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Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there
CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
This traditional text is intended for mainstream one- or two-semester differential equations courses taken by undergraduates majoring in engineering, mathematics, and the sciences. Written by two of the world's leading authorities on differential equations, Simmons/Krantz provides a cogent and accessible introduction to ordinary differential equations written in classical style. Its rich variety of modern applications in engineering, physics, and the applied sciences illuminate the concepts and techniques that students will use through practice to solve real-life problems in their careers. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
(Originally Published by Houghton Mifflin Company, 2004) There is a national consensus that teachers who teach middle-grades and elementary mathematics need deeper and broader exposure to mathematics in both their undergraduate and in their graduate studies. The Mathematics Education of Teachers, published by The Conference Board on the Mathematical Sciences, recommends 21 semester hours of mathematics for prospective teachers of middle-grades mathematics. In several states pre-service teachers preparing to teach middle-grades mathematics and pre-service teachers preparing to teach elementary school must complete 6- 9 semester hours of mathematics content at the junior-senior level. Graduate schools across the nation have developed special programs for educators who specialize in teaching mathematics to elementary school children and to middle grades students. However, there is a paucity of text materials to support those efforts at junior-senior level and graduate level courses. Faculty members must choose to teach yet another course out of one of the “Mathematics for Teachers” texts that have formed the basis of the curriculum for the last two decades. These texts tend to treat a very limited set of topics on a somewhat superficial level. Alternatively, faculty members can use mathematics textbooks written primarily for students majoring in mathematics or the sciences. Neither the topic choice nor the pedagogical style of these texts is optimal for pre-service and in-service teachers of middle grades and elementary mathematics. Discrete Mathematics for Teachers is a text designed to fill this void. The topic is right. Discrete mathematics provides a rich and varied source of problems for exploration and communication, expands knowledge of mathematics in directions related to elementary and middle school curricula, and is easily presented using our best understanding of the ways that mathematics is learned and taught. The presentation is right. In the spirit of NCTM’s Principles and Standards for School Mathematics, topics are presented with careful attention to the best traditions of problem solving, reasoning and proof, communication, connections with other disciplines and other areas of mathematics, and varied modes of representation.
This new text presents calculus with solid mathematical precision but with an everyday sensibility that puts the main concepts in clear terms. It is rigorous without being inaccessible and clear without being too informal--it has the perfect balance for instructors and their students. Also available in a late transcendentals version (0-7167-6911-5).
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.
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.
Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.
From one of the premier authors in higher education comes a new linear algebra textbook that fosters mathematical thinking, problem-solving abilities, and exposure to real-world applications. Without sacrificing mathematical precision, Anton and Busby focus on the aspects of linear algebra that are most likely to have practical value to the student while not compromising the intrinsic mathematical form of the subject. Throughout Contemporary Linear Algebra, students are encouraged to look at ideas and problems from multiple points of view.
Redesigned for the 11th edition of Contemporary Abstract Algebra, Student Solutions Manual, written by the author, has comprehensive solutions for all odd-numbered exercises and a large number of even-numbered exercises. This Manual also offers many alternative solutions to those appearing in the text. These will provide the student with a better understanding of the material. This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra, Eleventh Edition and the only official one. It is designed to supplement the text and the author's original approach to instruction.