Ramanujan

Srinivasa Ramanujan (1887 - 1920). This is what "Ramanujan is a role model for the possible," says When Ramanujan arrived in England he worked with Hardy on a range of mathematical topics. He arrived with little formal training, and had devised his very own way of writing mathematics that other mathematicians had never seen before. The certificate of Ramanujan's nomination to become a Fellow of the Royal Society. Click "Ramanujan didn't use the notation that everyone else in the world used," says Ono. "When he arrived here in England he knew nothing of modern mathematics. He made mistakes all the time." Ramanujan quickly learned a great deal of formal mathematics at Cambridge and went from an amateur to writing world class mathematics papers. "Very quickly, within the span of a year or two, he was formally trained. He was very smart so he could catch up quickly. The papers he wrote here [in England], by every professional standard, were world class papers. So that is also a testament to how gifted he was." One of these papers, written with Hardy, astonished the mathematical community as it gave a way to reliably calculate numbers that had eluded mathematicians for centuries – partition numbers. This paper was one of those quoted in his nomination to be elected as a Fellow of the Partition numbers The concept of partition numbers is quite straightforward. You can write any natural number as a sum of natural numbers. For example can be written as a sum in three different way...

Lived 1887 – 1920. Srinivasa Ramanujan was a largely self-taught pure mathematician. Hindered by poverty and ill-health, his highly original work has considerably enriched number theory. More recently his discoveries have been applied to physics, where his theta function lies at the heart of string theory. Advertisements Beginnings Srinivasa Ramanujan was born on December 22, 1887 in the town of Erode, in Tamil Nadu, in the south east of India. His father was K. Srinivasa Iyengar, an accounting clerk for a clothing merchant. His mother was Komalatammal, who earned a small amount of money each month as a singer at the local temple. His family were Brahmins, the Hindu caste of priests and scholars. His mother ensured the boy was in tune with Brahmin traditions and culture. Although his family were high caste, they were very poor. Ramanujan’s parents moved around a lot, and he attended a variety of different elementary schools. Early Mathematics At age 10, Ramanujan was the top student in his district and he started high school at the Kumbakonam Town High School. Looking at the mathematics books in his school’s library, he quickly found his vocation. By age 12, he had begun serious self-study of mathematics, working through cubic equations and arithmetic and geometric series. He invented his own method of solving quartic equations. As Ramanujan’s mathematical knowledge developed, his main source of inspiration and expertise became Synopsis of elementary results in pure mathem...

Srinivasa by Konrad Jacobs from Srinivasa Ramanujan (born December 22, 1887, in Erode, India—died April 26, 1920, in Kumbakonam), was an Indian mathematician whose contributions to number theory include the pioneering discovery of partition function features. He got a copy of George Shoobridge Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics, 2 vol. (1880–86) when he was 15 years old. This collection of thousands of theorems, many with very brief proofs and no material younger than 1860, piqued his interest. Ramanujan expanded on the conclusions in Carr’s work, establishing his own theorems and concepts. He received a scholarship at the University of Madras in 1903, but he forfeited it the following year because he abandoned all other subjects in pursuit of mathematics. Here are ten interesting thing you should know about him. 1. He is from a small Tamil Nadu town Tamin Nadu by mckaysavage from Srinivasa Ramanujan was born on December 22, 1887, in the home of his maternal grandmother in Erode. For a long period, this house was untraceable. His father was a textile merchant’s clerk, while his mother was a housewife. She used to sing at a nearby temple as well. 2. He was inspired by a book about Mathematics Ramanujan was primarily self-taught and grew up in abject poverty. He developed his passion for mathematics on his own and in complete isolation. He borrowed a copy of Loney’s book on Plane Trigonometry from a friend when he was 12 years old, which wa...

