The Legacy of Alladi Ramakrishnan -- Contributions of Alladi Ramakrishnan to the Mathematical Sciences -- Alladi Ramakrishnan’s Theoretical Physics Seminar -- Telegrams Received for the MATSCIENCE Inauguration -- The Miracle has Happened -- Overseas Trips of Alladi Ramakrishnan -- List of Publications of Alladi Ramakrishnan -- List of PhD Students of Alladi Ramakrishnan -- Pure Mathematics -- Inversion and Invariance of Characteristic Terms: Part I -- Partitions with Non-Repeating Odd Parts and Q-Hypergeometric Identities -- q-Catalan Identities -- Completing Brahmagupta’s Extension of Ptolemy’s Theorem -- A Transformation Formula Involving the Gamma and Riemann Zeta Functions in Ramanujan’s Lost Notebook -- Ternary Quadratic Forms, Modular Equations, and Certain Positivity Conjectures -- How Often is n! a Sum of Three Squares? -- Eulerian Polynomials: From Euler’s Time to the Present -- Crystal Symmetry Viewed as Zeta Symmetry II -- Positive Homogeneous Minima for a System of Linear Forms -- The Divisor Matrix, Dirichlet Series, and SL(2, Z) -- Proof of a Conjecture of Alladi Ramakrishnan on Circulants -- Probability and Statistics -- Branching Random Walks -- A Commentary on the Logistic Distribution -- Entropy and Cross Entropy: Characterizations and Applications -- Optimal Weights for a Class of Rank Tests for Censored Bivariate Data -- Connections Between Bernoulli Strings and Random Permutations -- Storage Models for a Class of Master Equations with Separable Kernels -- Theoretical Physics and Applied Mathematics -- Inverse Consistent Deformable Image Registration -- A Statistical Model for the Quark Structure of the Nucleon -- On Generalized Clifford Algebras and their Physical Applications -- (p, q)-Rogers-Szegö Polynomial and the (p, q)-Oscillator -- Rethinking Renormalization -- Magnetism, FeS Colloids, and Origins of Life -- The Ehrenfest Theorem in Quantum Field Theory.

In a distinguished scientific life that had spanned over five decades, Alladi Ramakrishnan made significant contributions to probability and statistics, elementary particle physics, cosmic rays and astrophysics, matrix theory, and the special theory of relativity. Inspired by his visit to the Institute of Advanced Study during 1957-1958, and the direct influences of Robert Oppenheimer, Niels Bohr, Sir C.V. Raman, S. Chandrasekhar, and other notable contemporaries, he later founded the Institute of Mathematical Sciences (MATSCIENCE) in Madras, India. In the spirit of Alladi Ramakrishnan’s profound interest and contributions to three fields of science — Mathematics, Statistics, and Physics — this volume contains invited surveys and research articles from prominent members of these communities who also knew Ramakrishnan personally and greatly respected his influence in these areas of science. Historical photos, telegrams, and biographical narratives of Alladi Ramakrishnan’s illustrious career of special interest are included as well.