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This book introduces the dilation theory of operators on Hilbert spaces and its relationship to complex geometry. Classical as well as very modern topics are covered in the book. On the one hand, it introduces the reader to the characteristic function, a classical object used by Sz.-Nagy and Foias and still a topic of current research. On the other hand, it describes the dilation theory of the symmetrized bidisc which has been developed mostly in the present century and is a very active topic of research. It also describes an abstract theory of dilation in the setting of set theory. This was developed very recently.A good portion of the book discusses various geometrical objects like the bidisc, the Euclidean unit ball, and the symmetrized bidisc. It shows the similarities and differences between the dilation theory in these domains. While completely positive maps play a big role in the dilation theory of the Euclidean unit ball, this is not so in the symmetrized bidisc for example. There, the central role is played by an operator equation. Targeted to graduate students and researchers, the book introduces the reader to different techniques applicable in different domains.

Treats some basic topics in the spectral theory of dynamical systems. The treatment is at a general level, but two more advanced theorems, one by H. Helson and W. Parry and the other by B. Host, are presented. Moreover, Ornstein's family of mixing rank one automorphisms is described with construction and proof.

A collection of problems from a competition for college students organised by the Iranian Mathematical Society. It compiles problems from these competitions between 1973 and 2007 and provides solutions to most of them. It is suitable for students of mathematics preparing for competitions and for advanced studies.

This book on integration theory is based on the lecture notes for courses that the author gave at the Tata Institute of Fundamental Research, Mumbai, and at ETH, Zurich. The subject matter is classical. The goal of the notes is to provide a concise, clear, and accurate treatment of the basic ideas of the subject.

Provides an elementary introduction to the basic concepts of the theory of ordinary representations to finite groups with a minimum of prerequisites; explores the for the important special case of the symmetric groups $S_n$ of permutations on $n$ letters; and uses the preparatory material of the first two parts, coupled with the $S_n$ theory, to do the same for some other important special groups.

Deals with topics usually studied in a masters or graduate level course on the theory of measure and integration. It starts with the Riemann integral and points out some of its shortcomings which motivate the theory of measure and the Lebesgue integral. There is a separate chapter on the change of variable formula and one on Lp- spaces.

Provides an introduction to basic topics in inequalities and their applications. These include the arithmetic mean-geometric mean inequality, Cauchy-Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. More than 400 problems are included and their solutions are explained.

Introduces the first concepts of Algebraic Topology, such as general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory, in detail. The text has been designed for undergraduate and beginning graduate students of Mathematics. It assumes a minimal background of linear algebra, group theory and topological spaces.

Including Affine and projective classification of Conics, 2 point homogeneity's of the planes, essential isometrics, non euclidean plan geometrics, in this book, the treatment of Geometry goes beyond the Kleinian views.

The material presented in this book is suited for a first course in Functional Analysis which can be followed by Masters students. The book includes a chapter on compact operators and the spectral theory for compact self-adjoint operators on a Hilbert space.

Provides an introduction to what has come to be known as Standard Monomial Theory (SMT). SMT deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of flag varieties (and their Schubert subvarieties) associated to these groups.

It gives Liouville's Theorem on the existence of invariant measure, entropy theory leading up to Kolmogorov-Sinai Theorem, and the topological dynamics proof of van der Waerden's theorem on arithmetical progressions.

Aims to convey 3 principal developments in the evolution of information theory, including Shannon's interpretation of Boltzmann entropy as a measure of information yielded by an elementary statistical experiment and basic coding theorems on storing messages and transmitting them through noisy communication channels in an optimal manner.

This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces.

Offers a self-contained elementary introduction to the fundamental concepts and techniques of Algebraic Geometry, leading to some gems of the subject like Bezout's Theorem, the Fundamental Theorem of Projective Geometry, and Zariski's Main Theorem.

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.

The newly developed field of Seiberg-Witten gauge theory has become a well-established part of the differential topology of four-manifolds and three-manifolds. This book offers an introduction and an up-to-date review of the state of current research.

Combines the spirit of a textbook and of a monograph on the topic of Semigroups and their applications. It is expected to have potential users across a broad spectrum including operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics.

Contains the author's notes for a course that he taught at ETH, Zurich. The aim is to lead the reader to a proof of the Peter-Weyl theorem, the basic theorem in the representation theory of compact topological groups. The topological, analytical, and algebraic groundwork needed for the proof is provided as part of the course.

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. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups.

Topics that have continued from the first edition include Minkowski's theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem.