He studied the structure,distribution and special forms of highly composite numbers. Hardy hardy recognised some of his formulae but other seemed scarcely possible to believe. In this lesson, learn about his very interesting and unusual life and all the. Ramanujans notebooks the institute of mathematical sciences.
Numbers oxford, clarendon press, 1938 as a school prize, i won another prize. I remember once going to see him when he was ill at putney. Number theory and combinatorics indian academy of sciences. The remarkable discoveries made by srinivasa ramanujan have made a great impact on several branches of mathematics, revealing deep and fundamental connections. Number theory in the spirit of ramanujan ams bookstore. Here was a man who could work out modular equations and theoremsto orders unheard o. By contrast, euclid presented number theory without the flourishes. This journal publishes papers of the highest quality in all areas of mathematics influenced by ramanujan, including. Riemann hypothesis, ramanujans theorem, robins theorem, sumofdivisors function, highly composite number, superabundant, colossally abundant, euler. Ramanujan, robin, highly composite numbers, and the riemann. It is a taxicab number, and is variously known as ramanujans number and the hardyramanujan number, after an anecdote of the british mathematician g. The third book in the series, number theory and combinatorics, is by.
Here, his 37 published papers, most of his first two and last letters to hardy, the famous 58 problems submitted to the journal of the indian mathematical society, and the commentary of the original. Hardyramanujan number srinivasa ramanujan, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Pdf contributions of srinivasa ramanujan to number theory. Most of ramanujans work in number theory arose out of qseries and theta functions. This book provides an introduction to these two important. Definitions of hypergeometric series and elliptic integrals.
Ramanujan theta function ramanujans sum rogersramanujan identities. Watson stored at the wren library at trinity college, cambridge. Chebyshev uses a stronger approach proving a lot more than bertrands postulate, in particular your statement follows directly from his bound while his methods are essentially the same as ramanujans. Krishnaswami alladi editor shelved 1 time as ramanujan. Hardyramanujan number once hardy visited to putney where ramanujan was hospitalized. See more ideas about mathematics, math genius and number theory. Magic squares, theory of partitions, ramanujans contribution to the. Ramanujans notebooks the history of the notebooks, in brief, is the following. Srinivasa ramanujan iyengar december 22, 1887 april 26, 1920 was an indian mathematician. He began book vii of his elements by defining a number as a multitude composed of units. A note on mathematics genius srinivasa ramanujan, frs article pdf available in international journal of information technology and decision making january 2014 with 42,753 reads. In his famous letters of 16 january 19 and 29 february 19 to g. The importance of his research continues to be studied and inspires.
One feels that ramanujan is ready to leave the subject of highly composite numbers, and to come back to another favourite topic, identities. Three puzzles inspired by ramanujan quanta magazine. Srinivasa ramanujan 18871920 was a mathematical genius who changed the world of mathematics in his short life. Hardy came to see ramanujan in taxi number 1729,ramanujan said that 1729 is the smallest number which can be written in the form of sum of cubes of two numbers in two ways,i. Carr, in three notebooks, between the years 1903 1914, before he left for england. Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by george andrews in 1976, in a box of effects of g. Srinivasa ramanujan frs 22 december 1887 26 april 1920 was an indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Still he made many contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable. A life of the genius ramanujan, little, brown book group 10 december 1992, isbn. Moreover, some of his work was so ahead of his time. Ramanujan conjecture ramanujan prime ramanujan soldner constant.
At the age of 16, ramanujan received a scholarship to. He later defined a prime as a number measured by a unit alone i. Hardy was an academician at cambridge university he was a prominent english mathematician, known for his achievements in number theory and mathematical analysis. Scribd is the worlds largest social reading and publishing site. Hypergeometric and basic hypergeometric series qseries. Srinivasa ramanujan s contributions in mathematics dharminder singh1, arun kumar chopra2. The influence of ramanujan on number theory is without parallel in mathematics. Ramanujan provided solutions to mathematical problems that were then considered unsolvable. Pdf a note on mathematics genius srinivasa ramanujan, frs.
The proposed course will mainly cover the following topics. Seshu aiyar, ramanujans mathematics teacher at the government college at kumbakonam, claims that he had suggested to ramanujan that he read hardys tract 8, p. Ramakrishnan, existence of ramanujan primes for gl3, in contributions to. His papers, problems and letters have spawned a remarkable number of later results by many different mathematicians. Ramanujans theory of qseries and theta functions with applications to various problems of number theory and related areas. The history of the notebooks, in brief, is the following. He was born in the year 1887 during the british rule in india. He quoted hardys mention of the suppressed part of hcn in a 1930. A note on mathematics genius srinivasa ramanujan, frs.
Some of those formulas were analyzed by hardy 3, 5, pp. His boss, the chief accountant, happened to be interested in academic mathematics, and became a lifelong supporter. Littlewood, two worldclass mathematicians at cambridge, and enjoyed an extremely fruitful period of collaboration with them. During his school days, he impressed his classmates, senior students and teachers with his extraordinary intuition and astounding pro. Highly composite numbers by srinivasa ramanujan universite. Hardy says elementary analysis of highly composite numbers is most remarkable and shows very clearly ramanujans extraordinary mastery over. Srinivasa ramanujan born december 22, 1887 in erode, india was an indian mathematician who made substantial contributions to mathematicsincluding results in number theory, analysis, and infinite seriesdespite having little formal training in math. Hardy is known for his achievements in number theory and mathematical analysis.
