can derive, but Pauli had the courage to identify them with `spin'. Likewise 2 x 2 circulant matrices are familiar to any student but Lorentz identified it with a transformation that preserves the difference of squares. Einstein had the imagination to interpret the transformation as relating to space and time and extend it to momentum and energy, a discovery which altered the course of civilisation! Dirac extended the anticommuting properties of 2 x 2 matrices to 4 x 4 matrices leading to the discovery of the equation of the electron which is the basis of quantum electro dynamics. He had the courage to interpret the positrons as holes in a sea of negative energy states while Feynman recognised that this was equivalent to a negative energy electron travelling back in time. What is important is to recognise that all these discoveries are related but made by different scientists proving the Sir C. V. Raman dictum that the new extensions of a new work is not usually done by the original discoverer. The following question remained open: How to derive Dirac matrices from Pauli's? I was able to obtain it by the operation which led to many problems good enough for doctorate degrees for more than six students of mine! Such situations arise over the whole domain of physics and it is a misleading claim that one can discover the `theory of everything' and reach the end of knowledge of natural phenomena. Actually extending the Churchillian phrase `We are not at the end, not even the beginning of the end, not even the end of the beginning, but at the beginning itself'. We have yet to understand the meaning of time, its origin and its reversal, the origin of creation, the expanding universe, the black holes and dark matter, the nature of three dimensional space and the extension to higher dimensions.Here is an open question to a young entrant to theoretical physics. If is a Lorentz matrix so is — . If reverses momentum keeping energy constant, — reverses energy keeping momentum constant, both reversing the velocity. If is expressed as the square of a matrix L, the Lorentz matrix L brings the particle to the rest system and then to -v. If — is expressed as the square of a matrix, that matrix with imaginary elements brings the particle to rest but with imaginary mass and then to negative energy. L* is a semi Lorentz matrix reversing the difference of squares. What is the physical meaning of L* and iL*?

source..the hindu

### math-phobia

THE KING of all arts is not rock. Definitely not. It's not cinema either. Not poetry, not painting. Not dance, yoga or poga. It is - hold your breath - Mathematics. After all, dance is about geometry, painting about patterns, rather algebra, as is music and the play of words. Art is about the logical and the illogical, about reality and the abstract, both elements of math. If it really is all that, math should be fun. If it isn't, the Ramanujan Museum and Math Education Centre is determined to make sure it is. In association with the Tamil Nadu Science and Technology Centre, the Ramanujan Centre has organised a training course for school teachers to introduce them to an innovative Math curriculum for pre-kindergarten, KG and class one students. So kids will play games, solve puzzles and investigate patterns to learn Mathelang - the Mathematician's language, known in normal terms as algebra. It will be all play for the kids, mostly with patterns and designs for which they have a natural flair. Algebra at pre-school might seem to be a bit too early, but it's a pattern followed worldwide, according to the centre. The idea is to introduce kids to a mathematics not quite viewed as a bitter pill, but to a study of patterns, relations and structures. A math that they learn to be fun, that it's a game of intuition and imagination. The centre also reckons that pre-school is a good time to bust math-phobia at its zero, and to introduce algebra at a time of least learner resistance.

### math learning can be enjoyable

THE PRESENT state of teaching mathematics in a majority of the schools is far from satisfactory. The rate of failures in mathematics is considerably higher than in other subjects. Many find mathematics a difficult subject. Limited English Proficient (LEP) students are often faced with the challenge of developing oral communication skills and academic skills in English. To succeed in the mainstream classroom, LEP students must learn both academic and communication skills. To develop academic skills, students must receive meaningful, relevant content-area instruction presented in a framework of appropriate English language development skills. There are two approaches for teaching LEP student's to improve their academic skills in mathematics, Cognitively Guided Instruction (CGI) and Active Mathematics Teaching (AMT). The NCERT, at the national level, and SCERT/SIEs at the State level have initiated several steps to improve the quality of mathematics education in our schools. The Association of Mathematics Teachers of India is doing very useful work in this regard. Nevertheless, ultimately it is with the classroom mathematics teacher that everything depends. Every teacher can do a lot in his/her own way, to make the learning of mathematics more enjoyable, leading to the qualitative improvement of mathematics education in our schools.

## Thursday, January 18, 2007

### india on top in WEF report

The annual report from the World Economic Forum (WEF) ranks india 7th for the quality of its maths and science teaching.Singapore, Finland and Belgium lead the 125 countries on the quality of their maths and science education with India ranked seventh followed by the Czech Republic and Tunisia.The WEF rankings were based on an assessment by business and industry .

### space university

The Indian Space Research Organisation (ISRO) is planning to set up a space training centre or a university in Kerala to meet the shortage of space scientists.

the proposed institute is expected to come up on the outskirts of the state capital on a 100-acre plot. It would be modelled on the lines of the Bhabha Atomic Research Centre in Mumbai. One reason why ISRO is planning such an institution is that its Vikram Sarabhai Space Centre here faces a crisis due to large-scale retirement of staff members. It was in the 1970s that large-scale recruitment was done. With most of the staff having either retired or on the verge of retirement, there is a crunch of experienced personnel.

the proposed institute is expected to come up on the outskirts of the state capital on a 100-acre plot. It would be modelled on the lines of the Bhabha Atomic Research Centre in Mumbai. One reason why ISRO is planning such an institution is that its Vikram Sarabhai Space Centre here faces a crisis due to large-scale retirement of staff members. It was in the 1970s that large-scale recruitment was done. With most of the staff having either retired or on the verge of retirement, there is a crunch of experienced personnel.

