Tuesday, August 6, 2013


ARCHIMEDIS [287BC-212BC]

Archimedis is considered to be one of the greatest mathematicians of all time. His father was a greek astronomer. He studied in Alexandria. Archimedis contributed to both pure and applied mathematics. He calculated the value of pie with a remarkable accuracy between 3.1408 and 3.1429.he also did a great amount of work on Analytical geometry. He wrote many books on mathematics such as Measurement of circles,On floating bodies.


Sunday, August 4, 2013

M.S.NARASIMHAN ANA C.P.RAMANUJAN

 Seshachalu Narasimhan (born 1932) is an eminent Indian mathematician. He is well known along with C S Seshadri for their proof of the Narasimhan–Seshadri theorem, and both were elected as FRS.
Education.
Narasimhan did his undergraduate studies at Loyola College, Chennai, where he was taught by Fr Racine. Fr Racine had studied with the famous French mathematicians Élie Cartan and Jacques Hadamard, and connected his students with the latest developments in modern mathematics. Among Racine's other students who achieved eminence, Mudumbaiwe may count Minakshisundaram, K. G. Ramanathan, C S Seshadri, Raghavan Narasimhan, and C. P. Ramanujam.
Narasimhan went to the Tata Institute of Fundamental Research (TIFR), Bombay, for his graduate studies. He obtained his Ph.D. from University of Mumbai in 1960; his advisor was K. Chandrasekharan. Among Narasimhan's distinguished students is M. S. Raghunathan who followed in this footsteps to bag the Shanti Swarup Bhatnagar Prize as well as become FRS. Two other students who made a mark as top-notch mathematicians are S. Ramanan and V. K. Patodi.
Degrees and posts held
              Awards and felicitations
•  Visiting Scholar, Institute for Advanced Study 
   (1968-1969)
•  Fellow of the Royal Society, London
•  Head, Mathematics Group of the Abdus Salam International Centre for Theoretical Physic
   (1992–1999)
•  Honorary Fellow, Tata Institute of Fundamental Research, Bangalore Centre.
•  Third World Academy Award for Mathematics (1987)
•  Padma Bhushan (1990)
•  King Faisal International Prize for Science, 2006 (jointly with Simon Donaldson, Imperial College)
            
CP RAMANUJAM

Chakravarthi Padmanabhan Ramanujam (January 9, 1938 – October 27, 1974) worked in the fields of number theory and algebraic geometry. He was elected a Fellow of the Indian Academy of Sciences in 1973.
Like his namesake Srinivasa Ramanujan, Ramanujam also had a very short life.
As David Mumford put it, Ramanujam felt that the spirit of mathematics demanded of him not merely routine developments but the right theorem on any given topic. "He wanted mathematics to be beautiful and to be clear and simple. He was sometimes tormented by the difficulty of these high standards, but in retrospect, it is clear to us how often he succeeded in adding to our knowledge, results both new, beautiful and with a genuinely original stamp".
Career
Ramanujam set out for Mumbai at the age of eighteen to pursue his interest in mathematics. He and his friend and schoolmate Raghavan Narasimhan, and S. Ramanan joined TIFR together in 1957. At the Tata Institute there was a stream of first rate visiting mathematicians from all over the world. It was a tradition for some graduate student to write up the notes of each course of lectures. Accordingly, Ramanujam wrote up in his first year, the notes of Max Deuring's lectures on Algebraic functions of one variable. It was a nontrivial effort and the notes were written clearly and were well received. The analytical mind was much in evidence in this effort as he could simplify and extend the notes within a short time period. "He could reduce difficult solutions to be simple and elegant due to his deep knowledge of the subject matter" states Ramanan. "Max Deuring's lectures gave him a taste for Algebraic Number Theory. He studied not only algebraic geometry and analytic number theory of which he displayed a deep knowledge but he became an expert in several other allied subjects as well".
On the suggestion of his doctoral advisor, K. G. Ramanathan, he began working on a problem relating to the work of the German number theorist Carl Ludwig Siegel. In the course of proving the main result to the effect that every cubic form in 54 variables over any algebraic number field K had a non-trivial zero over that field, he had also simplified the earlier method of Siegel. He took up Waring's problem in algebraic number fields and got interesting results. In recognition of his work and his contribution to Number Theory, the Institute promoted him as Associate Professor. He protested against this promotion as 'undeserved', and had to be persuaded to accept the position. He proceeded to write his thesis in 1966 and took his Doctoral examination in 1967. Dr. Siegel who was one of the examiners was highly impressed with the young man's depth of knowledge and his great mathematical abilities.
Ramanujam was a scribe for Igor Shafarevich's course of lectures in 1965 on minimal models and birational transformation of two dimensional schemes. Professor Shafarevich subsequently wrote to say that Ramanujam not only corrected his mistakes but complemented the proofs of many results. The same was the case with Mumford's lectures on abelian varieties which was delivered at TIFR around 1967. Mumford wrote in the preface to his book that the notes improved upon his work and that his current work on abelian varieties was a joint effort between him and Ramanujam. A little known fact is that during this time he started teaching himself German, Italian, Russian and French so that he could study mathematical works in their original form. His personal library contained quite a few non-English mathematical works.

