Tantrasangraha, composed in 1500 CE by the renowned Kerala astronomer Nilakantha Somayaji (c.1444–1545 CE) ranks along with Aryabhanaya of Aryabhaña and Siddhàntashiromaoi of Bhàskaràcàrya as a seminal work that significantly influenced further work on astronomy in India. One of the distinguishing features of this text is that it introduces a major revision of the traditional planetary models, leading to a unified theory ...

Number Theory and Applications: Proceedings of the International Conferences on Number Theory and Cryptography

The material presented in this book is suited for a first course in Functional Analysis which can be followed by masters students. While covering all the standards material expected of such a course, efforts have been made to illustrate the use of various theorems via examples taken from differential equations and the calculus of variations, either through brief sections or through exercises. In fact, this book will be particularly useful for students who would ...

"Insurance has become a necessary aspect of modern society. The mathematical basis of insurance modelling is best expressed in terms of continuous time stochastic processes.This introductory text on actuarial risk theory deals with the Cramer-Lundberg model and the renewal risk model. Their basic structure and properties including the renewal theorems, as well as the corresponding ruin problems are studied. As heavy tailed distributions have become ...

Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva (In 2 Volumes)

This book is an introduction to the study of fundamental inequalities like the arithmetic mean-geometric mean inequality, the Cauchy-Schwarz inequality, the Chebyshev inequality, the rearrangement inequality, inequalities for convex and concave functions. The emphasis is on the use of these inequalities for solving problems. Its special feature is a chapter on the geometrical inequalities which studies relations between various geometrical measures. It contains ...

These notes are a record of a one semester course on Functional Analysis given by the author to second year Master of Statistics students at the Indian Statistical Institute, New Delhi. Students taking this course have a strong background in real analysis, linear algebra, measure theory and probability, and the course proceeds rapidly from the definition of a normed linear space to the spectral theorem for bounded selfadjoint operators in a Hilbert space. The ...

Flag Varieties: An Interplay of Geometry, Combinatorics, and Representation Theory

Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics and representation theory. This book is detailed account of this interplay. In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discusses. In the area of algebraic geometry, the book gives a detailed ...

This book offers a self-contained elementary introduction to the fundamental concepts and techniques of Algebraic Geometry, leading to some gems of the subject like Bezoutâ€™s Theorem, the Fundamental Theorem of Projective Geometry, and Zariskiâ€™s Main Theorem. The book contains a detailed treatment of algebraic plane curves with a special emphasis on elliptic curves and their birational classification. The role played by elliptic curves in modern theory of ...

The theory of infinite permutation groups is a branch of algebra which has developed rapidly during the last twenty years, driven partly by connections with mathematical logic. This book is based on a course of lectures at the Indian Institute of Technology, Guwahati, in August and September 1996. It takes the reader from the most basic notions in group theory to a recently completed classification result for Jordon groups. Topics examined include : transitivity ...

This is a basic text on algebraic topology designed for use in a one year course at the masters or beginning Ph.D. level. Basic concepts of the subject like the fundamental group, covering projections, simplicial complexes, and simplicial homology are discussed at length. Singular homology is introduced to give a glimpse of an abstract homology theory in the sense of Elienberg and Steenrod. Interesting applications, examples and exercises are included. An ...

This volume is a collection of invited expository and research articles by well-known number theorists. The aim of this volume is to provide an overview of the developments together with open problems and results, which have attracted the attention of leading number theorists.