Beginning with algebraic structures in general, the author covers natural numbers, rings and fields, vector spaces, polynomials, real and complex number fields, linear operators, many other topics. Includes over 1,300 carefully selected exercises. 1965 edition. List of Symbols.
Here's a sample of other books in this Dover category
Fundamental Concepts of Algebra by Bruce E. Meserve Presents the fundamental concepts of algebra illustrated by numerous examples, and in many cases, suitable sequences of exercises — without solutions. Preface. Index. Bibliography. 39 figures.
Abstract Algebra by W. E. Deskins 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.
The Skeleton Key of Mathematics: A Simple Account of Complex Algebraic Theories by D. E. Littlewood Straightforward explanation of abstract principles common to science and math, including Euclid's algorithm; congruences; polynomials; complex numbers and algebraic fields; algebraic integers, ideals, and p-adic numbers; groups; Galois theory; algebraic geometry; more.
Basic Algebra II: Second Edition by Nathan Jacobson This classic text and standard reference comprises all subjects of a first-yeargraduate-level course, including in-depth coverage of groups and polynomials and extensive use of categories and functors. 1989 edition.
Basic Algebra I: Second Edition by Nathan Jacobson A classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.
Probabilities on Algebraic Structures by Ulf Grenander This systematic approach covers semi-groups, groups, linear vector spaces, and algebra. It states and studies fundamental probabilistic problems for these spaces, focusing on concrete results. 1963 edition.
Challenging Problems in Algebra by Alfred S. Posamentier, Charles T. Salkind Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.
Boolean Algebra by R. L. Goodstein This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
Algebraic Equations: An Introduction to the Theories of Lagrange and Galois by Edgar Dehn This text focuses on the basics of algebraic theory, giving detailed explanations of integral functions, permutations, and groups, and Lagrange and Galois theory. Many numerical examples with complete solutions. 1930 edition.
Linear Algebra by Georgi E. Shilov Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, and more.
Elements of Abstract Algebra by Allan Clark 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.
Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.