The world will soon remember the renowned Indian mathematician Srinivasa Ramanujan once again, as a biopic on his life, named The Man Who Knew Infinity, is set to release this April. Ramanujan,who lived a short but very productivelife, continues to be an inspiration for mathematicians across the world, and his work has inspired a lot of research over the years. Here are 10 things to know about him: 1. He was born in 1887 in Erode, located in Tamil Nadu. His father worked as a clerk with a cloth merchantand his mother was a homemaker who also used to sing at a local temple. Source: 2. His house in Kumbakonam, where the family had moved after his birth, is now maintained as the Srinivasa Ramanujan International Monument. Source: 3.He was married to Janaki Ammal in 1909, who was 9-year-old at that time. 4. He is recognised as one of the greatest mathematicians of his time, but Srinivasa Ramanujan had almost no formal training in math. Many of his mathematical discoveries were based on pure intuition – but most of them were later proved to be true. Srinivasa Ramanujan (centre) with other scientists at Trinity College at the University of Cambridge. Source: 5. He was the second Indian to be inducted as a Fellow of the Royal Society, which is a Fellowship of someof the world’s most eminent scientists. He joined the fellowship in 1918 at the age of 31, as one of youngest fellows in the history of the society. 6. A follower of his family goddess Mahalakshmi, Ramanujan credited her...

Download a PDF of the paper titled On the equidistribution properties of patterns in prime numbers Jumping Champions, metaanalysis of properties as Low-Discrepancy Sequences, and some conjectures based on Ramanujan's master theorem and the zeros of Riemann's zeta function, by Arturo Ortiz-Tapia Abstract: The Paul Erdős-Turán inequality is used as a quantitative form of Weyl' s criterion, together with other criteria to asses equidistribution properties on some patterns of sequences that arise from indexation of prime numbers, Jumping Champions (called here and in previous work, "meta-distances" or even md, for short). A statistical meta-analysis is also made of previous research concerning meta-distances to review the conclusion that meta-distances can be called Low-discrepancy sequences (LDS), and thus exhibiting another numerical evidence that md's are an equidistributed sequence. Ramanujan's master theorem is used to conjecture that the types of integrands where md's can be used more succesfully for quadratures are product-related, as opposite to addition-related. Finally, it is conjectured that the equidistribution of md's may be connected to the know equidistribution of zeros of Riemann's zeta function, and yet still have enough "information" for quasi-random integration ("right" amount of entropy). arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our we...

'Ramanujan' is a historical biopic set in early 20th century British India and England, and revolves around the life and times of the mathematical prodigy, Srinivasa Ramanujan. Directed by t... 'Ramanujan' is a historical biopic set in early 20th century British India and England, and revolves around the life and times of the mathematical prodigy, Srinivasa Ramanujan. Directed by the award-winning filmmaker Gnana Rajasekaran and with an international cast and crew, 'Ram... 'Ramanujan' is a historical biopic set in early 20th century British India and England, and revolves around the life and times of the mathematical prodigy, Srinivasa Ramanujan. Directed by the award-winning filmmaker Gnana Rajasekaran and with an international cast and crew, 'Ramanujan' is a cross-border venture. Considered one of the most romantic stories in the hist...

Biography Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on Ramanujan was born in his grandmother's house in Erode, a small village about 400 km southwest of Madras (now Chennai ). When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km nearer Madras. His father worked in Kumbakonam as a clerk in a cloth merchant's shop. In December 1889 he contracted smallpox. When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam although he would attend several different primary schools before entering the Town High School in Kumbakonam in January 1898. At the Town High School, Ramanujan was to do well in all his school subjects and showed himself an able all round scholar. In 1900 he began to work on his own on mathematics summing geometric and arithmetic series. Ramanujan was shown how to solve 1902 and he went on to find his own method to solve the (and of course failed ) to solve the quintic. It was in the Town High School that Ramanujan came across a mathematics book by G S Carr called Synopsis of elementary results in pure mathematics. This book, with its very concise style, allowed Ramanujan to teach himself mathematics, but the style of the book was to have a rather unfortunate effect on the way Ramanujan was later to write down mathematics since it provided the only model that he had of written mathematical arg...

