Steven H. Weintraub's Books

Algebra

An Approach via Module Theory

By: William A. Adkins,Steven H. Weintraub

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Algebra

An Approach via Module Theory

By: William A. Adkins,Steven H. Weintraub

This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book). Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations. Why modules? The answer is that they are a basic unifying concept in mathematics. The reader is probably already familiar with the basic role that vector spaces play in mathematics, and modules are a generaliza tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.

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Page Count

540

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461209234

ISBN 13

9781461209232

Representation Theory of Finite Groups: Algebra and Arithmetic

Algebra and Arithmetic

By: Steven H. Weintraub

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Representation Theory of Finite Groups: Algebra and Arithmetic

Algebra and Arithmetic

By: Steven H. Weintraub

``We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his/her own.'' --from the Preface Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, representation theory has been one of the great tools in the study and classification of finite groups. There are some beautiful results that come from representation theory: Frobenius's Theorem, Burnside's Theorem, Artin's Theorem, Brauer's Theorem--all of which are covered in this textbook. Some seem uninspiring at first, but prove to be quite useful. Others are clearly deep from the outset. And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers. The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.

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Page Count

226

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821832220

ISBN 13

9780821832226

Moduli Spaces of Abelian Surfaces

Compactification, Degenerations and Theta Functions

By: Klaus Hulek,Constantin Kahn,Steven H. Weintraub

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Moduli Spaces of Abelian Surfaces

Compactification, Degenerations and Theta Functions

By: Klaus Hulek,Constantin Kahn,Steven H. Weintraub

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

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Page Count

361

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110891921

ISBN 13

9783110891928

Fundamentals of Algebraic Topology

By: Steven H. Weintraub

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Fundamentals of Algebraic Topology

By: Steven H. Weintraub

This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography.

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Page Count

169

Publisher

Springer

Published Date

ISBN 10

1493918443

ISBN 13

9781493918447

Linear Algebra for the Young Mathematician

By: Steven H. Weintraub

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Linear Algebra for the Young Mathematician

By: Steven H. Weintraub

Linear Algebra for the Young Mathematician is a careful, thorough, and rigorous introduction to linear algebra. It adopts a conceptual point of view, focusing on the notions of vector spaces and linear transformations, and it takes pains to provide proofs that bring out the essential ideas of the subject. It begins at the beginning, assuming no prior knowledge of the subject, but goes quite far, and it includes many topics not usually treated in introductory linear algebra texts, such as Jordan canonical form and the spectral theorem. While it concentrates on the finite-dimensional case, it treats the infinite-dimensional case as well. The book illustrates the centrality of linear algebra by providing numerous examples of its application within mathematics. It contains a wide variety of both conceptual and computational exercises at all levels, from the relatively straightforward to the quite challenging. Readers of this book will not only come away with the knowledge that the results of linear algebra are true, but also with a deep understanding of why they are true.

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Page Count

406

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470450844

ISBN 13

9781470450847

A Guide to Advanced Linear Algebra

By: Steven H. Weintraub

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A Guide to Advanced Linear Algebra

By: Steven H. Weintraub

A thorough development of a topic at the core of mathematics, ideal for graduate students and professional mathematicians.

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267

Publisher

MAA

Published Date

ISBN 10

0883853515

ISBN 13

9780883853511

Galois Theory

By: Steven H. Weintraub

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Galois Theory

By: Steven H. Weintraub

Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois Theory. The second edition, with a new chapter on transcendental extensions, will only further serve to make the book appreciated by and approachable to undergraduate and beginning graduate math majors.

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Page Count

220

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387875751

ISBN 13

9780387875750

The Siegel Modular Variety of Degree Two and Level Four/Cohomology of the Siegel Modular Group of Degree Two and Level Four

By: Ronnie Lee,Steven H. Weintraub,Jerome William Hoffman

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The Siegel Modular Variety of Degree Two and Level Four/Cohomology of the Siegel Modular Group of Degree Two and Level Four

By: Ronnie Lee,Steven H. Weintraub,Jerome William Hoffman

Enthält: The Siegel modular variety of degree two and level four / Ronnie Lee, Steven H. Weintraub. Cohomology of the Siegel modular group of degree two and level four / J. William Hoffman, Steven H. Weintraub.