### iit-jee math

QUESTION.THE equation of a circle with origin as centre and passing through the vertics of an equilateral triangle ,whose median of length 3a.

answer...we have to find equation of circum circle.we are given

1..origin is the centre.

2..tringle is equilateral.

method

1..quation of circle have three unknowns,if we find three vertices of triangle,we can find circle.

2.centre of circle is given ,if we find its radius,we can find circle.

we leave first method????,in case of equilateral triangle

circum radius =3/2(median) =3/2(3a)=2a

so equation of circle is x*2 +y*2 = ( 2a)*2.

### India’s scientific tradition

The treasure of knowledge (included science) of India lay in our Vedas, Upnishads, Smritis, shrutis, shlokas, classics Ramayana, Mahabharata and other literature. These were made to appear as if these contained only Hindu philosophy and ideology. These classics had no tag of science. In fact, scientific knowledge formed the very part and parcel of our philosophy and dharma trove.Metallurgy formed part of Ayurveda and ancient Indian physicians like Charak, Sushruta and Nagarjuna have described in detail how to prepare medicines from gold, silver, copper, iron, mica, mercy, etc. Qutab Minar is another example of India’s excellence in metallurgy. Al Baruni makes a mention of it in 11th century. Qutab Minar was “made in the 4th century…it is also called the Garuda pillar. It was brought to Delhi in 1050 by Anang Pal, the founder of Delhi”.

## Wednesday, January 17, 2007

### cut in fee for girls by iit-k

In an effort to attract more girl students towards Engineering, the Indian Institute of Technology (IIT-K) has proposed to reduce the fee for girl students.

The proposal, which is in its initial stage, is likely to be given a proper shape within a short period.The decision to revise and reduce the fee for the girl students was taken considering the fact that only 12 per cent of girl students opted for various disciplines at the IIT-K. Despite the fact that the institute has better hostel accommodation for girls and the institute administration has constantly been making efforts to raise the number of girl students, no significant change could be observed in this number.

The proposal, which is in its initial stage, is likely to be given a proper shape within a short period.The decision to revise and reduce the fee for the girl students was taken considering the fact that only 12 per cent of girl students opted for various disciplines at the IIT-K. Despite the fact that the institute has better hostel accommodation for girls and the institute administration has constantly been making efforts to raise the number of girl students, no significant change could be observed in this number.

## Tuesday, January 16, 2007

### Wolf prize

Leading Israeli and American mathematicians will share the $100,000 Wolf Foundation for Mathematics in May, to be presented at the Knesset by the president of Israel. In addition, the Wolf Prize in Physics, also worth $100,000, will be divided between leading experts from Germany and France. Considered Israel's Nobel Prizes, the Wolf Prizes - five of which are awarded every year, were established by the late German-born inventor, diplomat and philanthropist, Dr. Ricardo Wolf. Prof. Harry Furstenberg of the Hebrew University of Jerusalem will receive half of the mathematics prize "for his profound contributions to ergodic theory, probability, topological dynamics, analysis on symmetric spaces and homogenous flows". The other half will go to Prof. Stephen Smale of the University of California at Berkeley "for ground-breaking contributions that have played a fundamental role in shaping differential topology, dynamical systems, mathematical economics, and other subjects in mathematics," the international jury said. Born in Germany in 1935, Furstenberg received his doctorate from Princeton University and since 1965 has been at Hebrew University; he has already received the Israel Prize. Smale, who was born in the US in 1930, received his Ph.D. from the University of Michigan and joined UC in 1964. He also was a professor at the City University of Hong Kong for six years. His proof in the early 60's of the Poincar Conjecture for dimensions bigger or equal to five is one of the great mathematical achievements of the 20th century.

### cannonball conjecture

for four centuries, mathematicians had been unable to prove famed astronomer and mathematician Johannes Kepler's 1611 conjecture that the pyramid is the best way to stack cannonballs. That is, until July 2006 when University of Pittsburgh mathematician Thomas C. Hales, and his former graduate student, Samuel P. Ferguson, published their proof of one of mathematics' most famous puzzles -- the Kepler conjecture.Dr. Ferguson is a mathematician with the National Security Agency. Dr. Hales, 48, is Pitt's Andrew Mellon Professor of Mathematics. The cannonball proof has blasted Dr. Hales and Dr. Ferguson's names into the stratosphere of mathematical accomplishment.The proof is about 300 pages long -- not counting 40,000 lines of computer code and three billion bytes of data necessary to solve the puzzle that left mathematicians scratching their scalps for centuries.