Oberwolfach Photo Collection Srinivasa Ramanujan was one of the world’s greatest mathematicians. His life story, with its humble and sometimes difficult beginnings, is as interesting in its own right as his astonishing work was. • The book that started it all A Synopsis of Elementary Results in Pure and Applied Mathematics (1880, revised in 1886), by George Shoobridge Carr. The book consists solely of thousands of • Early failures Despite being a prodigy in mathematics, Ramanujan did not have an auspicious start to his career. He obtained a scholarship to college in 1904, but he quickly lost it by failing in nonmathematical subjects. Another try at college in • Go west, young man Ramanujan rose in prominence among Indian mathematicians, but his colleagues felt that he needed to go to the West to come into contact with the forefront of mathematical research. Ramanujan started writing letters of introduction to professors at the • Get pi fast In his notebooks, Ramanujan wrote down 17 ways to represent 1/ • Taxicab numbers In a famous anecdote, Hardy took a cab to visit Ramanujan. When he got there, he told Ramanujan that the cab’s number, 1729, was “rather a dull one.” Ramanujan said, “No, it is a very interesting number. It is the smallest number expressible as a sum of two cubes in two different ways. That is, 1729 = 1^3 + 12^3 = 9^3 + 10^3. This number is now called the Hardy-Ramanujan number, and the smallest numbers that can be expressed as the sum of two cubes in n dif...

The result is stated as follows: If a complex-valued function f ( x ) . A multivariate integral may assume this form. :8 ∫ 0 ∞ ⋯ ∫ 0 ∞ ∑ n 1 , … , n S = 0 ∞ φ ( n 1 ⋯ n S ) ∏ j = 1 S ( ( − 1 ) n j n j ! ) ∏ j = 1 M ( x j ) ( − c j + a j 1 ⋅ n 1 + ⋯ + a j S ⋅ n S − 1 ) d x 1 ⋯ d x M ( ∑ k = 1 P u k ) ∓ d → ∑ n 1 , … , n P = 0 ∞ φ n 1 , … , n P ∏ k = 1 P u k n k ⟨ ± d + ∑ j = 1 P n j ⟩ Γ ( ± d ) ( B.5) • Each bracket series has an index defined as index=number of sums−number of brackets. • Among all bracket series representations of an integral, the representation with a minimal index is preferred. :984 Solve linear equations [ ] • The array of coefficients a j k . ( B.8) • These rules apply. :985 • A series is generated for each choice of free summation parameters, . • Series converging in a common region are added. • If a choice generates a • A bracket series of negative index is assigned no value. • If all series are rejected, then the method cannot be applied. • If the index is zero, the formula ( det | A | − 1 ) ⋅ ∫ 0 ∞ ⋯ ∫ 0 ∞ ∑ n 1 , … , n S = 0 ∞ φ ( n 1 ⋯ n S ) ∏ j = 1 S ( ( − 1 ) n j n j ! ) ∏ j = 1 M ( y j ) − n j ∗ + n j − 1 d y 1 ⋯ d y M ( B.12) • The number of brackets (B) equals the number of integrals (M) ( :14 Example [ ] • The bracket integration method is applied to this integral. ∫ 0 ∞ x 3 / 2 ⋅ e − x 3 / 2 d x References [ ] • Berndt, B. (1985). Ramanujan's Notebooks, PartI. New York: Springer-Verlag. • ^ a b c d González, Iván; Moll, V.H.; Schmid...

Oberwolfach Photo Collection Srinivasa Ramanujan was one of the world’s greatest mathematicians. His life story, with its humble and sometimes difficult beginnings, is as interesting in its own right as his astonishing work was. • The book that started it all A Synopsis of Elementary Results in Pure and Applied Mathematics (1880, revised in 1886), by George Shoobridge Carr. The book consists solely of thousands of • Early failures Despite being a prodigy in mathematics, Ramanujan did not have an auspicious start to his career. He obtained a scholarship to college in 1904, but he quickly lost it by failing in nonmathematical subjects. Another try at college in • Go west, young man Ramanujan rose in prominence among Indian mathematicians, but his colleagues felt that he needed to go to the West to come into contact with the forefront of mathematical research. Ramanujan started writing letters of introduction to professors at the • Get pi fast In his notebooks, Ramanujan wrote down 17 ways to represent 1/ • Taxicab numbers In a famous anecdote, Hardy took a cab to visit Ramanujan. When he got there, he told Ramanujan that the cab’s number, 1729, was “rather a dull one.” Ramanujan said, “No, it is a very interesting number. It is the smallest number expressible as a sum of two cubes in two different ways. That is, 1729 = 1^3 + 12^3 = 9^3 + 10^3. This number is now called the Hardy-Ramanujan number, and the smallest numbers that can be expressed as the sum of two cubes in n dif...