Mastering Algebra: An Axiomatic Approach - Softcover

Oster, Roger W

Softcover

ISBN 10: 0998713309 ISBN 13: 9780998713304

Publisher: Oster, 2018

Synopsis

This easy-to-read, relatively brief, and well-thought-out book takes a different approach to learning algebra: instead of just mindlessly practicing a (seemingly) random and baffling collection of rules, this book explains the "why" of the rules--it clearly explains the function, purpose and necessity of algebra's axioms, definitions and theorems while ignoring all the superfluous and often confusing "rules" found in many modern algebra textbooks (like the butterfly rule, the invert-and-multiply rule, the cross-multiply rule, P.E.M.D.A.S., and so on and on.). Consequently, the number of rules needed to understand and perform algebra is reduced to the bare-minimum. This book was also designed to take advantage of your innately creative and logical abilities and to show you how to effectively utilize the repetitive characteristics--the patterns, if you will--of algebra's axioms to quickly master the subject. 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, you will not only surpass your goals with this book, but also and above all you will become a master of algebra: you will (1) understand the entire structure of algebra; (2) learn how to do mathematical proofs; (3) acquire mechanical proficiency and the skills to confidently tackle more advanced courses in mathematics; (4) bolster your powers of critical thinking; and (5) develop a deep admiration for mathematical structures and for the intuitive and logical techniques that drive the creation of all mathematics. This edition has almost 40% more material than the first edition.·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, multiplicative inverses, and distribution.·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 and explains logarithms; how to logically solve simultaneous equations and inequalities; functions and graphs; and concludes with a brief discussion of 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 for every problem is included in the back pages. 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.)

About this title

From the Author

    This is the second (and final) edition of this title. It explains the function of algebra's axioms, their purpose and necessity, along with their logical consequences, and it exploits your creative and logical skills for you to effectively utilize the patterns inherent in the axioms to not only master algebra, but to also gain a deep appreciation for the logical structures that govern all of mathematics.     This book was four years in the making. Most of the problems that I have had writing this math book were with formatting the equations, efficiently utilizing page space and choosing fonts that would be aesthetically pleasing, while at the same time would render the mathematical information in a straight forward and very readable fashion. Beyond that, proof-reading and correcting a math book always requires a considerable, focused effort.      If you have any comments or questions please send them to Roger@rogeroster.com. For the latest updates regarding this and other published works please visit rogeroster.com.

About the Author

Roger W. Oster is a magna cum laude graduate of the University of Pittsburgh. After receiving his degree in mathematics, he went on to complete two years of post-graduate studies in education and German. He is a certified high school mathematics teacher of twenty years.

Edition details

• Publisher: Oster
• Publication date: 2018
• ISBN 10: 0998713309
• ISBN 13: 9780998713304
• Binding: Paperback
• Language: English
• Edition number: 2
• Number of pages: 176