Srinivasa Ramanujan: His Life, Legacy, and Mathematical Influence

Preface.- Part. I. Life and History - Life and Family.- Srinivasa Ramanujan.- The name, Srinivasa Ramanujan.- S. Janaki Ammal (Mrs. Ramanujan).- The Ramanujan family record.- Ramanujan's father, Kuppuswamy Srinivasa Aiyangar.- Ramanujan's brothers, Lakshmi Narasimhan and Tirunarayanan.- Ramanujan's illness.- On the discovery of the photograph of S. Ramanujan, FRS.- Komalattammal.- Namagiri, The Goddess of Namakkal.- Ramanujan bust.- Paul T. Granlund.- Part II: Life and History - Places.- Erode, the birthplace of Ramanujan.- Kumbakonam, Ramanujan's hometown.- Ramanujan's home in Kumbakonam.- Government Arts College, Kumbakonam.- Kumbakonam higher secondary school.- Madras Port Trust.- The Madras Port Trust and Sir Francis Spring.- University of Madras.- Pachaiyappa's College.- The Sarangapani Temple.- The Ramanujan Math Park.- Part III Life and History - Ramanujan's Books .- Carr's Synopsis.- Matriculation exams taken by Ramanujan.- The books studied by Ramanujan in India.- Part IV Life and History - Correspondences.- Introduction to the Correspondence between Ramanujan and Hardy.- S. Ramanujan to G. H. Hardy 16 January 1913.- G. H. Hardy to S. Ramanujan 8 February 1913.- S. Ramanujan to G. H. Hardy 27 February 1913.- G. H. Hardy to S. Ramanujan 26 March 1913.- Letters to G. H. Hardy from nursing homes.- Ramanujan's quarterly reports.- Ramanujan's last letter to Hardy.- Ramanujan's slate.- Part V Life and History - Institutions.- The Ramanujan Mathematical Society.- The Royal Society and its Fellowship.- Trinity College and its Fellowship.- SASTRA Deemed University.- Part VI Biographies.- S. Narayana Aiyar.- Richard A. Askey.- A. O. L. Atkin.- W. N. Bailey.- H. F. Baker.- Arthur Berry.- SubrahmanyamChandrasekhar.- Ramanujan's Physician, P. S. Chandrasekhara Iyer.- Sir Francis Dewsbury.- Freeman Dyson.- Leonhard Euler.- A. G. Greenhill.- G. H. Hardy.- M. J. M. HILL.- E. W. Hobson.- V. Ramaswami Iyer.- P. V. Seshu Iyer.- C. G. J. Jacobi.- Richard Littlehailes.- J. E. Littlewood.- P. A. MacMahon.- P. C. Mahalanobis.- Louis J. Mordell.- E. H. Neville.- Hans Rademacher.- R. Ramachandra Rao.- A. S. Ramalingam.- S. R. Ranganathan.- Robert A. Rankin.- L. J. Rogers.- Issai Schur.- Lucy Joan Slater.- Sir Francis Spring.- P. K. Srinivasan.- Swinnerton-Dyer and the Ramanujan congruences for _ (n).- V. R. Thiruvenkatachar.- K. Venkatachaliengar.- Sir Gilbert Walker.- G. N. Watson.- B. M. Wilson.- Part VII. Legacy - Notebooks.- Ramanujan's Notebooks.- Ramanujan's Notebooks Part I.- Ramanujan's NotebooksPart II.- Ramanujan's Notebooks Part III.- Ramanujan's Notebooks Part IV.- Ramanujan's Notebooks Part V.- The discovery of Ramanujan's Lost Notebook.- Ramanujan's Lost Notebook Part I.- Ramanujan's Lost Notebook Part II.- Ramanujan's Lost Notebook Part III.- Ramanujan's Lost Notebook Part IV.- Ramanujan's Lost Notebook Part V.- Your hit parade: The top ten most fascinating formulas in Ramaujan's Lost Notebook.- Part VIII. Legacy - Books and Journal Articles.- A Mathematician's Apology.- Honoring a gift from Kumbakonam.- Mathematics Wizard Srinivasa Ramanujan.- Number Theory in the Spirit of Ramanujan.- Ramanujan Memorial Number Vol. 1, Letters and Reminiscences: Vol. 2, An Inspiration, P. K. Srinivasan, ed.- Ramanujan - The Man and the Mathematician.- Ramanujan: Man of Mathematics (comic book).- Ramanujan: Twelve Lectures on Subjects suggested by his Life and Work, by G.H. Hardy.- Collected Papers.- Ramanujan's Place in the World of Mathematics: Essays providing a comparitive study.- Resonance of Ramanujan's Mathematics (in three volumes) Books by R. P. Agarwal.- Srinivasa Ramanujan - Life and Work of a Natural Mathematical Genius, Swayambhu.- The Boy Who Dreamed of Infinity: A Tale of the Genius of Ramanujan (children's book).- The final problem: an account of the mock theta functions.- The Man Who Knew Infinity - a life of the genius Ramanujan.- The Mathematical Legacy of Srinivasa Ramanujan.- The Ramanujan Journal.- Part IX. Legacy - Plays Movies and TV.- A First Class Man.- A disappearing number.- Documentaries on Srinivasa Ramanujan by Mr. Nandan Kudhyadi.- On the man who loved numbers.- Partition - A Play on Ramanujan.- Ramanujan - The Opera.- The Man Who Knew Infinity (Movie).- The Ramanujan CD.- Part X. Legacy - Conferences Events and Prizes.- The ICTP Ramanujan Prize.- The SASTRA Ramanujan Prize.- Some Ramanujan Centenary Conferences.- Ramanujan at 125.- The Ramanujan Trust in Mauritius.- India's efforts to commemorate Ramanujan including national mathematics day.- Part XI Mathematics - Classical.- Stirling and Bell numbers and related topics.- Bernoulli numbers.- Busche-Ramanujan identities.- Circular summation.