Mastering Algebra: An Axiomatic Approach (Second Edition)

Mastering Algebra: An Axiomatic Approach (Second Edition)

by Roger W Oster

Paperback(Second)

$19.85
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Product Details

ISBN-13: 9780998713304
Publisher: Oster
Publication date: 08/02/2018
Edition description: Second
Pages: 178
Product dimensions: 7.00(w) x 10.00(h) x 0.38(d)

About the Author

• I was born in Newark, New Jersey and spent my elementary school years growing up in Keansburg, NJ. It was a time when the beach there was closed to swimmers, and the boardwalk, although badly splintered, was still open to barefoot children. It was a time when the penny arcade rattled and rang with the clacks and dings of pinball wizards performing their magic (an "(rt" I was exceedingly good at). I spent my high school years in Tunkhannock, Pennsylvania, a small, one-street-light farming town (it was quiet).
• Although I (along with my siblings and nephew) grew up poor in Keansburg, I always found a way to satisfy my appetite for logic, mathematics, art and poetry. At the age of eight I made a chessboard out of paper and cardboard and began a chess-game correspondence with another player through the FIDE (the world chess federation). Unfortunately, I soon drew the ire of my opponent because I could rarely afford the stamps, and on those occasions when I could scrape up the change--by collecting soda bottles to return--a chocolate covered Ring Ding, or a game of pinball was always more immediately gratifying. Nevertheless, I would eventually go on to attain the rank of chess master and learn to play simultaneous chess games blindfolded.
• While in the 9th grade, on the other hand, I proved that there are three pyramids in a rectangular prism of equal base and height. Although that in and of itself may not be particularly remarkable, the impulse to do it came from my math teacher who claimed that the only way that this could be proved was by pouring sand from the pyramid to the prism and observing that the prism was exactly full after the third pour. I found his declaration that it could not be proved in any other way difficult to believe and so I immediately began work to prove it on paper with pencil. Although I would like to say that I had amazing and wonderful math teachers in high school, my teacher was not amused, and dismissed my work out of hand. Nevertheless, I gained an important lesson. I learned that I could self-improve myself by continuously exercising my mind to visualize objects in three dimensions, by learning how to use my left hand to accomplish feats (such as eating, writing, nailing, etc.) that I would have normally done with my right hand, and by practicing yoga, all of which, I would like to suggest to my readers, is a very reasonable prescription for self-improving one's mind, body and spirit.
• All that aside, I was always good at math; however, there was one aspect about algebra that troubled me in high school more than any other. What was the purpose of the associative rules of addition and multiplication [i.e., what was the purpose of having rules such as (2+3)+4=2+(3+4) and (2x3)x4=2x(3x4)]? Why, I thought to myself, was I being bothered with rules that are so ridiculously obvious? The rule itself didn't confuse me, what confused me is that my teacher thought it was important enough to not only acknowledge it, but to acclaim it. Regardless, I was always good with patterns-and the axioms of algebra are all about patterns-so, not knowing the "why" to this question never affected my grade. I ignored it and forgot all about it.
- It would not be until years later that I would finally answer that question in the form of the book "Mastering Algebra: An Axiomatic Approach". Which not only answers that question, but many other troubling math questions as well. I hope you will find the book interesting, informative and an overall good read.
• I am currently working on my collection of poems which I have written over the years, and a science fiction thriller involving tin men, space monkeys and chemistry (or some such), which, I admit, is long overdue. Please stay tuned and visit my website at rogeroster.com for more information regarding this book and any updates. You may email me regarding any comments about my writings or to just leave a note at Roger@rogeroster.com

Table of Contents

Introduction …………………………………………………………… 1

Chapter 1: Preliminaries ……………………………………….…….. 9

Chapter 2: The Axioms of Comparison ……………………………… 37

Chapter 3: The Axioms of Addition ………………………………..… 49

Chapter 4: The Axioms of Multiplication and Distribution …....…….. 77

Chapter 5: Irrational and Real Numbers; Roots and Exponents ….. 117

Chapter 6: Continued Study …………..……….……………………… 129

Solutions to Chapter Exercises ………………………………………... 149

Appendix A: Answers to Star (✰) Questions ………………..……….. 159

Appendix B: Constructing the Set ………………….............……….. 163

Appendix C: List of Axioms, Theorems & Definitions …….………. 164

Acknowledgements ……………………………………………….……. 169

Bibliography ………………………………………….…………………. 170

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