Introduction to Proof in Abstract Mathematics

Author: Andrew Wohlgemuth

Publisher: Courier Corporation

ISBN: 0486141683

Category: Mathematics

Page: 384

View: 5005

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This undergraduate text teaches students what constitutes an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. 1990 edition.
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An Introduction to Algebraic Structures

Author: Joseph Landin

Publisher: Courier Corporation

ISBN: 0486150410

Category: Mathematics

Page: 272

View: 4852

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This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
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A Combinatorial Introduction to Topology

Author: Michael Henle

Publisher: Courier Corporation

ISBN: 9780486679662

Category: Mathematics

Page: 310

View: 9063

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Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
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Number Theory

Author: George E. Andrews

Publisher: Courier Corporation

ISBN: 0486135101

Category: Mathematics

Page: 288

View: 5836

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Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more
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The Nuts and Bolts of Proofs

An Introduction to Mathematical Proofs

Author: Antonella Cupillari

Publisher: Academic Press

ISBN: 0123822173

Category: Mathematics

Page: 283

View: 3826

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The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. New chapter on proof by contradiction New updated proofs A full range of accessible proofs Symbols indicating level of difficulty help students understand whether a problem is based on calculus or linear algebra Basic terminology list with definitions at the beginning of the text
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Advanced Number Theory

Author: Harvey Cohn

Publisher: Courier Corporation

ISBN: 9780486640235

Category: Mathematics

Page: 276

View: 2038

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"A very stimulating book ... in a class by itself." — American Mathematical Monthly Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject. The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups. Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints. In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory.
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Elements of Abstract Algebra

Author: Allan Clark

Publisher: Courier Corporation

ISBN: 0486140350

Category: Mathematics

Page: 224

View: 1451

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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.
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An Introduction to Symbolic Logic

Author: Langer

Publisher: Courier Corporation

ISBN: 9780486601649

Category: Mathematics

Page: 384

View: 9636

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Famous classic has introduced countless readers to symbolic logic with its thorough and precise exposition. Starts with simple symbols and conventions and concludes with the Boole-Schroeder and Russell-Whitehead systems. No special knowledge of mathematics necessary. "One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.
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Introduction to the Theory of Abstract Algebras

Author: Richard S Pierce

Publisher: Courier Corporation

ISBN: 0486799425

Category: Mathematics

Page: 160

View: 9330

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Suitable for introductory graduate-level courses and independent study, this text explores major themes of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebras. Includes problems and a bibliography. 1968 edition.
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Introduction to Field Theory

Author: Iain T. Adamson

Publisher: Courier Corporation

ISBN: 0486462668

Category: Mathematics

Page: 181

View: 2288

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Acclaimed by American Mathematical Monthly as "an excellent introduction,"this treatment ranges from basic definitions to important results and applications, introducing both the spirit and techniques of abstract algebra. It develops the elementary properties of rings and fields, explores extension fields and Galois theory, and examines numerous applications. 1982 edition.
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