Kepler came up with conjecture after Sir Walter Raleigh asked mathematicians to determine the best way to stack cannonballs on ship decks. Intuition suggests the pyramid is the most efficient -- or densest -- way to stack cannonballs, but Kepler never proved the conjecture.Centuries of mathematicians solved portions of it but never proved that cannonballs in a pyramid occupy less space than in any other configuration.Twentieth century mathematicians figured out how many calculations were necessary to solve the conjecture, but the number was too enormous to undertake. Dr. Hales started considering the conjecture in 1988 and had two things going for him -- computers and enjoyment of exhaustive mathematical problems to solve.He and Dr. Ferguson studied 5,000 configurations of stacked spheres, which they reduced to 100 candidate configurations. Then after years of effort, the "eureka moment" occurred in November 1994, when Dr. Hales figured out the ideal geometric forms that best described the relationship between spheres and the space they occupied.Reducing the problem into creative geometry allowed a computer to do the calculations. But the computer had to run nonstop for three months to do many billions of calculations to complete the proof, he said.

### private school

Between 60 and 70 per cent of urban Indian students are located in private schools, the shift is quite large in even rural India as the latest Pratham survey shows -- while 16.3 per cent of rural children were in private schools in 2005, this increased to 18.8 per cent in 2006, which implies an increase of over 15 per cent in terms of the number of children.Private education costs a lot less, delivers better results, and yet politicians talk about increasing government education -- one of the focus areas of the 11th Plan is to universalise the Sarva Shiksha Abhiyan through more government school. the government can still pay for schooling but let parents decide if they want to give these vouchers to government schools or to private ones. Second, on a per capita basis, the poorest 40 per cent of the country's population spends around 30 per cent of the all-India average on education -- since government schooling is free, this means they're either spending on tuition or are sending their children to private schools

## Sunday, January 14, 2007

### ancient math

Indian mathematicians developed the

number system in the pre Greek/Roman era. The conceptualisation

of, and the mathematical symbolisation of, the Zero particularly

is acknowledged to be the gift of India. Sometime since the

visit of Alexander the Great, this number system reached

Arabia/Asia Minor. With the Moor Invasion of Europe, and the

Crusades, the number system reached Europe. Since the Europeans

got it from the Arabs, it became know to them as the Arabic

Numerals.Until then, Europe used the Roman numbering system (which is

based on the Roman Script/alphabet) where the progression is

somewhat clumsy in comparison to the Arabic. So that the

denotation of larger numbers becomes almost messy. And note that

there is no zero used in the Roman numbering system - even

though it too is a decimal system

Om prunamadah purnamidam purnat purnamuddachayate

Purnasya purnmadaya purnamevavashishyate.

That is the first, most enduring, and most concise

definition/descriptio of Infinity - both Divine and mathematical.

number system in the pre Greek/Roman era. The conceptualisation

of, and the mathematical symbolisation of, the Zero particularly

is acknowledged to be the gift of India. Sometime since the

visit of Alexander the Great, this number system reached

Arabia/Asia Minor. With the Moor Invasion of Europe, and the

Crusades, the number system reached Europe. Since the Europeans

got it from the Arabs, it became know to them as the Arabic

Numerals.Until then, Europe used the Roman numbering system (which is

based on the Roman Script/alphabet) where the progression is

somewhat clumsy in comparison to the Arabic. So that the

denotation of larger numbers becomes almost messy. And note that

there is no zero used in the Roman numbering system - even

though it too is a decimal system

Om prunamadah purnamidam purnat purnamuddachayate

Purnasya purnmadaya purnamevavashishyate.

That is the first, most enduring, and most concise

definition/descriptio of Infinity - both Divine and mathematical.

### math news

A video clip of a Glebe Collegiate math teacher drawing what seems to be a perfect circle by hand has attracted hundreds of thousands of hits online in just a few days.

### math series

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10= 1111111111

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10= 1111111111

## Saturday, January 13, 2007

### problem

a + b + c = 100 a,b,c belongs to natural numbers then howmany triplets (a,b,c) are possible where two elements (say a,b are odd and the third c is even ) and try to solve with more than one method.

### what is π

The mathematical constant π is an irrational number, approximately equal to 3.14159, which is the ratio of a circle's circumference to its diameter in Euclidean geometry, and has many uses in mathematics, physics, and engineering. It is also known as Archimedes' constant.In Euclidean plane geometry, π is defined either as the ratio of a circle's circumference to its diameter, or as the ratio of a circle's area to the area of a square whose side is the radius.

### Maths books for IIT-JEE

Tata McGraw Hill book for IIT JEE ,IIT Maths by M.L. Khanna,IIT MATH by Das Gupta,CRC Standard Mathematical Tables and Formulae,IIT Math R.D.SHARMA ,

Dr. k.c. sinha's initial maths book.

Dr. k.c. sinha's initial maths book.

### Prime Twins Conjecture

Professor Terence Tao of the University of California, Los Angeles (UCLA), was awarded the 2006 SASTRA's Ramanujan Prize at the International Conference on Number Theory and Combinatorics at the Srinivasa Ramanujan Centre, SASTRA University, Kumbakonam.This $10,000 prize comes on the heels of the Fields Medal that was awarded to Professor Tao in August for revolutionary contributions to several areas of mathematics.One of the most famous unsolved problems in mathematics is the Prime Twins Conjecture, which asserts that there are infinitely many prime pairs that differ by 2. More generally, the prime k-tuples conjecture states that if a k-tuple is admissible, then there are infinitely many such k-tuples of primes. Here by admissible one means that the k-tuple must satisfy certain non-divisibility conditions. If the prime k-tuples conjecture is true, then it follows that there are arbitrarily long arithmetic progressions of primes. For example, 7, 37, 67, 97, 127, 157, is an arithmetic progression of 6 primes with common difference 30.

