Fundamental Concepts of Algebra

By Bruce E. Meserve

Book Overview

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.

• Format: Paperback
• Language: English
• ISBN: 0486614700
• ISBN13: 9780486614700
• Release Date: October 1982
• Publisher: Dover Publications
• Length: 320 Pages
• Weight: 0.76 lbs.
• Dimensions: 0.7" x 5.4" x 8.4"

Customer Reviews

Bruce, Almighty! :-)

Just kidding about the title. This book is about algebra - more about the concepts and the "language" of mathematics and in fact is written basically in usual math book format. Thats really important since it lets the novice see what goes where in the structure of typical "math problems." The first 4 chapters are about the basic arithmetic functions (up to polynomials) and the rest of the book gets into much more advanced topics - trig, derivatives, linear equations, and many other parts of the algebras. Keep in mind: this book is really from the early '50s from U. Ill. courses (stated in preface). Going from start to finish doesnt require calculus but its not enough to replace a formal calculus course. Also all excercises are "without solutions" - states so on back of book.

Thorough treatment of Algebra

I've enjoyed reading this book. Coverage is fairly broad and is presented as an advanced treatment of the typical topics in Algebra. While there is much overlap with texts on mathematical analysis, the treatment here is more focused on basic number and polynomial theory. The book is a nice recap of advanced precalculus topics and can be used as a refresher if you've been away from math for a while. Overall, it's a good, lightweight read. There are no solutions to problems but the exercises are pretty easy so I don't think this is a substantial problem.

interesting, readable, engaging, detailed..

First of all, I should say that I have just finished the first chapter of the book (including many of the exercises), which is called "Our Number System." I'm no expert, but I think this books gives a very interesting and rigorous account of various topics in algebra.