Journey into Mathematics: An Introduction to Proofs [NOOK Book]

Overview


Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics.
Journey into Mathematics offers a coherent story, with intriguing ...
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Journey into Mathematics: An Introduction to Proofs

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Overview


Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics.
Journey into Mathematics offers a coherent story, with intriguing historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers.
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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: 9780486151687
  • Publisher: Dover Publications
  • Publication date: 12/21/2012
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 256
  • Sales rank: 445,576
  • File size: 9 MB

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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