Sieve theory was developed in the 20th century to attack problems such as the k-tuples conjecture. Although this conjecture is still unsolved, sieve methods have succeeded in establishing similar results for almost primes, namely, those integers with very few prime factors, but not for the primes themselves. Thus, the world was astonished when Professor Tao and Professor Green proved in 2003 that there are arbitrarily long arithmetic progressions of primes. The road to the Green-Tao theorem has been long, and in his lecture, Professor Tao surveyed the history of the problem and described the techniques that led to the recent breakthrough.

The first major advance was made in 1939 by van der Corput, who showed that there are infinitely many triples of primes in arithmetic progression. He used the circle method, originally invented by Hardy and Ramanujan to estimate the number of partitions of an integer and subsequently improved by Hardy and Littlewood to apply to a wide class of problems in additive number theory. van der Corput's result was improved in 1981 by the British mathematician Heath Brown, who showed that there are infinitely many quadruples in arithmetic progression of which three are primes, and the fourth an almost prime with at most two prime factors. That such an improvement came after more than 40 years indicates the difficulty of the problem. Another problem was the study of finite arithmetic progressions within sets of positive density. This was pioneered by the 1958 Fields medallist K.F. Roth, who in 1956 showed that any set of integers with positive density contains infinitely many triples in arithmetic progression. This study culminated in 1975 with the grand result of the Hungarian mathematician Szemeredi, who proved that any set of integers with positive density contains arithmetic progressions of arbitrary length. Professor Tim Gowers of Cambridge University, who won the Fields Medal in 1994, has recently given a simpler proof of Szemeredi's theorem. It is to be noted that since the primes have zero density, Szemeredi's theorem does not imply that there are arbitrarily long arithmetic progressions of primes. Professor Green was a Ph.D student of Professor Gowers, who introduced him to Szemeredi's theorem. One of Professor Green's first major accomplishments was the result that any subset of the primes, which has relative positive density, contains infinitely many triples on arithmetic progressions. Professor Tao and Professor Green then corresponded due to their common interest on such problems. They studied the general problem of arithmetic progressions in sparse sets of integers. By combining ideas from ergodic theory, the techniques of Professor Gowers, and repeated use of Szemeredi's theorem, they were able to prove the astonishing result that there are arbitrarily long arithmetic progressions of primes. The ingredients of the proof were put together when Professor Green visited Professor Tao at UCLA in 2003. The great Hungarian mathematicians Paul Erdös and Paul Turan conjectured that if A is an infinite set of integers the sum of whose reciprocals is divergent, then there are arbitrarily long arithmetic progressions in A. Since the sum of the reciprocals of the primes is a divergent series, the Green-Tao theorem is a special case of the Erdös-Turan conjecture, which remains unsolved in full generality. Erdös has offered $10,000 for a resolution of this conjecture. The Green-Tao theorem resolves an important special case of the Erdös-Turan conjecture and is a phenomenal achievement by two brilliant young mathematicians. Thus, it was a fitting tribute to Ramanujan that this great work was presented in his hometown on his birthday.

SOURCE..THE HINDU...

### Maths gets practical for Class X

Central Board of Secondary Education (CBSE) is introducing a practical component in the mathematics paper.For the first time, there are changes in the question papers of mathematics and science for class X. The mathematics question paper will comprise 80 marks for theory and 20 marks for internal assessment, while the science paper will have 60 marks for theory and 40 marks for practicals.Earlier, the science question paper had 75 marks for theory and 25 per cent for practicals, while there was no practical component in the maths paper. The CBSE had earlier introduced an internal assessment component in social sciences. In the maths paper, internal assessment, that will account for a total of 20 marks will cover evaluation of activities, project work and continuous evaluation. Similarly in science, the practical exam will have two components — hands-on school based year-end practical examination and practical skill-based multiple choice type year-end written examination — each comprising 20 marks.Maths paper for Class X Board exams will have practical.Chances for compartmental exams extended to 5 from 3

Internal assessment for maths will cover evaluation of activities and project work

Additional 15 minutes of time introduced last year for reading question papers in Board exams will continue this year.

Internal assessment for maths will cover evaluation of activities and project work

Additional 15 minutes of time introduced last year for reading question papers in Board exams will continue this year.

## Friday, January 12, 2007

### elementry math learning

Knowledge of mathematics can be useful in many respects, including decreasing stress and anxiety by encouraging children to think in a rational manner.The abstract concepts of mathematics make it a difficult discipline for children to understand. Experts have suggested that parents or teachers introduce abstract concepts using real situations and the experiences of children. "I teach my kid math by making him learn from real experiences.Properly taught, mathematics could one day be used by children to make sense of turbulent political times in an academic manner.Using math in every day life can help inspire children to make an effort to pursue studies of the discipline at a higher level in later years.

## Thursday, January 11, 2007

### problem

In triangle ABC if the angle bisector of angle A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of triangle ABC.