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American Mathematical Soc.

Published Date

ISBN 10

0821806203

ISBN 13

9780821806203

Differential Forms

Theory and Practice

By: Steven H. Weintraub

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Differential Forms

Theory and Practice

By: Steven H. Weintraub

Differential forms are a powerful mathematical technique to help students, researchers, and engineers solve problems in geometry and analysis, and their applications. They both unify and simplify results in concrete settings, and allow them to be clearly and effectively generalized to more abstract settings. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems. Differential Forms, Second Edition, is a solid resource for students and professionals needing a general understanding of the mathematical theory and to be able to apply that theory into practice. - Provides a solid theoretical basis of how to develop and apply differential forms to real research problems - Includes computational methods to enable the reader to effectively use differential forms - Introduces theoretical concepts in an accessible manner

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Page Count

409

Publisher

Elsevier

Published Date

ISBN 10

0123946174

ISBN 13

9780123946171

Fundamentals of Algebraic Topology

By: Steven H. Weintraub

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Fundamentals of Algebraic Topology

By: Steven H. Weintraub

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169

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Springer

Published Date

ISBN 10

1493918443

ISBN 13

9781493918447

Jordan Canonical Form

Application to Differential Equations

By: Steven Weintraub

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Jordan Canonical Form

Application to Differential Equations

By: Steven Weintraub

Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. In this book we develop JCF and show how to apply it to solving systems of differential equations. We first develop JCF, including the concepts involved in it—eigenvalues, eigenvectors, and chains of generalized eigenvectors. We begin with the diagonalizable case and then proceed to the general case, but we do not present a complete proof. Indeed, our interest here is not in JCF per se, but in one of its important applications. We devote the bulk of our attention in this book to showing how to apply JCF to solve systems of constant-coefficient first order differential equations, where it is a very effective tool. We cover all situations—homogeneous and inhomogeneous systems; real and complex eigenvalues. We also treat the closely related topic of the matrix exponential. Our discussion is mostly confined to the 2-by-2 and 3-by-3 cases, and we present a wealth of examples that illustrate all the possibilities in these cases (and of course, exercises for the reader). Table of Contents: Jordan Canonical Form / Solving Systems of Linear Differential Equations / Background Results: Bases, Coordinates, and Matrices / Properties of the Complex Exponential

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Springer Nature

Published Date

ISBN 10

3031023951

ISBN 13

9783031023958

The Induction Book

By: Steven H. Weintraub

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The Induction Book

By: Steven H. Weintraub

Every mathematician and student of mathematics needs a familiarity with mathematical induction. This volume provides advanced undergraduates and graduate students with an introduction and a thorough exposure to these proof techniques. 2017 edition.

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Page Count

129

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486821234

ISBN 13

9780486821238

Differential Forms

Theory and Practice

By: Steven H. Weintraub

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Differential Forms

Theory and Practice

By: Steven H. Weintraub

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Page Count

409

Publisher

Elsevier

Published Date

ISBN 10

0123946174

ISBN 13

9780123946171

Linear Algebra for the Young Mathematician

By: Steven H. Weintraub

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Linear Algebra for the Young Mathematician

By: Steven H. Weintraub

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Page Count

406

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470450844

ISBN 13

9781470450847

Differential Forms

Integration on Manifolds and Stokes's Theorem

By: Steven H. Weintraub

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Differential Forms

Integration on Manifolds and Stokes's Theorem

By: Steven H. Weintraub

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods. * Treats vector calculus using differential forms * Presents a very concrete introduction to differential forms * Develops Stokess theorem in an easily understandable way * Gives well-supported, carefully stated, and thoroughly explained definitions and theorems. * Provides glimpses of further topics to entice the interested student

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Page Count

276

Publisher

Academic Press

Published Date

ISBN 10

0127425101

ISBN 13

9780127425108

Galois Theory

By: Steven H. Weintraub

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Galois Theory

By: Steven H. Weintraub

Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, makes this book a more than worthwhile addition to the existing literature on Galois Theory. It will be appreciated by undergraduate and beginning graduate math majors.

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