Fundamental Concepts of Algebra (Dover Books on Mathematics) by Bruce E. Meserve (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There is a golden idea in the first few pages. The rest of the book and the technical knowledge is just bonus.

⭐Somewhere after the algebra most people know but before Real And Complex Analysis (another awesome Dover title), is this, the ‘Fundamental Concepts Of Algebra’. What a stunning balance of a diamond-hard logical approach to dissecting number and a humane and readable book. I’m a musician who happens to love math so I’m not an expert or very widely read, but having encountered a plethora of books near and around this subject, I’ve found this one has kept my attention where others have made me want something more accessible and yet more gritty and fundamental. Because this book takes what is for me a rigorous step-by-step approach, I find along the way answers to questions I’ve had since my schooldays but suppressed because school wasn’t about learning, but about trying not to be seen. I wish I’d had this back then. P.S. Dover books are sexy.

⭐This is the companion book to fundamental concepts of geometry by B. Meserve. It is well writtenand has an historical viewpoint of the subject. Many excellent topics.

⭐school book

⭐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.

⭐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.

⭐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.

⭐Good

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