66 books
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 ...
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 ...
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 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 ...
The theme of the workshop was Algebraic number theory with special emphasis on Elliptic curves. The theory of Elliptic curves has been the source of new approaches to classical problems in number theory. It has also found applications in cryptography. The workshop also covered some aspects of cryptography. The volume is in three parts, the first part contains articles in the field of Elliptic curves, the second contains articles on Modular forms. Some basics as ...
This book provides a quick introduction to Fourier Series. The author begins by describing one of the problems actually studied by Fourier and how this leads to a differential equation to solve which Fourier introduced his famous series. The mathematical problems this leads to are then discussed rigorously. After that, applications of the theory to four different problems are given. A novel feature of the book is the inclusion of a detailed history of the ...
This book is an introductory graduate level text on game theory, which grew out of courses for students in Mathematics in Nijmegen and for students in Econometrics and Operations Research in Tilburg. Game theory deals with mathematical models of conflict and cooperation. In the first nine chapters attention is paid to non-cooperative games in extensive and strategic form and to some economic applications. Relations with the theory of linear programming and the ...