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Conquering Mathematics – tekijä: Lloyd…
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Conquering Mathematics (vuoden 1991 painos)

– tekijä: Lloyd Motz

JäseniäKirja-arvostelujaSuosituimmuussijaKeskimääräinen arvioKeskustelut
201868,939--
We have designed and written this book. not as a text nor for the professional mathematician. but for the general reader who is naturally attracted to mathematics as a great intellec­ tual challenge. and for the special reader whose work requires him to have a deeper understanding of mathematics than he acquired in school. Readers in the first group are drawn to mental recreational activities such as chess. bridge. and various types of puzzles. but they generally do not respond enthusiastically to mathematics because of their unhappy learning experiences with it during their school days. The readers in the secondgrouptum to mathematics as a necessity. but with painful resignation and considerable apprehension regarding their abilities to master the branch ofmathematics they need in their work. In either case. the fear of and revulsion to mathematics felt by these readers usually stem from their earlier frustrating encounters with it. vii viii PREFACE This book will show these readers that these fears, frustrations, and general antipathy are unwarranted, for, as stated, it is not a textbook full of long, boring proofs and hundreds of problems, rather it is an intellectual adventure, to be read with pleasure. It was written to be easily accessible and with concern for the mental tranquilityofthe reader who willexperience considerable fulfillment when he/she sees the simplicity of basic mathematics. The emphasis throughout this book is on the clear explanation of mathematical con­ cepts.… (lisätietoja)
Jäsen:tonygreenpersonal
Teoksen nimi:Conquering Mathematics
Kirjailijat:Lloyd Motz
Info:Basic Books (1991), Hardcover, 305 pages
Kokoelmat:Oma kirjasto
Arvio (tähdet):
Avainsanoja:Science; Mathematics

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Conquering Mathematics (tekijä: Lloyd Motz)

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"Since all mathematics is essentially arithmetic in various guises..." What? [viii] The book is written both for those attracted to intellectual challenges (puzzles, or bridge games) and for those who must turn to maths as a necessity in their work. Yet the author means to fully develop an understanding drawn from the "aspects" of numbers (ordinal and cardinal) through the categories of them: integers, fractions, irrational (algebraic and transcendental), prime and complex. He concludes the section on maths with a discussion of the different bases (e.g. base 10) and discusses logarithms.

The next two chapters are on algebra, developing the logical steps from abstraction to representation and the function concept. "The graph (the plot of the dependence of one quantity on another) shows the relationship between the two entities being plotted and thus defines a function." [x] "The function leads to the polynomial and the algebraic equation", he explains by illustrating the contour of an imaginary road.

The next three chapters are on geometry--from points on a plane, to triangles, and the angle concept. The trigonometric properties of angles can be deduced from the unit circle. "This method of introducing trigonometry removes all mystery associated with it."

In the penultimate chapter, the authors show how differential calculus arose simultaneously from Newton's study of the instantaneous speed of a body, and Leibnitz's analysis of the rate of change of a function with respect to the entity on which it depends. The Epilogue discusses the role of maths in the sciences: "Physics and mathematics are thus coupled in a never-ending dance which may produce wonders we cannot even dream of now. It is exciting and, in a very abstract sense, beautiful that two intellectual disciplines, one probing the universe and the other constructing pure thought, without reference to the universe, can produce such magical results." Magical.
  keylawk | Jan 9, 2016 |
ei arvosteluja | lisää arvostelu
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Englanninkielinen Wikipedia (1)

We have designed and written this book. not as a text nor for the professional mathematician. but for the general reader who is naturally attracted to mathematics as a great intellec­ tual challenge. and for the special reader whose work requires him to have a deeper understanding of mathematics than he acquired in school. Readers in the first group are drawn to mental recreational activities such as chess. bridge. and various types of puzzles. but they generally do not respond enthusiastically to mathematics because of their unhappy learning experiences with it during their school days. The readers in the secondgrouptum to mathematics as a necessity. but with painful resignation and considerable apprehension regarding their abilities to master the branch ofmathematics they need in their work. In either case. the fear of and revulsion to mathematics felt by these readers usually stem from their earlier frustrating encounters with it. vii viii PREFACE This book will show these readers that these fears, frustrations, and general antipathy are unwarranted, for, as stated, it is not a textbook full of long, boring proofs and hundreds of problems, rather it is an intellectual adventure, to be read with pleasure. It was written to be easily accessible and with concern for the mental tranquilityofthe reader who willexperience considerable fulfillment when he/she sees the simplicity of basic mathematics. The emphasis throughout this book is on the clear explanation of mathematical con­ cepts.

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