Mastering Algebra: An Axiomatic Approach (Second Edition) (Paperback)
* This easy-to-read and well-thought-out book takes a different approach to learning algebra: instead of just robotically practicing the rules of algebra, this book explains the "why" of the rules. It explains the function of all the axioms and definitions of algebra along with their logical consequences while ignoring all the superfluous and often confusing rules found in so many other algebra texts (like the butterfly rule, invert and multiply rule, cross multiply rule, P.E.M.D.A.S., etc.). It was designed for you to take advantage of your innate creative and logical abilities and for you to effectively utilize the repetitive characteristics--the patterns, if you will--of algebra's axioms to not only master algebra, but to also gain a deep understanding of and appreciation for the intuitive and logical structures that govern the creation of all mathematics.
- The first chapter touches on the prerequisites that are fundamental to almost every branch of mathematics: the nature of numbers, logic, and set theory.
- The second chapter discusses and explains the axioms of comparison: equality and inequality.
- The third chapter discusses and explains the axioms of addition: closure, commutativity, associativity, the existence of the number 0, and additive inverses.
- The fourth chapter discusses and explains the axioms of multiplication: closure, commutativity, associativity, the existence of the number 1, and multiplicative inverses.
- The fifth chapter takes us deeper into algebra and discusses and explains rational and irrational numbers, roots and exponents.
- The final chapter takes us deeper still and discusses logarithms; the proper way to solve multiple equalities and inequalities; functions and graphs; and touches on complex numbers and higher mathematics.
*Each chapter is followed by a series of problems to reinforce your memory and understanding, and a complete-solutions section is included in the back pages.
* Whether you're a high school student struggling to understand Algebra II (this book is not recommended for students who have not completed a course in Algebra I and geometry); a college student preparing to take a course in higher mathematics; a person who would just like to learn algebra without performing reams of problems; or an educator looking for ways to better help your students, this book was designed to clearly explain the rationale behind algebra. You will (1) understand the fundamental structure of algebra; (2) learn what proofs are, how they relate to the axioms and how to use them; (3) acquire the skills to confidently tackle more advanced courses in mathematics; (4) gain a deep appreciation for how mathematicians perceive mathematics and the difficulties they encounter; (5) bolster your powers of critical thinking.
* This second edition includes almost 40% more material than the first, covering topics about logarithms, solving equations and inequalities, functions, and complex numbers. There are many more pages of practice problems along with their solutions.
NOTE: To all of my many readers who have purchased, and have proof of purchase of, the first edition of this book prior to August 1, 2018 and have an original copy of the first edition to exchange, please email me at Roger@RogerOster.com. I will be happy to make arrangements for you to receive a free copy of the second edition. (Please accept my sincerest apologies, but this courtesy is not extended to book sellers.)