                                               DONE BY
                                                         SUCHITRA

Friday, August 2, 2013

BHRMAGUPTHA.........


                   BRAHMAGUPTHA


BRAHMAGUPTA -Indian Mathematicians And Their Contributions * Brahma Gupta was born in 598A.D in Pakistan. * He gave four methods of multiplication. * He gave the following formula, used in G.P series a + ar + ar2 + ar3 +……….. + arn-1 = (arn-1) ÷ (r – 1) * He gave the following formulae : Area of a cyclic quadrilateral with side a, b, c, d= √(s -a)(s- b)(s -c)(s- d) where 2s = a + b + c + d Length of its diagonals = bio1 2 Indian Mathematicians And Their Contributions

ARCHIMEDES............


 ARCHIMEDES...........

 Archimedes of Syracuse (Greek: ρχιμήδης; c.287 BC – c.212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined thArchimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere inscribed within a cylinder. Archimedes had proven that the sphere has two thirds of the volume and surface area of the cylinder (including the bases of the latter), and regarded this as the greatest of his mathematical achievements.

 Archimedes' principle

 The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a votive crown for a temple had been made for King Hiero II, who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (Greek: ρηκα!" meaning "I have found it!"). The test was conducted successfully, proving that silver had indeed been mixed in.

The story of the golden crown does not appear in the known works of Archimedes. Moreover, the practicality of the method it describes has been called into question, due to the extreme accuracy with which one would have to measure the water displacement. Archimedes may have instead sought a solution that applied the principle known in hydrostatics as Archimedes' principle, which he describes in his treatise On Floating Bodies. This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Using this principle, it would have been possible to compare the density of the golden crown to that of solid gold by balancing the crown on a scale with a gold reference sample, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. Galileo considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself." In a 12th-century text titled Mappae clavicula there are instructions on how to perform the weighing in the water in order to calculate the percentage of silver used, and thus solve the problem. The Latin poem Carmen de ponderibus et mensuris of the 4th or 5th century describes the use of a hydrostatic balance to solve the problem of the crown, and attributes the method to Archimedes.e spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.


BY-ASISH E.S

                                     

Tuesday, July 30, 2013

BHASKARACHARYA............


BHASKARACHARYA......

Bhāskarāchārya ("Bhāskara the teacher") and as Bhāskara II to avoid confusion with Bhāskara(also known as Bhāskarāchārya ("Bhāskara the teacher") and as Bhāskara II to avoid confusion with  I) (1114–1185), was an Indian mathematician and astronomer. He was born near Vijjadavida (Bijapur in modern Karnataka). Bhāskara is said to have been the head of an astronomical observatory aUjjain, the leading mathematical center of ancient India. He lived in the Sahyadri region (Patnadevi, Jalgaon, Maharashtra).And was the first Indian mathematician to use zero in its current form and also gave zero its current symbol as his sign, Bhaskara in hindi means sun and is round.

 He is particularly known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that  was a pioneer in some of the principles of differential calculus.He was perhaps the first to                                                             conceive the differential coefficient and differential calculus................                                                             

                                                       akshay krishnan

SHAKUNTALA DEVI............


   

SHAKUNTALA DEVI


  • She was born in 1939
  • In 1980, she gave the product of two, thirteen digit numbers within 28 seconds, many countries have invited her to demonstrate her extraordinary talent.
  • In Dallas she competed with a computer to see who give the cube root of 188138517 faster, she won. At university of USA she was asked to give the 23rd root of 91674867692003915809866092758538016248310668014430862240712651642793465704086709659 32792057674808067900227830163549248523803357453169351119035965775473400756818688305 620821016129132845564895780158806771.
She answered in 50seconds. The answer is 546372891. It took a UNIVAC 1108 computer, full one minute (10 seconds more) to confirm that she was right after it was fed with 13000 instructions.
  • Now she is known to be Human Computer.


