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A Journey into Mathematics: An Introduction to Proofs / Edition 1

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Overview

Rotman, Joseph, Journey into Mathematics: The World of Proof Prompting readers to do mathematics, not merely read about it, this proactive book has users reading and writing proofs at the outset. Complete proofs are given from the start, and coverage begins with elementary mathematics to allow focus on the writing and reading of proofs without the distraction of absorbing new ideas simultaneously. Contains material that is familiar to calculus readers (i.e., induction, binomial theorem, polygonal, using the Diophantine parametrization of the circle by rational functions to solve trigonometric identities, etc.), and engages readers throughout with interesting expositions using history, etymology, and humorous asides.
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Editorial Reviews

Booknews
Intended as a textbook for a one-semester course between calculus and the first courses in abstract algebra and real variables. Starts with concepts such as trigonometry and integration that are already to familiar to students at this level, so that they can concentrate on the mechanics of writing proofs. Synthetic geometry is then used as an inroad to introducing convergence of sequences. The text ends with a discussion of complex numbers, De Moivre's Theorem, and irrationalities. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780138423605
  • Publisher: Pearson
  • Publication date: 8/13/1997
  • Edition number: 1
  • Pages: 237
  • Product dimensions: 6.24 (w) x 9.32 (h) x 0.68 (d)

Table of Contents

Preface
To the Reader
To the Instructor
1 Setting Out 1
Induction 1
Binomial Coefficients 22
2 Things Pythagorean 31
Area 31
The Pythagorean Theorem 45
Pythagorean Triples 56
The Method of Diophantus 64
Trigonometry 72
Integration 86
3 Circles and [pi] 98
Approximations 98
The Area of a Disk 107
The Circumference of a Disk 117
Sequences 134
4 Polynomials 149
Quadratics 149
Complex Numbers 160
De Moivre's Theorem 171
Cubics and Quartics 183
Irrationalities 204
Epilogue 213
Bibliography 215
Glossary of Logic 217
Propositional Calculus 217
Proofs 222
Set Theory 224
Quantifiers 228
Index 233
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