Fundamental Concepts of Algebra (Dover Books on Mathematics) (Paperback)
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This uncommonly interesting volume has been a favorite for 30 years, and is now available for the first time in a modestly priced paperback edition. Beginning with the fundamentals of numbers and sets, the author clearly guides the reader through the often discouraging complexities of algebra. Meserve presents the fundamental concepts of algebra illustrated by numerous examples- and, in many cases, the theory is further explicated by suitable sequences of exercises.
The author's aim is to introduce the concepts of higher mathematics while bringing the reader to a more thorough understanding of elementary mathematics. His lucid explanations cover these major areas:
OUR NUMBER SYSTEM: Sets, Cardinal Numbers, Order Relations, Real Numbers, Fields and Number Systems, more.
THEORY OF NUMBERS: Divisibility, Prime Numbers, Bases, Division Algorithm, Decimal Notations, Linear Congruences, more.
THEORY OF POLYNOMIALS: Rational Functions, Irreducible Polynomials, Functions, Limits, Continuity, Derivatives, more.
THEORY OF EQUATIONS: Zeros of a Polynomial, Change of a Variable, Number of Roots, Quartic Equations, more.
DETERMINANTS AND MATRICES: Historical Development, Permutations, Inversions, Transpositions, Cramer's Rule, more.
CONSTRUCTIONS: The Algebraic Viewpoint, Classical Constructions, Mechanical Angle Trisectors, Linkages, more.
GRAPHICAL REPRESENTATIONS: Euclidean and Complex Spaces, Conic Sections, Quadric Surfaces, Curve Tracing, more.
While intended for students who have previously studied college mathematics through calculus, this book has also been successfully used where calculus was not a prerequisite. It provides a very easily followed presentation and may also be used as an introductory or supplementary textbook. For prospective teachers of secondary mathematics, for students preparing for specialized advanced undergraduate courses in mathematics, and for the general reader in search of a firmer grasp of the essentials of algebra, there is no better, more helpful guide than Meserve.