Roger W Oster

Broschiertes Buch

Mastering Algebra

An Axiomatic Approach (Second Edition)

Beschreibung

* 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 [e-mail]. 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.)

Autor

- 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 [e-mail]

Produktdetails

• 2nd edition
• Seitenzahl: 178
• Erscheinungstermin: 14. Juli 2018
• Englisch
• Abmessung: 254mm x 178mm x 10mm
• Gewicht: 318g
• ISBN-13: 9780998713304
• ISBN-10: 0998713309
• Artikelnr.: 72897936