- Class invariants.- Diophantine approximation.- Elementary algebraic identities and polynomial equations.- Highly composite numbers and other champion numbers.- Partial fractions.- Problems solved by Ramanujan in the Journal of the Indian Mathematical Society.- The Problems submitted by Ramanujan to the Journal of the Indian Mathematical Society.- Radicals.- Ramanujan and modular forms.- Ramanujan and odd zeta values.- Ramanujan and ?.- Ramanujan and Probabilistic Number Theory.- Ternary quadratic forms.- Ramanujan and the Riemann zeta-function.- Ramanujan complexes.- Ramanujan Graphs.- Ramanujan summation in quantum field theory.- Ramanujan sums.- Ramanujan sums and the general linear group.- Ramanujan's continued fraction involving gamma functions.- Ramanujan's paper on Riemann's functions ?(s) and ?(t) and a transformation from the Lost Notebook.- Ramanujan's series for 1/ ?.- Ramanujan's taxi cab number.- Ramanujan's work on Euler products.- Ramanujan's Question.- Signal processing and Ramanujan sums.- The 'Constant' of a series.-The Hardy-Littlewood-Ramanujan Method.- The normal number of prime factors of a number n.- G. N. Watson - 31 papers inspired by Ramanujan.- Missing works of Ramanujan.- Part XII Mathematics - q-Series.- The Rogers-Ramanujan identities.- The Rogers-Ramanujan identities: Antecedents.- Bailey's tranform and lemma.- Rogers-Ramanujan identities in the hard hexagon model.- A touch of quantum field theory.- K3 Surfaces and sums of two cubes.- Knot theory and Rogers-Ramanujan type identities.- Lepowsky-Wilson Z-algebra and Rogers-Ramanujan-type identities: recent advances.- Nahm's Conjecture.- Ramanujan and Computer Algebra.- Ramanujan and Heine's method.- Ramanujan and hypergeometric series.- The Rogers-Ramanujan continued fraction.- Evaluations of the Rogers-Ramanujan continued fraction.- Ramanujan's continued fractions involving hypergeometric functions The Rogers-Ramanujan continued fraction.- Ramanujan's general q-continued fractions.- The 1 1 summation.- Watson's q-Whipple transformation formula.- Part XIII Mathematics - Integrals.- Beautiful integrals.- Elliptic and related integrals.- Mordell integrals.- q-Beta integrals.- Ramanujan's published papers on definite integrals.- Trigonometric Dirichlet series and Eichler integrals.- Part XIV Mathematics - Mock Theta Functions.- A century of answering the question: What is a mock theta function?.- A survey article on Appell-Lerch functions.- False theta functions classical theory.- False theta functions and modular forms.- Harmonic Maass forms and mock modular forms.- Mock theta functions.- Partial theta functions.- Combinatorics of Ramanujan's third order mock theta functions.- Polar Harmonic Maass forms.- Quantum modular forms.- Ramanujan and quantum black holes.- Part XV Mathematics - Partitions.- An algebraic formula for the partition function.- Dyson's rank and crank conjectures and partition congruences.- Identities for the Rogers-Ramanujan functions.- Ramanujan and the Nekrasov-Okounkov formula.- Ramanujan's modular equations with applications to partitions.- Ramanujan's partition congruences.- Ramanujan's Unpublished Manuscript on the Partition and Tau Functions.- The G?ollnitz-Gordon identities.- Overpartitions.- Part XVI Mathematics - Theta Functions Elliptic Functions and Modular Forms.- Automatic discovery and proofs of formulas of Ramanujan-Kolberg type.- Divisibility of fourier coefficients of modular forms.- Eichler cohomology: A view of Ramanujan's mock modular forms.- Eisenstein series I.- Eisenstein series II.- Elliptic functions.- Explicit values of theta functions.- Indefinite theta series.- The Langlands Program.- Modular Equations.- The modular j-invariant.- Modular forms and the modular group.- Monster denominator formula.- Monstrous moonshine.- Pariah moonshine.- Umbral moonshine.- Ramanujan's alternative theories of theta functions.- Rankin-Cohen brackets.- Singular moduli.- Combinatorial formulas for Ramanujan's tau function.- The Ramanujan ? -function.- Theta functions.- Part XVII Mathematics - Analysis.- Bessel functions and summation formulae.- Gaussian quadrature and orthogonal polynomia.- The Euler-Maclaurin and Abel-Plana Summation Formulas.- Asymptotic expansions.- Ramanujan's master theorem.- Part XVIII Mathematics - Squares and Cubes.- Gauss's circle problem and Dirichlet's divisor problem.- Magic squares.- Number of numbers representable as a square or sum of two squares.- Ramanujan and sums of two cubes.- The Ramanujan-Mordell Theorem on sums of an even number of squares.-

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Srinivasa Ramanujan;Handbook Ramanujan;mathematical legacy;Indian mathematician;sub-disciplines mathematical research