                                                                                                BY :   AMALMURALI

Monday, July 29, 2013

MATHEMATICIANS

"TOP 10 GREATEST                                                                  MATHEMATICIANS"

Often called the language of the universe, mathematics is fundamental to our understanding of the world and, as such, is vitally important in a modern society such as ours. Everywhere you look it is likely mathematics has made an impact, from the faucet in your kitchen to the satellite that beams your television programs to your home. As such, great mathematicians are undoubtedly going to rise above the rest and have their name embedded within history. This list documents some such people. I have rated them based on contributions and how they effected mathematics at the time, as well as their lasting effect. I also suggest one looks deeper into the lives of these men, as they are truly fascinating people and their discoveries are astonishing – too much to include here. As always, such lists are highly subjective, and as such please include your own additions in the comments!
10
Pythagoras of Samos
Pythagoras
Greek Mathematician Pythagoras is considered by some to be one of the first great mathematicians. Living around 570 to 495 BC, in modern day Greece, he is known to have founded the Pythagorean cult, who were noted by Aristotle to be one of the first groups to actively study and advance mathematics. He is also commonly credited with the Pythagorean Theorem within trigonometry. However, some sources doubt that is was him who constructed the proof (Some attribute it to his students, or Baudhayana, who lived some 300 years earlier in India). Nonetheless, the effect of such, as with large portions of fundamental mathematics, is commonly felt today, with the theorem playing a large part in modern measurements and technological equipment, as well as being the base of a large portion of other areas and theorems in mathematics. But, unlike most ancient theories, it played a bearing on the development of geometry, as well as opening the door to the study of mathematics as a worthwhile endeavor. Thus, he could be called the founding father of modern mathematics.
9
Andrew Wiles
Picture-Right
The only currently living mathematician on this list, Andrew Wiles is most well known for his proof of Fermat’s Last Theorem: That no positive integers, a, b and c can satisfy the equation a^n+b^n=c^n For n greater then 2. (If n=2 it is the Pythagoras Formula). Although the contributions to math are not, perhaps, as grand as other on this list, he did ‘invent’ large portions of new mathematics for his proof of the theorem. Besides, his dedication is often admired by most, as he quite literally shut himself away for 7 years to formulate a solution. When it was found that the solution contained an error, he returned to solitude for a further year before the solution was accepted. To put in perspective how ground breaking and new the math was, it had been said that you could count the number of mathematicians in the world on one hand who, at the time, could understand and validate his proof. Nonetheless, the effects of such are likely to only increase as time passes (and more and more people can understand it).
8
Isaac Newton and Wilhelm Leibniz
Newtonleibniz
I have placed these two together as they are both often given the honor of being the ‘inventor’ of modern infinitesimal calculus, and as such have both made monolithic contributions to the field. To start, Leibniz is often given the credit for introducing modern standard notation, notably the integral sign. He made large contributions to the field of Topology. Whereas all round genius Isaac Newton has, because of the grand scientific epic Principia, generally become the primary man hailed by most to be the actual inventor of calculus. Nonetheless, what can be said is that both men made considerable vast contributions in their own manner.
7
Leonardo Pisano Blgollo
Fibonacci
Blgollo, also known as Leonardo Fibonacci, is perhaps one of the middle ages greatest mathematicians. Living from 1170 to 1250, he is best known for introducing the infamous Fibonacci Series to the western world. Although known to Indian mathematicians since approximately 200 BC, it was, nonetheless, a truly insightful sequence, appearing in biological systems frequently. In addition, from this Fibonacci also contributed greatly to the introduction of the Arabic numbering system. Something he is often forgotten for.
Haven spent a large portion of his childhood within North Africa he learned the Arabic numbering system, and upon realizing it was far simpler and more efficient then the bulky Roman numerals, decided to travel the Arab world learning from the leading mathematicians of the day. Upon returning to Italy in 1202, he published his Liber Abaci, whereupon the Arabic numbers were introduced and applied to many world situations to further advocate their use. As a result of his work the system was gradually adopted and today he is considered a major player in the development of modern mathematics.
6
Alan Turing
Alan Turing Photo
Computer Scientist and Cryptanalyst Alan Turing is regarded my many, if not most, to be one of the greatest minds of the 20th Century. Having worked in the Government Code and Cypher School in Britain during the second world war, he made significant discoveries and created ground breaking methods of code breaking that would eventually aid in cracking the German Enigma Encryptions. Undoubtedly affecting the outcome of the war, or at least the time-scale.
After the end of the war he invested his time in computing. Having come up with idea of a computing style machine before the war, he is considered one of the first true computer scientists. Furthermore, he wrote a range of brilliant papers on the subject of computing that are still relevant today, notably on Artificial Intelligence, on which he developed the Turing test which is still used to evaluate a computers ‘intelligence’. Remarkably, he began in 1948 working with D. G. Champernowne, an undergraduate acquaintance on a computer chess program for a machine not yet in existence. He would play the ‘part’ of the machine in testing such programs.
5René Descartes
Descarte
