Logic, Sets and the Techniques of Mathematical Proofs: A Companion for High School and College Students

Portada
AuthorHouse, 2011 - 356 pàgines
As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.
 

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Continguts

Preface
11
Chapter 1 Propositional logic
17
Chapter 2 Tautologies and contradictions
37
Chapter 3 Theorems and Proof methods
49
Chapter 4 Sets
62
Chapter 5 Operations on sets
81
Chapter 6 Singlevariable sentential logic
101
Chapter 7 Sentential implications and equivalences
115
Chapter 12 Methods of proof by mathematical induction
203
Chapter 13 Relations
218
Chapter 14 Functions and absolute value
239
Chapter 15 types of functions
254
Chapter 16 Sequences
273
Chapter 17 Fundamental and monotonic sequences
295
Chapter 18 Finite and Infinite sets
309
Chapter 19 Indexed Family of sets
328

Chapter 8 Twovariable predicate logic
125
Chapter 9 Real numbers
139
Subtraction and Division
160
The axiom of continuity
176

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