### Genetic Algorithm

Genetic programming (GP) is one of the most useful, general-purpose problem solving techniques available to developers. It has been used to solve a wide range of problems, such as symbolic regression, data mining, optimization, and emergent behavior in biological communities.GP is one instance of the class of techniques called evolutionary algorithms, which are based on insights from the study of natural selection and evolution. Living things are extraordinarily complex, far more so than even the most advanced systems designed by humans. Evolutionary algorithms solve problems not by explicit design and analysis, but by a process akin to natural selection.An evolutionary algorithm solves a problem by first generating a large number of random problem solvers (programs). Each problem solver is executed and rated according to a fitness metric defined by the developer. In the same way that evolution in nature results from natural selection, an evolutionary algorithm selects the best problem solvers in each generation and breeds them.Genetic programming and genetic algorithms are two different evolutionary algorithms. Genetic algorithms involve encoded strings that represent particular problem solutions. These encoded strings are run through a simulator and the best strings are mixed to form a new generation. Genetic programming, the subject of this article, follows a different approach. Instead of encoding a representation of a solution, GP breeds executable computer programs

### Genetic Algorithm

An algorithm (pronounced AL-go-rith-um) is a procedure or formula for solving a problem. The word derives from the name of the mathematician, Mohammed ibn-Musa al-Khwarizmi, who was part of the royal court in Baghdad and who lived from about 780 to 850. Al-Khwarizmi's work is the likely source for the word algebra as well.

A computer program can be viewed as an elaborate algorithm. In mathematics and computer science, an algorithm usually means a small procedure that solves a recurrent problem.

Physics, Biology, Economy or Sociology often have to deal with the classical problem of optimization. Economy particularly has become specialist of that field1. Generally speaking, a large part of mathematical development during the 18th century dealt with that topic (remember those always repeated problems where you had to obtain the derivative of a function to find its extremes).A genetic algorithm (or short GA) is a search technique used in computing to find true or approximate solutions to optimization and search problems. Genetic algorithms are categorized as global search heuristics. Genetic algorithms are a particular class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover.Genetic algorithms make it possible to explore a far greater range of potential solutions to a problem than do conventional programs. Furthermore, as researchers probe the natural selection of programs under controlled an well-understood conditions, the practical results they achieve may yield some insight into the details of how life and intelligence evolve in the natural world.A 'fitness' function evaluates each solution to decide whether it will contribute to the next generation of solutions. Then, through operations analogous to gene transfer in sexual reproduction, the algorithm creates a new population of candidate solutions."

## Wednesday, January 10, 2007

### mca entrance

MCA (Master of Computer Applications) is a 3-year postgraduate program in computers (some institutes have 2 year programs). It is also called PGDCA or PGDIT. They all refer to the same postgraduate program, MCA. It can be either a degree or diploma. MCAs generally are concerned with the SOFTWARE field. A great career for those having a mathematical or analytical mindset.Despite the recent slowdown in IT, an MCA still remains a sought after career option. MacroByte helps you to prepare and consequently crack the entrances of prestigious universities/institutes like Delhi University, Pune University, Jawaharlal Nehru University among many other. Learning is a life long experience and no matter how old you are or what you do or how many people you teach, you can always improve and upgrade yourself. Knowledge or Gyan is a one of the few things in this world that increases when you share it with others. In this section, what you will find is a series of articles related to your area of interest. In addition to this, we invite you to join in in the chat sessions, opinion polls and discussion forums, which will not only enrich you but also enrich us. All the best.

### math study

"The essential quality for a mathematician is the habit of thinking things out for oneself. That habit is usually acquired in childhood. It is hard to acquire it later." Professor W.W. Sawyer, mathematician

children are taught maths in alphanumeric language through written numbers. "Both writing and numbers are abstract skills, which are new and unfamiliar. This is the main reason why kids fail in maths. Knowledge is monopolised and distorted today, particularly with the greater commercialisation of education. Ours is a systematic attempt to break knowledge monopolies

children are taught maths in alphanumeric language through written numbers. "Both writing and numbers are abstract skills, which are new and unfamiliar. This is the main reason why kids fail in maths. Knowledge is monopolised and distorted today, particularly with the greater commercialisation of education. Ours is a systematic attempt to break knowledge monopolies

## Tuesday, January 09, 2007

### news

"What good will this do me?" asks the 10th grader picking at an algebra problem.It's a pointed, timeless question that doesn't always have a quick answer. When parents and teachers are hounded by students wanting to know the practical applications of math, answers have to go beyond balancing the checkbook and grocery shopping.Many teachers agree that the biggest problems in math education have to do with motivating two very different groups of kids. Some students need convincing that all the headaches associated with math are for a good reason. And for others, the ones with a natural hunger for those brain tugging problems, it's a matter of challenging them.

### news

Performance of students in Mathematics at primary level remains a major area of concern across the country, according to a recent survey.The survey conducted by an NGO, Pratham, in which students were tested on arithmetic, writing, reading and comprehension, showed that about 60 per cent of students at Standard I and II could recognise numbers or do more mathematics. At Standard 3 to 5, only 65 per cent of the students could do substraction.The Annual Status of Education Report (Rural) 2006, which compiled the findings of the survey conducted across the country in 549 districts, said the performance of students was improving by only four to five per cent in the subject over the previous year's dismal figures.

