Logic, Sets and the Techniques of Mathematical Proofs: A Companion for High School and College StudentsAuthorHouse, 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. |
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 |
Bibliography | 348 |
349 | |
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LOGIC, SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS: A COMPANION FOR HIGH ... Brahima MBODJE, Ph.D. Previsualització limitada - 2011 |
Frases i termes més freqüents
algebra antisymmetric Assume Axiom 12 Axiom of Continuity biconditional bijection called card(S cardinality Chapter 9 cl(a clearly codomain completes the proof contrapositive Corollary countably infinite countably infinite set counting number deduce defined Definition 9 denial Direct proof empty set equal equinumerous equivalent relation Example F F F F T F false family of sets finite sets fixed real number function f greatest lower bound Hence implication Induction hypothesis inequality injective integer least upper bound mathematical induction natural number nonempty set nonempty subset ordered pairs pre-image Problem proper subset properties propositional expression propositional variables rational number reader to supply real number Remark S₁ sequence Sn)n-1 set-builder notation Sn)n-1 converges SN+1 Solution surjection tautology Theorem Theorem 24 true proposition truth set truth table truth values universal quantifier universal set words