Introduction to Modern Algebra and Matrix Theory

Second Edition
Author: O. Schreier,E. Sperner
Publisher: Courier Corporation
ISBN: 0486278654
Category: Mathematics
Page: 400
View: 7013
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This unique text provides students with a basic course in both calculus and analytic geometry — no competitive editions cover both topics in a single volume. Its prerequisites are minimal, and the order of its presentation promotes an intuitive approach to calculus. Algebraic concepts receive an unusually strong emphasis. Numerous exercises appear throughout the text. 1951 edition.

Elementary Matrix Theory


Author: Howard Eves
Publisher: Courier Corporation
ISBN: 0486150275
Category: Mathematics
Page: 352
View: 3887
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Concrete treatment of fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, and similarity and congruence. Each chapter has many excellent problems and optional related information. No previous course in abstract algebra required.

Algebra

Aus dem Englischen übersetzt von Annette A’Campo
Author: Michael Artin
Publisher: Birkhäuser
ISBN: 9783764359386
Category: Mathematics
Page: 705
View: 9075
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Important though the general concepts and propositions may be with which the modem and industrious passion for axiomatizing and generalizing has presented us, in algebra perhaps more than anywhere else, nevertheless I am convinced that the special problems in all their complexity constitute the stock and core of mathematics, and that to master their difficulties requires on the whole the harder labor. HERMANN WEYL Die Arbeit an diesem Buch begann vor etwa zwanzig Jahren mit Aufzeichnungen zur Ergänzung meiner Algebravorlesungen. Ich wollte einige konkrete Themen, wie Symmetrie, lineare Gruppen und quadratische Zahlkörper, ausführlicher be­ handeln als dies im vorgesehenen Text der Fall war, und darüberhinaus wollte ich den Schwerpunkt in der Gruppentheorie von den Permutationsgruppen auf Matrixgruppen verlagern. Ein anderes ständig wiederkehrendes Thema, nämlich Gitter, sind spontan aufgetaucht. Ich hoffte, der konkrete Stoff könne das Interesse der Studenten wecken und gleichzeitig die Abstraktionen verständlicher machen, kurz gesagt, sie sollten weiter kommen, indem sie beides gleichzeitig lernten. Das bewährte sich gut. Es dauerte einige Zeit, bis ich entschieden hatte, welche Themen ich behandeln wollte, und allmählich verteilte ich mehr und mehr Aufzeichnungen und ging schließlich dazu über, die ganze Vorlesung mit diesem Skript zu bestrei­ ten. Auf diese Weise ist ein Buch entstanden, das, wie ich meine, etwas anders ist als die existierenden Bücher. Allerdings haben mir die Probleme, die ich damit hatte, die einzelnen Teile des Buches zu einem Ganzen zusammenzufügen, einige Kopfschmerzen bereitet; ich kann also nicht empfehlen, auf diese Art anzufangen, ein Buch zu schreiben.

Abstract Algebra


Author: W. E. Deskins
Publisher: Courier Corporation
ISBN: 0486158462
Category: Mathematics
Page: 656
View: 4171
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Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problems.

Matrix Theory


Author: Joel N. Franklin
Publisher: Courier Corporation
ISBN: 0486136388
Category: Mathematics
Page: 304
View: 2076
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Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.

Advanced Number Theory


Author: Harvey Cohn
Publisher: Courier Corporation
ISBN: 9780486640235
Category: Mathematics
Page: 276
View: 1992
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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.

Modern Higher Algebra


Author: Abraham Adrian Albert
Publisher: Courier Dover Publications
ISBN: 0486823849
Category: Mathematics
Page: 336
View: 7633
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Originally published: Chicago: University of Chicago Press, 1937.

Algebraic Logic


Author: Paul R. Halmos
Publisher: Courier Dover Publications
ISBN: 0486810410
Category: Mathematics
Page: 272
View: 9272
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Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic and polyadic algebras, these articles are essentially self-contained and accessible to a general mathematical audience, requiring no specialized knowledge of algebra or logic. Part One addresses monadic algebras, with articles on general theory, representation, and freedom. Part Two explores polyadic algebras, progressing from general theory and terms to equality. Part Three offers three items on polyadic Boolean algebras, including a survey of predicates, terms, operations, and equality. The book concludes with an additional bibliography and index.

