Math Proofs Demystified

by
Edition: 1st
Format: Paperback
Pub. Date: 2005-05-13
Publisher(s): McGraw-Hill Education
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Summary

Almost every student has to study some sort of mathematical proofs, whether it be in geometry, trigonometry, or with higher-level topics. In addition, mathematical theorems have become an interesting course for many students outside of the mathematical arena, purely for the reasoning and logic that is needed to complete them. Therefore, it is not uncommon to have philosophy and law students grappling with proofs. This book is the perfect resource for demystifying the techniques and principles that govern the mathematical proof area, and is done with the standard "Demystified" level, questions and answers, and accessibility.

Author Biography

Stan Gibilisco (Chippewa Falls, WI) is a best-selling Demystified author. His prior titles include The TAB Encyclopedia of Electronics for Technicians, Teach Yourself Electricity and Electronics, and, most recently, Geometry Demystified.

Table of Contents

Foreword xi
Preface xiii
Acknowledgments xv
PART ONE: THE RULES OF REASON
The Basics of Propositional Logic
3(28)
Operations and Symbols
3(6)
Truth Tables
9(4)
Some Basic Laws
13(4)
Truth Table Proofs
17(11)
Quiz
28(3)
How Sentences are Put Together
31(26)
Sentence Structure
31(6)
Quantifiers
37(5)
Well-formed Formulas
42(5)
Venn Diagrams
47(6)
Quiz
53(4)
Formalities and Techniques
57(26)
Seeds of a Theory
57(6)
Theorems
63(6)
A Theory Grows
69(2)
Techniques for Proving Things
71(9)
Quiz
80(3)
Vagaries of Logic
83(48)
Cause, Effect, and Implication
83(8)
The Probability Fallacy
91(2)
Weak and Flawed Reasoning
93(9)
Paradoxes and Brain Teasers
102(11)
Quiz
113(4)
Test: Part One
117(14)
PART TWO: PROOFS IN ACTION
Some Theoretical Geometry
131(42)
Some Definitions
131(11)
Similar and Congruent Triangles
142(8)
Some Axioms
150(5)
Some Proofs at Last!
155(14)
Quiz
169(4)
Sets and Numbers
173(28)
Some Definitions
173(7)
Axioms
180(2)
Some Proofs at Last!
182(16)
Quiz
198(3)
A Few Historic Tidbits
201(52)
You ``Build'' It
201(15)
The Theorem of Pythagoras
216(4)
The Square Root of 2
220(6)
The Greatest Common Divisor
226(3)
Prime Numbers
229(8)
Quiz
237(4)
Test: Part Two
241(12)
Final Exam 253(22)
Answers to Quiz, Test, and Exam Questions 275(4)
Suggested Additional References 279(2)
Index 281

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