Ramanujans theory of qseries and theta functions with applications to various problems of number theory and related areas. 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. Ramanujan conjecture ramanujan prime ramanujan soldner constant. Julius axelrod, nobel laureate this is the best biography of a mathematician, in fact of any scientist, that i have ever read.
A life of the genius ramanujan, little, brown book group 10 december 1992, isbn. He was born in the year 1887 during the british rule in india. One feels that ramanujan is ready to leave the subject of highly composite numbers, and to come back to another favourite topic, identities. On 1st october 1892 ramanujan was enrolled at local school. Hardy was an academician at cambridge university he was a prominent english mathematician, known for his achievements in number theory and mathematical analysis. This journal publishes papers of the highest quality in all areas of mathematics influenced by ramanujan, including. Ramanujan, robin, highly composite numbers, and the riemann. Srinivasa ramanujan 18871920and the theory of core. Life and work of the mathemagician srinivasa ramanujan. Srinivasa ramanujan iyengar december 22, 1887 april 26, 1920 was an indian mathematician. Some of those formulas were analyzed by hardy 3, 5, pp. He is considered to be one of the most talented mathematicians in recent history. 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.
Pdf a note on mathematics genius srinivasa ramanujan, frs. 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. Life and a brief overview of his contributions in various fields, his earlier notebooks, the lost notebook and. Hardy in developing the formula for the number, pn, of partitions of a number n.
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. By contrast, euclid presented number theory without the flourishes. 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. Hardy arranged for ramanujan to come to england, and the rest is history. Number theory and combinatorics indian academy of sciences. Original scribners hardcover edition, 1991 a fascinating account of ramanujans life which reads like a sad romantic novel.
Highly composite numbers by srinivasa ramanujan universite. His discoveries also led to the infinite series for infinity formulation. At the age of 16, ramanujan received a scholarship to. During his school days, he impressed his classmates, senior students and teachers with his extraordinary intuition and astounding pro. Pdf contributions of srinivasa ramanujan to number theory. Mathematician ramanujan biographical book pdf download free. In this lesson, learn about his very interesting and unusual life and all the. Srinivasa ramanujan was one of indias greatest mathematical geniuses. 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. Hypergeometric and basic hypergeometric series qseries. No doubt that this book has had a profound influence on him and his familiarity with it. In his famous letters of 16 january 19 and 29 february 19 to g. Robert kanigel goodreads author shelved 4 times as ramanujan.
What are the mathematical contributions of ramanujan. This book contained many theorems but was short on proofs, and was in fact. Srinivasa ramanujan simple english wikipedia, the free. See more ideas about mathematics, math genius and number theory. 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. He later defined a prime as a number measured by a unit alone i. He studied the structure,distribution and special forms of highly composite numbers. Due to his great achievements in the field of mathematics, indian govt. Scribd is the worlds largest social reading and publishing site. The importance of his research continues to be studied and inspires. Biography of srinivasa ramanujan, mathematical genius. The fourth chapter on riemann zeta function, which is of importance in the theory of numbers, asymptotic theory, and series transformations etc. 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. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.
Numbers oxford, clarendon press, 1938 as a school prize, i won another prize. Most of ramanujans work in number theory arose out of qseries and theta functions. Ramanujan devoted all of his efforts to mathematics and continued to record his. Here was a man who could work out modular equations and theoremsto orders unheard o. A highly composite number has more divisions than any preceding number like. 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. H hardy summed up his contibution in following words, the limitations of his knowledge were as startling as its profundity. Krishnaswami alladi editor shelved 1 time as ramanujan. 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. Hardy when he visited indian mathematician srinivasa ramanujan in hospital. 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. The remarkable discoveries made by srinivasa ramanujan have made a great impact on several branches of mathematics, revealing deep and fundamental connections. Riemann hypothesis, ramanujans theorem, robins theorem, sumofdivisors function, highly composite number, superabundant, colossally abundant, euler.
The third book in the series, number theory and combinatorics, is by. Ramanujans notebooks the institute of mathematical sciences. The purpose of this paper is to introduce some of the contributions of srinivasa ramanujan to number theory. Srinivasa ramanujan made substantial contributions to the analytical theory of numbers and worked. Number theory in the spirit of ramanujan ams bookstore. Then, without assuming the prime number theorem, we can show that the.
His geniusness was that he discovered his own theorems. This is a great book for those of you who want to learn the works of the great indian mathematician srinivasa ramanujan. Still he made many contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable. The proposed course will mainly cover the following topics.
Ramanujan was sent to kangeyam primary school in kumbakonam at the age of seven. Hardy says elementary analysis of highly composite numbers is most remarkable and shows very clearly ramanujans extraordinary mastery over. His fathers name was kuppuswami and mothers name was komalatammal. Ramanujan theta function ramanujans sum rogersramanujan identities. Popular ramanujan books showing 18 of 8 the man who knew infinity. Hardy hardy recognised some of his formulae but other seemed scarcely possible to believe. This book provides an introduction to these two important. His papers, problems and letters have spawned a remarkable number of later results by many different mathematicians. Ramanujans proof is actually a simplification of chebyshevs original 1852 proof of bertrands postulate the article is memoire sur les nombres premiers.
Carr, in three notebooks, between the years 1903 1914, before he left for england. Contributions of srinivasa ramanujan to number theory. Ramanujans notebooks the history of the notebooks, in brief, is the following. 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. His papers, problems, and letters have spawned a remarkable number of later results by many different mathematicians. I remember once going to see him when he was ill at putney. Ramanujan was born in his grandmothers house in erode, a small village about 400 km southwest of madras now chennai. At age 15 srinivasa ramanujan obtained a mathematics book containing. Ramanujan is recognized as one of the great number theorists of the twentieth century. 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. Littlewood, two worldclass mathematicians at cambridge, and enjoyed an extremely fruitful period of collaboration with them. Srinivasa ramanujan s contributions in mathematics dharminder singh1, arun kumar chopra2.
Ramakrishnan, existence of ramanujan primes for gl3, in contributions to. Srinivasa ramanujan was a mathematical genius who made numerous contributions in the field, namely in number theory. His boss, the chief accountant, happened to be interested in academic mathematics, and became a lifelong supporter. A note on mathematics genius srinivasa ramanujan, frs. Srinivasa ramanujan 18871920 was a mathematical genius who changed the world of mathematics in his short life. 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. He began book vii of his elements by defining a number as a multitude composed of units. The history of the notebooks, in brief, is the following. 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. 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. 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.
Srinivasa ramanujan made great contributions to the field of mathematics, including a collaboration with wellknown mathematician h. Definitions of hypergeometric series and elliptic integrals. Ramanujan provided solutions to mathematical problems that were then considered unsolvable. Hardy, who intorduced ramanujan to the western world of mathematics. Here now is the first book to provide an introduction to his work in number theory. Watson stored at the wren library at trinity college, cambridge. Pdf ramanujan s theta functions download ebook for free. 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. Ramanujan s theory of qseries and theta functions with applications to various problems of number theory and related areas. Most of ramanujans work in number theory arose out of \q\series and theta functions. Highly composite numbers 121 75, the number of representations of n by some other quadratic forms is considered, but no longer its maximal order. Hardyramanujan number once hardy visited to putney where ramanujan was hospitalized. The influence of ramanujan on number theory is without parallel in mathematics.
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