Mathematical Brain Benders

2nd Miscellany of Puzzles
Author: Stephen Barr
Publisher: Courier Corporation
ISBN: 0486242609
Category: Games
Page: 224
View: 8476
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Challenge yourself with over 100 fresh paradoxes, puzzles, riddles, conundrums, word and number games for the jaded, skeptical puzzlist. Over 100 pages of comprehensive answers. Approximately 300 illustrations. "Excellent collection of unusual, offbeat, and completely original puzzles." ? Scientific American.

An Introduction to the Theory of Linear Spaces


Author: Georgi E. Shilov,Richard A. Silverman
Publisher: Courier Corporation
ISBN: 0486139433
Category: Mathematics
Page: 320
View: 6832
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Introductory treatment offers a clear exposition of algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. Numerous examples illustrate many different fields, and problems include hints or answers. 1961 edition.

Introduction to Linear Algebra


Author: Marvin Marcus,Henryk Minc
Publisher: Courier Corporation
ISBN: 9780486656953
Category: Mathematics
Page: 261
View: 1995
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Rigorous, self-contained introduction at undergraduate level covers vector spaces and linear transformations, linear equations and determinants, characteristic roots. Includes 16 sets of true-false quizzes and exercises — with worked-out solutions — a complete theory of permutations and much more.

A Combinatorial Introduction to Topology


Author: Michael Henle
Publisher: Courier Corporation
ISBN: 9780486679662
Category: Mathematics
Page: 310
View: 8813
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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.

An Introduction to Mathematical Modeling


Author: Edward A. Bender
Publisher: Courier Corporation
ISBN: 9780486411804
Category: Mathematics
Page: 256
View: 7958
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Accessible text features over 100 reality-based examples pulled from the science, engineering and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

Introduction to Linear Algebra and Differential Equations


Author: John W. Dettman
Publisher: Courier Corporation
ISBN: 9780486651910
Category: Mathematics
Page: 404
View: 4409
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Excellent introductory text for students with one year of calculus. Topics include complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions and boundary-value problems. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

Abstract Algebra and Solution by Radicals


Author: John Edward Maxfield,Margaret W. Maxfield
Publisher: Courier Corporation
ISBN: 9780486671215
Category: Mathematics
Page: 209
View: 9334
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Easily accessible undergraduate-level text covers groups, polynomials, Galois theory, radicals, much more. Features many examples, illustrations and commentaries as well as 13 appendices. 1971 edition.

Inversive Geometry


Author: Frank Morley
Publisher: Courier Corporation
ISBN: 0486493393
Category: Mathematics
Page: 288
View: 8999
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This introduction to algebraic geometry makes particular reference to the operation of inversion. Topics include Euclidean group; inversion; quadratics; finite inversive groups; parabolic, hyperbolic, and elliptic geometries; differential geometry; and more. 1933 edition.

Foundations of Modern Analysis


Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486640624
Category: Mathematics
Page: 250
View: 4375
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Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

A Survey of Matrix Theory and Matrix Inequalities


Author: Marvin Marcus,Henryk Minc
Publisher: Courier Corporation
ISBN: 9780486671024
Category: Mathematics
Page: 180
View: 9030
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Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography.

How to Solve Applied Mathematics Problems


Author: B. L. Moiseiwitsch
Publisher: Courier Corporation
ISBN: 0486285227
Category: Mathematics
Page: 336
View: 6053
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This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.

Introduction to Modern Optics


Author: Grant R. Fowles
Publisher: Courier Corporation
ISBN: 048613492X
Category: Science
Page: 336
View: 7388
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A complete basic undergraduate course in modern optics for students in physics, technology, and engineering. The first half deals with classical physical optics; the second, quantum nature of light. Solutions.