A Course in Abstract Analysis
A Course in Abstract Analysis

Author: John B. Conway

Publisher: American Mathematical Soc.

Published: 2012-10-03

Total Pages: 385

ISBN-13: 0821890832

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This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.

A Book of Abstract Algebra
A Book of Abstract Algebra

Author: Charles C Pinter

Publisher: Courier Corporation

Published: 2010-01-14

Total Pages: 402

ISBN-13: 0486474178

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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Abstract Algebra
Abstract Algebra

Author: Ronald Solomon

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 248

ISBN-13: 9780821847954

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This undergraduate text takes a novel approach to the standard introductory material on groups, rings, and fields. At the heart of the text is a semi-historical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. Avoiding excessive abstraction whenever possible, the text focuses on the central problem of studying the solutions of polynomial equations. Highlights include a proof of the Fundamental Theorem of Algebra, essentially due to Euler, and a proof of the constructability of the regular 17-gon, in the manner of Gauss. Another novel feature is the introduction of groups through a meditation on the meaning of congruence in the work of Euclid. Everywhere in the text, the goal is to make clear the links connecting abstract algebra to Euclidean geometry, high school algebra, and trigonometry, in the hope that students pursuing a career as secondary mathematics educators will carry away a deeper and richer understanding of the high school mathematics curriculum. Another goal is to encourage students, insofar as possible in a textbook format, to build the course for themselves, with exercises integrally embedded in the text of each chapter.

Foundations of Abstract Analysis
Foundations of Abstract Analysis

Author: Jewgeni H. Dshalalow

Publisher: Springer Science & Business Media

Published: 2012-11-09

Total Pages: 756

ISBN-13: 1461459621

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Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study. While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of the potential overload of new words, definitions, and concepts, the book (in its unique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded by informal discussions and blueprints followed by thorough details and supported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of the book, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. Prerequisites include advanced calculus, linear algebra, complex variables, and calculus based probability.

Abstract Comics
Abstract Comics

Author: Andrei Molotiu

Publisher:

Published: 2009

Total Pages: 242

ISBN-13:

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Collects comic stories that feature abstract art from R. Crumb, Victor Moscoso, Bill Shut, Gary Panter, and other artists.

The New Bill James Historical Baseball Abstract
The New Bill James Historical Baseball Abstract

Author: Bill James

Publisher: Simon and Schuster

Published: 2010-05-11

Total Pages: 1026

ISBN-13: 1439106932

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When Bill James published his original Historical Baseball Abstract in 1985, he produced an immediate classic, hailed by the Chicago Tribune as the “holy book of baseball.” Now, baseball's beloved “Sultan of Stats” (The Boston Globe) is back with a fully revised and updated edition for the new millennium. Like the original, The New Bill James Historical Baseball Abstract is really several books in one. The Game provides a century's worth of American baseball history, told one decade at a time, with energetic facts and figures about How, Where, and by Whom the game was played. In The Players, you'll find listings of the top 100 players at each position in the major leagues, along with James's signature stats-based ratings method called “Win Shares,” a way of quantifying individual performance and calculating the offensive and defensive contributions of catchers, pitchers, infielders, and outfielders. And there's more: the Reference section covers Win Shares for each season and each player, and even offers a Win Share team comparison. A must-have for baseball fans and historians alike, The New Bill James Historical Baseball Abstract is as essential, entertaining, and enlightening as the sport itself.

Problems in Abstract Algebra
Problems in Abstract Algebra

Author: A. R. Wadsworth

Publisher: American Mathematical Soc.

Published: 2017-05-10

Total Pages: 290

ISBN-13: 1470435837

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This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.