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 volume is a collection of invited articles by well-known algebraists, several of them working in the group rings. The aim of this volume is to provide accessible surveys/reviews of topics of current research, provide recent trends, problems and their current status as well as glimpse into an active area of research in algebra.

This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing. The necessary background in matrices, multivariate normal distribution and distributions of quadratic forms is developed along the way. It is primarily aimed at advanced undergraduate and first year masters students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. It should also be of use to ...

This book, which is intended for undergraduate students having no background in calculus, attempts to trace the growth of algebra from its origins in ancient times to its present state as a major part of mathematics and a powerful tool in theoretical physics. Especially interesting is the treatment of Indian mathematics in the period between the sixth and twelfth centuries, and the work of the Italian mathematicians during the fifteenth and sixteenth centuries ...

This book is designed to be a concise and rigorous introduction to the theory of functions of a complex variable, suitable for a one-semester course. The aim of the notes is to help students of mathematics and related sciences acquire a basic understanding of the subject, as a preparation for pursuing it at a higher level or for employing it in other areas. The approach is standard and somewhat old-fashioned. This book should be accessible to students in ...