French Philosopher, Physicist and Mathematician Rene Descartes is best known for his ‘Cogito Ergo Sum’ philosophy. Despite this, the Frenchman, who lived 1596 to 1650, made ground breaking contributions to mathematics. Alongside Newton and Leibniz, Descartes helped provide the foundations of modern calculus (which Newton and Leibniz later built upon), which in itself had great bearing on the modern day field. Alongside this, and perhaps more familiar to the reader, is his development of Cartesian Geometry, known to most as the standard graph (Square grid lines, x and y axis, etc.) and its use of algebra to describe the various locations on such. Before this most geometers used plain paper (or another material or surface) to preform their art. Previously, such distances had to be measured literally, or scaled. With the introduction of Cartesian Geometry this changed dramatically, points could now be expressed as points on a graph, and as such, graphs could be drawn to any scale, also these points did not necessarily have to be numbers. The final contribution to the field was his introduction of superscripts within algebra to express powers. And thus, like many others in this list, contributed to the development of modern mathematical notation.
4
Euclid
Euklid-Von-Alexandria 1
Living around 300BC, he is considered the Father of Geometry and his magnum opus: Elements, is one the greatest mathematical works in history, with its being in use in education up until the 20th century. Unfortunately, very little is known about his life, and what exists was written long after his presumed death. Nonetheless, Euclid is credited with the instruction of the rigorous, logical proof for theorems and conjectures. Such a framework is still used to this day, and thus, arguably, he has had the greatest influence of all mathematicians on this list. Alongside his Elements were five other surviving works, thought to have been written by him, all generally on the topic of Geometry or Number theory. There are also another five works that have, sadly, been lost throughout history.
3
G. F. Bernhard Riemann
Riemann
Bernhard Riemann, born to a poor family in 1826, would rise to become one of the worlds prominent mathematicians in the 19th Century. The list of contributions to geometry are large, and he has a wide range of theorems bearing his name. To name just a few: Riemannian Geometry, Riemannian Surfaces and the Riemann Integral. However, he is perhaps most famous (or infamous) for his legendarily difficult Riemann Hypothesis; an extremely complex problem on the matter of the distributions of prime numbers. Largely ignored for the first 50 years following its appearance, due to few other mathematicians actually understanding his work at the time, it has quickly risen to become one of the greatest open questions in modern science, baffling and confounding even the greatest mathematicians. Although progress has been made, its has been incredibly slow. However, a prize of $1 million has been offered from the Clay Maths Institute for a proof, and one would almost undoubtedly receive a Fields medal if under 40 (The Nobel prize of mathematics). The fallout from such a proof is hypothesized to be large: Major encryption systems are thought to be breakable with such a proof, and all that rely on them would collapse. As well as this, a proof of the hypothesis is expected to use ‘new mathematics’. It would seem that, even in death, Riemann’s work may still pave the way for new contributions to the field, just as he did in life.
2
Carl Friedrich Gauss
508Px-Bendixen - Carl Friedrich Gauß, 1828
Child prodigy Gauss, the ‘Prince of Mathematics’, made his first major discovery whilst still a teenager, and wrote the incredible Disquisitiones Arithmeticae, his magnum opus, by the time he was 21. Many know Gauss for his outstanding mental ability – quoted to have added the numbers 1 to 100 within seconds whilst attending primary school (with the aid of a clever trick). The local Duke, recognizing his talent, sent him to Collegium Carolinum before he left for Gottingen (at the time it was the most prestigious mathematical university in the world, with many of the best attending). After graduating in 1798 (at the age of 22), he began to make several important contributions in major areas of mathematics, most notably number theory (especially on Prime numbers). He went on to prove the fundamental theorem of algebra, and introduced the Gaussian gravitational constant in physics, as well as much more – all this before he was 24! Needless to say, he continued his work up until his death at the age of 77, and had made major advances in the field which have echoed down through time.
1
Leonhard Euler
480Px-Leonhard Euler 2
If Gauss is the Prince, Euler is the King. Living from 1707 to 1783, he is regarded as the greatest mathematician to have ever walked this planet. It is said that all mathematical formulas are named after the next person after Euler to discover them. In his day he was ground breaking and on par with Einstein in genius. His primary (if that’s possible) contribution to the field is with the introduction of mathematical notation including the concept of a function (and how it is written as f(x)), shorthand trigonometric functions, the ‘e’ for the base of the natural logarithm (The Euler Constant), the Greek letter Sigma for summation and the letter ‘/i’ for imaginary units, as well as the symbol pi for the ratio of a circles circumference to its diameter. All of which play a huge bearing on modern mathematics, from the every day to the incredibly complex.
As well as this, he also solved the Seven Bridges of Koenigsberg problem in graph theory, found the Euler Characteristic for connecting the number of vertices, edges and faces of an object, and (dis)proved many well known theories, too many to list. Furthermore, he continued to develop calculus, topology, number theory, analysis and graph theory as well as much, much more – and ultimately he paved the way for modern mathematics and all its revelations. It is probably no coincidence that industry and technological developments rapidly increased around this time.

                                                                    BY                                                                    MEGHANA DAS