| Description |
1 online resource (218 pages) |
| Series |
Textbooks in Mathematics Ser |
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Textbooks in Mathematics Ser
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| Contents |
Cover; Half Title; Title Page; Copyright Page; Contents; Preface; 1 Elements of logic; 1.1 True and false statements; 1.2 Logical connectives and truth tables; 1.3 Logical equivalence; 1.4 Quantifiers; 1.5 Exercises; 2 Proofs: Structures and strategies; 2.1 Axioms, theorems and proofs; 2.2 Direct proof; 2.3 Contrapositive proof; 2.4 Proof by contradiction; 2.5 Proofs of equivalent statements; 2.6 Proof by cases; 2.7 Existence proofs; 2.8 Proof by counterexample; 2.9 Proof by mathematical induction; 2.10 Exercises; 3 Elementary theory of sets; 3.1 Axioms for set theory; 3.2 Inclusion of sets |
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3.3 Union and intersection of sets3.4 Complement, difference and symmetric difference of sets; 3.5 Ordered pairs and the Cartesian product; 3.6 Exercises; 4 Functions; 4.1 Definition and examples of functions; 4.2 Direct image, inverse image; 4.3 Restriction and extension of a function; 4.4 One-to-one and onto functions; 4.5 Composition and inverse functions; 4.6 *Family of sets and the axiom of choice; 4.7 Exercises; 5 Relations; 5.1 General relations and operations with relations; 5.2 Equivalence relations and equivalence classes; 5.3 Order relations |
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5.4 *More on ordered sets and Zorn's lemma5.5 Exercises; 6 Axiomatic theory of positive integers; 6.1 Peano axioms and addition; 6.2 The natural order relation and subtraction; 6.3 Multiplication and divisibility; 6.4 Natural numbers; 6.5 Other forms of induction; 6.6 Exercises; 7 Elementary number theory; 7.1 Absolute value and divisibility of integers; 7.2 Greatest common divisor and least common multiple; 7.3 Integers in base 10 and divisibility tests; 7.4 Exercises; 8 Cardinality: Finite sets, infinite sets; 8.1 Equipotent sets; 8.2 Finite and infinite sets |
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8.3 Countable and uncountable sets8.4 Exercises; 9 Counting techniques and combinatorics; 9.1 Counting principles; 9.2 Pigeonhole principle and parity; 9.3 Permutations and combinations; 9.4 Recursive sequences and recurrence relations; 9.5 Exercises; 10 The construction of integers and rationals; 10.1 Definition of integers and operations; 10.2 Order relation on integers; 10.3 Definition of rationals, operations and order; 10.4 Decimal representation of rational numbers; 10.5 Exercises; 11 The construction of real and complex numbers; 11.1 The Dedekind cuts approach |
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11.2 The Cauchy sequences approach11.3 Decimal representation of real numbers; 11.4 Algebraic and transcendental numbers; 11.5 Complex numbers; 11.6 The trigonometric form of a complex number; 11.7 Exercises; Bibliography; Answers to select exercises; Index |
| Notes |
Print version record |
| Form |
Electronic book
|
| Author |
Pfaff, Donald C
|
| ISBN |
9781498775267 |
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1498775268 |
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