No doubt that this book has had a profound influence on him and his familiarity with it. Then, without assuming the prime number theorem, we can show that the. Hardy, who intorduced ramanujan to the western world of mathematics. On 1st october 1892 ramanujan was enrolled at local school. Ramanujan was sent to kangeyam primary school in kumbakonam at the age of seven. The fourth chapter on riemann zeta function, which is of importance in the theory of numbers, asymptotic theory, and series transformations etc.
Ramanujan s theory of qseries and theta functions with applications to various problems of number theory and related areas. His fathers name was kuppuswami and mothers name was komalatammal. His papers, problems, and letters have spawned a remarkable number of later results by many different mathematicians. Julius axelrod, nobel laureate this is the best biography of a mathematician, in fact of any scientist, that i have ever read.
Srinivasa ramanujan made substantial contributions to the analytical theory of numbers and worked. The purpose of this paper is to introduce some of the contributions of srinivasa ramanujan to number theory. Srinivasa ramanujan was one of indias greatest mathematical geniuses. Hardy in developing the formula for the number, pn, of partitions of a number n. His geniusness was that he discovered his own theorems. This book contained many theorems but was short on proofs, and was in fact.
Life and work of the mathemagician srinivasa ramanujan. Ramanujan devoted all of his efforts to mathematics and continued to record his. Srinivasa ramanujan made great contributions to the field of mathematics, including a collaboration with wellknown mathematician h. Hardy arranged for ramanujan to come to england, and the rest is history.
This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the ramanujan tau function. Srinivasa ramanujan simple english wikipedia, the free. Srinivasa ramanujan 18871920and the theory of core. Ramanujans proof is actually a simplification of chebyshevs original 1852 proof of bertrands postulate the article is memoire sur les nombres premiers. Ramanujan had noted down the results of his researches, without proofs, as in a synopsis of elementary results, a book on pure mathematics, by g. Due to his great achievements in the field of mathematics, indian govt. Highly composite numbers 121 75, the number of representations of n by some other quadratic forms is considered, but no longer its maximal order. Resonance for the last two decades, as well the ramanujan math soci. Srinivasa ramanujan 18871920 was an indian mathematician who made great and original contributions to many mathematical fields, including complex analysis, number theory, infinite series, and continued fractions. Ramanujan was born in his grandmothers house in erode, a small village about 400 km southwest of madras now chennai. Srinivasa ramanujan was a mathematical genius who made numerous contributions in the field, namely in number theory. What are the mathematical contributions of ramanujan. Most of ramanujans work in number theory arose out of \q\series and theta functions.
Contributions of srinivasa ramanujan to number theory. Srinivasa ramanujan frs 1887 1920 was a selftaught indian mathematical genius who made numerous contributions in several mathematical fields including mathematical analysis, infinite series, continued fractions, number theory and game theory. Pdf ramanujan s theta functions download ebook for free. Hardy when he visited indian mathematician srinivasa ramanujan in hospital. When ramanujans mathematical friends didnt succeed in getting him a scholarship, ramanujan started looking for jobs, and wound up in march 1912 as an accounting clerkor effectively, a human calculatorfor the port of madras which was then, as now, a big shipping hub. Robert kanigel goodreads author shelved 4 times as ramanujan. His discoveries also led to the infinite series for infinity formulation. When he was nearly five years old, ramanujan entered the primary school in kumbakonam. H hardy summed up his contibution in following words, the limitations of his knowledge were as startling as its profundity. Srinivasa ramanujan, born december 22, 1887, erode, indiadied april 26, 1920, kumbakonam, indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function. This is a great book for those of you who want to learn the works of the great indian mathematician srinivasa ramanujan. At age 15 srinivasa ramanujan obtained a mathematics book containing. He has also made some extraordinary contributions to the fields like hypergeometric series, elliptic functions, prime numbers, bernoullis numbers, divergent series, continued fractions, elliptic modular equations, highly composite numbers, riemann zeta functions, partition of.
Life and a brief overview of his contributions in various fields, his earlier notebooks, the lost notebook and. Mathematician ramanujan biographical book pdf download free. Popular ramanujan books showing 18 of 8 the man who knew infinity. The work that ramanujan did in his brief professional life a century ago has spawned whole new areas of mathematical investigation, kept top mathematicians busy for their whole professional lives, and is finding applications in computer science, string theory, and the mathematical basis of black hole physics.
Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to. Original scribners hardcover edition, 1991 a fascinating account of ramanujans life which reads like a sad romantic novel. As the reader might have taken from the name, ant expands and. Ramanujans lost notebook is the manuscript in which the indian mathematician srinivasa ramanujan recorded the mathematical discoveries of the last year 19191920 of his life. He is considered to be one of the most talented mathematicians in recent history. Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. But he is perhaps even better known for his adoption and mentoring of the selftaught indian mathematical genius, srinivasa ramanujan hardy himself was a prodigy from a young age, and stories are told about how he would write numbers up to millions at just two years of age. Biography of srinivasa ramanujan, mathematical genius. A highly composite number has more divisions than any preceding number like.
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