Fundamental Concepts of Algebra

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.

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.

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.