One of the landmarks in the history of mathematics is the proof of the nonex- tence of algorithms based solely on radicals and elementary arithmetic operations (addition, subtraction, multiplication, and division) for solutions of general al- braic equations of degrees higher than four. This proof by the French mathema- cian Evariste Galois in the early nineteenth century used the then novel concept of the permutation symmetry of the roots of algebraic equations and led to the invention of group theory, an area of mathematics now nearly two centuries old that has had extensive applications in...
One of the landmarks in the history of mathematics is the proof of the nonex- tence of algorithms based solely on radicals and elementary arithmetic o...
" The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author has a] student-friendly style The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature appear for the first time in a text."
Mathematical Reviews (Review of the Second...
" The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically clos...
Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including: (1) divisibility, (2) congruences, (3) the Riemann zeta function, (4) Diophantine equations and Fermat s conjecture, (5) the theory of partitions.
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Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. Th...
To this reviewer s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method via the Ellipsoid algorithm to Karmarkar s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing...
To this reviewer s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys ...
The authors have backgrounds which are ideally suited for writing this book. The late C. Truesdell is well known for his monumental treatises on continuum thermomechanics. K.R. Rajagopal has made many important contributions to the mechanics of continua in general, and to nonlinear fluids in particular. They have produced a compact, moderately general book which encompasses many fluid models of current interest The book is written very clearly and contains a large number of exercises and their solutions. The level of mathematics is that commonly taught to undergraduates in mathematics...
The authors have backgrounds which are ideally suited for writing this book. The late C. Truesdell is well known for his monumental treatises o...
Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values.
This work explains some of the early results of this theory to mathematicians and theoretical physicists,...
Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an inte...
"The book is largely self-contained...There is a nice introduction to symplectic geometry and a charming exposition of equivariant K-theory. Both are enlivened by examples related to groups...An attractive feature is the attempt to convey some informal 'wisdom' rather than only the precise definitions. As a number of results are] due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory...it has already proved successful in introducing a new generation to the subject." (Bulletin of the AMS)
"The book is largely self-contained...There is a nice introduction to symplectic geometry and a charming exposition of equivariant K-theory. Both a...
"This is a delightful little paperback which presents a day-by-day transcription of a course taught jointly by Polya and Tarjan at Stanford University...One can count on Polya and Tarjan] for new insights and a fresh outlook. Both instructors taught by presenting a succession of examples rather than by presenting a body of theory... The book] is very well suited as supplementary material for any introductory class on combinatorics; as such, it is very highly recommended. Finally, for all of us who like the topic and delight in observing skilled professionals at work, this...
"This is a delightful little paperback which presents a day-by-day transcription of a course taught jointly by Polya and Tarjan at Stanford Uni...
Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques.
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Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation ...
"Visions in Mathematics - Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematicians worldwide. The goals of the conference were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas.
The aims of the conference are reflected in the present set of survey articles, documenting the state of art and future prospects in many branches...
"Visions in Mathematics - Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 2...
