Mathematics and Physics, (Collections)

Connected at Infinity II: A Selection of Mathematics by Indians by Rajendra Bhatia, C. S. Rajan And Ajit Iqbal Singh from Hindustan Book Agency.

Like its predecessor volume, this is a special collection of articles describing the work of some of the best known mathematicians from India. It contains eight articles written by experts, each of whom has chosen one major research contribution by an Indian mathematician, and explained its context, significance and impact.

This is done in a way that makes the main ideas accessible to someone whose own research interests might be in a different area. Included here are commentaries on important works by R. C. Bose, S. S. Shrikhande and E.T. Parker, H. Cramer and C. R. Rao, V. B. Mehta and A. Ramanathan, R. Narasimha, K. R. Parthasarathy, R. Ranga Rao and V. S. Varadarajan, R. Parthasarathy, D.N. Verma, N. Wiener and P. R. Masani.

In our Mathematics section, Rs. 350, in hardcover, 194 pages, ISBN: 9789380250519

Probability Theory: A Foundational Course by R. P. Pakshirajan from Hindustan Book Agency.

This book shares the dictum of J. L. Doob in treating Probability Theory as a branch of Measure Theory and establishes this relation early. Probability measures in product spaces are introduced right at the start by way of laying the ground work to later claim the existence of stochastic processes with prescribed finite dimensional distributions.

Other topics analyzed in the book include supports of probability measures, zero-one laws in product measure spaces, Erdös-Kac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains.

This book is offered as a text book for students pursuing graduate programs in Mathematics and or Statistics. The book aims to help the teacher present the theory with ease, and to help the student sustain his interest and joy in learning the subject.

In our Mathematics section, Rs. 850, in hardcover, 564 pages, ISBN: 9789380250441

Combinatorial Techniques by Sharad S. Sane from Hindustan Book  Agency.

This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks,   techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law.

Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.

In our Mathematics section, Rs. 725, in hardcover, 482 pages, ISBN: 9789380250489

Lectures on the Structure of Algebraic Groups and Geometric Applications by Michel Brion, Preena Samuel from Hindustan Book Agency.

This book originates from a series of 10 lectures given by Professsor Michel Brion at the Chennai Mathematical Institute during January 2011. The book presents a theorem due to Chevalley on the structure of connected algebraic groups, over algebraically closed fields, as the starting point of various other structure results developed in the recent past. Chevalley's structure theorem states that any connected algebraic group over an algebraically closed field is an extension of an abelian variety by a connected affine algebraic group.

This theorem forms the foundation for the classification of anti-affine groups which plays a central role in the development of the structure theory of homogeneous bundles over abelian varieties and for the classification of complete homogeneous varieties. All these results are presented in this book. The book begins with an overview of the results exposed, the proofs of which constitute the rest of the book.

Various open questions also have been indicated in the course of the exposition. This book assumes certain preliminary knowledge of linear algebraic groups, abelian varieties and algebraic geometry. The book is intended for graduate students and researchers in algebraic geometry.

In our Mathematics section, Rs. 225, in paperback, 128 pages, ISBN: 9789380250465

The Classical Groups: Their Invariants and Representations by Hermann Weyl from Hindustan Book Agency.

In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate.

The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.

In our Mathematics section, Rs. 490, in hardcover, 334 pages, ISBN: 9789380250359

Morse Theory by John Milnor from Hindustan Book Agency.

One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of proble

occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory.

Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scientific disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after reflection that this ease is the mark of a master."

In our Mathematics section, Rs. 250, in hardcover, 162 pages, ISBN: 9789380250366