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Interior Point Approach to Linear, Quadratic and Convex Programming:

`This book presents a general and rigorous foundation for solving nonlinear convex optimization problems. The book is well and clearly written. It is comprehensive and well-balanced ... excellent text for an advanced or seminar course on optimization, primarily addressed to graduate students in mathematics, pure or applied, computer science and engineering schools. ... researchers will also find it a valuable reference because the th...

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Discriminants, Resultants, and Multidimensional Determinants

…the book is almost perfectly written, and thus I warmly recommend it not only to scholars but especially to students. The latter do need a text with broader views, which shows that mathematics is not just a sequence of apparently unrelated expositions of new theories, … but instead a very huge and intricate building whose edification may sometimes experience difficulties … but eventually progresses steadily. "It is very much represe...

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Smooth Dynamical Systems

This is a reprint of M C Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area.

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Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician

This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. This second volume is intended as a bridge between introductory set theory courses and advanced monographs that cover selected branches of set theory, such as forcing or large cardinals. The authors give short but rigorous introductions to set-theor...

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Six Themes On Variation

The purpose of this series is to introduce undergraduates to the varied areas of current research in mathematics; and this text, of all in the series, most clearly achieves that goal. There are six essays here written by different authors. The best is the introduction to Morse theory by Forman. This author is gifted with the ability to know when to include and exclude detail so as to not lose the developing intuitive thrust. What thi...

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New Directions in Hopf Algebras

This volume of articles arising from the MSRI workshop on Hopf Algebras in October 1999 forms a broad survey of this exciting field and its connection with quantum groups and related areas. Topics include pointed Hopf algebras, triangular Hopf algebras, Hopf algebra extensions and cohomology, quantum groups and groupoids, quantum symmetric pairs, monoidal categories, and the Brauer group of a Hopf algebra. The volume also includes an...

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The Classification of the Finite Simple Groups

The classification of the finite simple groups is one of the major feats of contemporary mathematical research, but its proof has never been completely extricated from the journal literature in which it first appeared. This book serves as an introduction to a series devoted to organizing and simplifying the proof. The purpose of the series is to present as direct and coherent a proof as is possible with existing techniques. This firs...

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Differential Geometry of Curves and Surfaces: A Concise Guide

Centraltopics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels

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Quasiconformal Teichmuller Theory

[The authors] have produced a formidable treatise on the modern theories of quasiconformal mappings, Riemann surfaces and Teichm\"uller spaces. They have gathered, into a unified exposition, results which ... have not previously been found in book form ... Many of the approaches and results are new, others are more detailed than can be found elsewhere ... this monograph is now the standard reference on two-dimensional quasiconformal ...