## Monday, January 08, 2007

### harold widom

Harold Widom, professor emeritus of mathematics, will share the 2007 Norbert Wiener Prize in Applied Mathematics with UC Davis professor of mathematics Craig Tracy. Presented every three years by the American Mathematical Society and the Society for Industrial and Applied Mathematics, the Wiener Prize is awarded for outstanding contributions to applied mathematics in the highest and broadest sense.

## Sunday, January 07, 2007

### math news

there is a good article about prime numbers.http://www.drobe.co.uk/riscos/artifact1779.html

### CAT CUT-OFFS and IIM SELECTION

The overall cut-off is expected to be at the 98th percentile at a score of 120 this year, and 95% of the calls for Group Discussion (GD) and Personal Interview (PI) will happen above this.a section-wise cut-off expectation would be 35-40 marks in Maths and DI and 30-35 marks in Logic and 20-25 in English. Last year the overall cut-off was 45-55 marks. IIM-A’s cut-off is already out and it requires students to score 95.33 percentile in each section and an overall 98 percentile to get a call.

IIM Ahmedabad (IIM-A) has shortlisted over 820 students for around 280 seats, 30 more than last year, for the institute’s flagship PGP programme. A section-wise cut-off expectation would be 35-40 marks in Maths and DI and 30-35 marks in Logic and 20-25 in English.

### news

1..The American Mathematical Society is presenting several prizes at the Joint Mathematics Meetings in New Orleans, including two prizes that are awarded jointly with two other mathematics organizations, the Mathematical Association of America and the Society for Industrial and Applied Mathematics.AMS Steele Prize for Mathematical Exposition: DAVID MUMFORD of Brown University for "his beautiful expository accounts of a host of aspects of algebraic geometry".AMS Steele Prize for a Seminal Contribution to Research: KAREN UHLENBECK, University of Texas at Austin "for her foundational contributions in analytic aspects of mathematical gauge theory".AMS Steele Prize for Lifetime Achievement: HENRY P. MCKEAN, Courant Institute of Mathematical Sciences, New York University, "for his rich and magnificent mathematical career".

2..A UGC sponsored three-day National Seminar on Graph Theory and Its Applications, was inaugurated here on Thursday 4 January at the Xavier block auditorium, St Aloysius College Mangalore.The seminar began with the rendition of the prayer song by the students. The event was inaugurated by Rev. Fr. Eugene Lobo, Principal, St. Aloysius College, an economist. The inaugural function was presided over by Vice Principal, Prof. Eric Patrao, who gave the welcome speech and gave some colorful anecdotes about mathematics and how important a role it plays in everyday life. Prof. Dr. M Abdul Rahiman former Vice Chancellor Kannur University and the Calicut University was the guest of honour. Prof. E. Sampath Kumar delivered the Keynote address and Dr. Parameshwara Bhat, the chairman, Dept of Mathematics, Mangalore University released the abstract and seminar proceedings.

3.What students need is better math instruction in elementary and junior high. If they don't receive a solid foundation in math in early years, it is very difficult to "catch up" in high school.A recent article in the National Council of Teachers of Mathematics newsletter stated the main reason why students are failing math in large numbers is that "U.S. mathematics curricula are a mile wide and an inch deep." In general, teachers in each grade level are accountable to teach a wide range of math standards. However, the large number of standards makes it virtually impossible to spend enough adequate time on each topic to ensure mastery of every skill by every student.

2..A UGC sponsored three-day National Seminar on Graph Theory and Its Applications, was inaugurated here on Thursday 4 January at the Xavier block auditorium, St Aloysius College Mangalore.The seminar began with the rendition of the prayer song by the students. The event was inaugurated by Rev. Fr. Eugene Lobo, Principal, St. Aloysius College, an economist. The inaugural function was presided over by Vice Principal, Prof. Eric Patrao, who gave the welcome speech and gave some colorful anecdotes about mathematics and how important a role it plays in everyday life. Prof. Dr. M Abdul Rahiman former Vice Chancellor Kannur University and the Calicut University was the guest of honour. Prof. E. Sampath Kumar delivered the Keynote address and Dr. Parameshwara Bhat, the chairman, Dept of Mathematics, Mangalore University released the abstract and seminar proceedings.

3.What students need is better math instruction in elementary and junior high. If they don't receive a solid foundation in math in early years, it is very difficult to "catch up" in high school.A recent article in the National Council of Teachers of Mathematics newsletter stated the main reason why students are failing math in large numbers is that "U.S. mathematics curricula are a mile wide and an inch deep." In general, teachers in each grade level are accountable to teach a wide range of math standards. However, the large number of standards makes it virtually impossible to spend enough adequate time on each topic to ensure mastery of every skill by every student.

## Saturday, January 06, 2007

### PROPOSED IITS

In the 1950s Bihar Institute of Technology, Sindri, was to get converted into an IIT but then it was set up in Kharagpur due to then West Bengal chief minister B C Roy's friendship with Jawaharlal Nehru. The second new IIT will come up in the Telengana region of Andhra Pradesh most likely in Medak. Earlier, it was decided to have it in Adilabad. And the third will be in Rajasthan, the exact site having not yet been finalised. There is also a plan to have two new Indian Institutes of Science Education and Research, one likely in Madhya Pradesh and other in South India, and two new Schools of Planning and Architecture. Though the bulk of increase in the budget outlay would be to accomplish 56% increase in seats and related infrastructure over the next three years to accommodate 27% reservation for Other Backward Castes, it would also go towards setting up of three new IITs, two new IISERs and two new SPAs.An expenditure of Rs 600 crores would be incurred for establishing IIT institute while Rs 150 crores would be spent for opening IIIT institute .

### IIT at ANDHRA PRADESH

The prestigious Indian Institute of Technology will come up in Andhra Pradesh on 600 acres of land near Patancheru in Medak district, near Hyderabad.Patancheru is infamous as the most polluted place in the state. Unregulated industrialization over the last two decades has polluted the air and groundwater in the area.Of the nearly 4000 students in IITs all over the country, students from Andhra Pradesh on an average bag 850 to 1000 seats, and IIT Medak may finally bring some cheer to the people of Patancheru.The government also plans to set up three water treatment plants in the area. Despite the controversy, the announcement of an IIT in Andhra Pradesh has also generated much euphoria among the student community. Experts say, with institutes like the ISB, a branch of the Bits Pilani, an annexe of the IIM being proposed, the IIT will put the state on the global education map.

### "Martin Kruskal

Mr. Kruskal, one of the world's pre-eminent applied mathematicians and mathematical physicists, died Dec. 26 at Princeton Medical Center after suffering a stroke in mid-December. He was 81. He had suffered an earlier stroke in August, but had fought his way back to health and was working as an active scholar when he was felled again last month. Officials at Princeton University announced his death yesterday. Mr. Kruskal spent 38 years on the Princeton faculty before moving to Rutgers University in 1989.

Mr. Kruskal is best known for his work in the 1960s in which he pioneered the understanding of the soliton, a powerful energy wave. His mathematical analysis of solitons, conducted with colleague Norman Zabusky, proved that such waves were possible and brought them within the realm of practical use, including their use as boosters of the signals conveyed along long-distance, undersea, fiber optic communication cables.In the 1950s, Kruskal made a number of seminal contributions including Kruskal-Shafranov Instability, Bernstein-Greene-Kruskal ( BGK ) Modes and the MHD Energy Principle, which laid the theoretical foundations of controlled nuclear fusion and the then undeveloped field of plasma physics. In 1960, he developed the well-known Kruskal Coordinates ( also called Kruskal-Szekeres Coordinates ), used in the theory of relativity to explain black holes.

He is most famous for his role in starting the "soliton revolution," considered one of the great mathematical advances of the last half of the 20th century. He and Norman Zabusky discovered nonlinear waves that behave in many ways like linear waves, which they termed "solitons." Solitons are now known to be ubiquitous in nature, from physics to chemistry to biology. Their unique properties make them useful for communications, such as in undersea fiber optic cables, and they have been considered as a basis for computing.

## Friday, January 05, 2007

### news

Professor Alastair Gillespie, chairman of the Scottish Mathematical Council, believes that by introducing simple gambling games into Maths lessons, children will become more engaged and will likely to improve their mathematical skills.Gillespie claims that young children have problems with mathematical problems such as probability, a concept at the heart of gambling."Things like tossing coins and cutting cards are simple techniques which teach pupils about basic maths and I think it would catch the interest of students if we were to introduce that in schools. What you are trying to do is engage with pupils and present them with scenarios which interest them because it shows how maths can be relevant and we need to do more of that," Gillespie advised.Gillespie immediately came under fire for his comments from anti-gambling societies, claiming that his ideas would only serve to encourage children to gamble.

## Thursday, January 04, 2007

### ramanujan award

An international prize for mathematics has been won by Ramdorai Sujatha, an Indian woman, according to a report on the Science and Development Network website (www.scidev.net). The $10 000 prize is named after Srinivasa Ramanujan, the Indian mathematics genius, a college dropout who ended up at the University of Cambridge in England during World War One.A movie about Ramanujan's passion for mathematics and his friendship with a cricket-loving university don who recognised his talent is being produced by Stephen Fry, the British actor-writer and Dev Benegal, the renowned Indian director.When your automated teller machines divide and arrange your money before coughing it up, they are all using Ramanujan's partition theory." The winner of the Ramanujan prize, was Ramdorai Sujatha, an associate professor from the Tata Institute of Fundamental Research in Mumbai. She was awarded the prize at a ceremony at the Abdus Salam International Centre for Theoretical Physics in Trieste, Italy.

The Centre was founded by Abdus Salam, the Pakistan-born physicist and Nobel prizewinner, who once said "scientific thought is the common heritage of mankind". The Ramanujan Prize is the only international prize honouring mathematicians from developing countries, including those in Africa, Latin America and Asia.

The Centre was founded by Abdus Salam, the Pakistan-born physicist and Nobel prizewinner, who once said "scientific thought is the common heritage of mankind". The Ramanujan Prize is the only international prize honouring mathematicians from developing countries, including those in Africa, Latin America and Asia.

### math music

Marcus du Sautoy, Professor of Mathematics at the University of Oxford, said that while the introduction of the numeracy strategy had enthused a generation of younger children about maths, too often this momentum was lost between the ages of 11 to 14.

“Pupils often get very bored with the first stage of secondary school maths. There is too much emphasis on numbers and sums. People think maths should be all about arithmetic, but that is wrong.

Professor du Sautoy, who often plays a trumpet during lectures to illustrate the similarities between harmonics and the sine waves used to predict prime numbers, suggested that maths teaching should be similar to music teaching.He also suggested that teenagers struggling with maths may benefit from learning a musical instrument. “There is evidence that if you play an instrument during the early teenage years it stimulates the mathematical side of your brain. Both music and maths are about searching for and recognising patterns,” he said.He also advocates mixed-age group teaching for maths, believing that the subject has to be taught as a pyramid from bottom to top

“Pupils often get very bored with the first stage of secondary school maths. There is too much emphasis on numbers and sums. People think maths should be all about arithmetic, but that is wrong.

Professor du Sautoy, who often plays a trumpet during lectures to illustrate the similarities between harmonics and the sine waves used to predict prime numbers, suggested that maths teaching should be similar to music teaching.He also suggested that teenagers struggling with maths may benefit from learning a musical instrument. “There is evidence that if you play an instrument during the early teenage years it stimulates the mathematical side of your brain. Both music and maths are about searching for and recognising patterns,” he said.He also advocates mixed-age group teaching for maths, believing that the subject has to be taught as a pyramid from bottom to top

### news

The 'There is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world.'

-– Nicolai Lobachevsky

'If you think the math isn't important, you don't know the right math.'

Chris.Ferguson. Theorists who first created the mathematics that describe the behavior of the recently announced "invisibility cloak" have revealed a new analysis that may extend the current cloak's powers, enabling it to hide even actively radiating objects like a flashlight or cell phone.Allan Greenleaf, professor of mathematics at the University of Rochester, working with colleagues around the globe, has announced a mathematical theory that predicts some strange goings on inside the cloak—and that what happens inside is crucial to the cloak's effectiveness.

In October, David R. Smith, associate professor of electrical and computer engineering at Duke University, led a team that used a circular cloaking device to successfully bend microwaves around a copper disk as if the disk were invisible. In 2003, however, Greenleaf and his colleagues had already developed the mathematics of invisibility.

-– Nicolai Lobachevsky

'If you think the math isn't important, you don't know the right math.'

Chris.Ferguson. Theorists who first created the mathematics that describe the behavior of the recently announced "invisibility cloak" have revealed a new analysis that may extend the current cloak's powers, enabling it to hide even actively radiating objects like a flashlight or cell phone.Allan Greenleaf, professor of mathematics at the University of Rochester, working with colleagues around the globe, has announced a mathematical theory that predicts some strange goings on inside the cloak—and that what happens inside is crucial to the cloak's effectiveness.

In October, David R. Smith, associate professor of electrical and computer engineering at Duke University, led a team that used a circular cloaking device to successfully bend microwaves around a copper disk as if the disk were invisible. In 2003, however, Greenleaf and his colleagues had already developed the mathematics of invisibility.

### CARTOGRAPHY

Globe is, of course, the only possible medium for showing all geograpical relationships in true perspective...But globes have a serious drawback:they are limited in scale. A globe which would show a continent on the same scale as most standard maps would have to be two, three, perhaps four meters in diameter."

John Noble Wilford from The Mapmakers.

Maps are the primary tools by which spatial relationships are depicted. Maps therefore become important documents. There are several key elements that should be included each time a map is created in order to aid the viewer in understanding the communications of that map. The recording of spatial data on maps is known as cartography.

John Noble Wilford from The Mapmakers.

Maps are the primary tools by which spatial relationships are depicted. Maps therefore become important documents. There are several key elements that should be included each time a map is created in order to aid the viewer in understanding the communications of that map. The recording of spatial data on maps is known as cartography.

## Wednesday, January 03, 2007

### math history

How different concerns of society influenced mathematics. How the development of the concept of number is reflected in language. How the concept of how many led to arithmetic. How the concept of how much led to geometry. Efforts to keep time led to trigonometry. Navigation and associated astronomical problems led to logarithms [and more trigonometry]. Problems in artillery led to graphs. Both required an understanding of motion. Analytic geometry and calculus were invented in part to better understand motion. Statistics developed to understand problems in the social sciences.Surveys some of Neugebauer's remarkable discoveries on Babylonian mathematics, at a time when many of these discoveries were just made. Discusses notation, tables of squares, cubes, and n3+n2. Also exponentials, approximations to compound interest problems where we would use logarithms, a sum of a finite geometric series and a finite sum of squares. Geometric results, including the Pythagorean theorem, proportionality of sides in similar right triangles, a perpendicular bisecting the base in an isosceles triangle, the angle in a semicircle being a right angle, formulas for the circumference and area of a circle (using pi = 3).

### ph.d at HRI

Candidates who wish to apply for ph.d programme in at HRI and IMSc

NEED NOTsend in any application. However, they MUST apply for the PhD Scholarships of the National Board for Higher Mathematics (NBHM) and appear for that screening test. The advertisement of the NBHM PhD Scholarships examination is expected to appear in national newspapers in the last quarter of each year. IMSc and HRI will directly get the test scores and copies of the applications from the NBHM and will independently send call letters for interview to successful candidates.

Date of NBHM screeing test: 27 January 2007 , LINK =http://www.mri.ernet.in/~mathjest/

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