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Produktbild: Mathematical Proofs: A Transition to Advanced Mathematics
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Mathematical Proofs: A Transition to Advanced Mathematics

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.11.2013

Verlag

Pearson Education Limited

Seitenzahl

424

Maße (L/B/H)

27,6/21,6/2,3 cm

Gewicht

921 g

Auflage

3

Sprache

Englisch

ISBN

978-1-292-04064-6

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.11.2013

Verlag

Pearson Education Limited

Seitenzahl

424

Maße (L/B/H)

27,6/21,6/2,3 cm

Gewicht

921 g

Auflage

3

Sprache

Englisch

ISBN

978-1-292-04064-6

Herstelleradresse

Pearson
St.-Martin-Straße 82
81541 München
DE

Email: salesde@pearson.com

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  • Produktbild: Mathematical Proofs: A Transition to Advanced Mathematics

  • 0. Communicating Mathematics

    Learning Mathematics

    What Others Have Said About Writing

    Mathematical Writing

    Using Symbols

    Writing Mathematical Expressions

    Common Words and Phrases in Mathematics

    Some Closing Comments About Writing

     

    1. Sets

    1.1. Describing a Set

    1.2. Subsets

    1.3. Set Operations

    1.4. Indexed Collections of Sets

    1.5. Partitions of Sets

    1.6. Cartesian Products of Sets

    Exercises for Chapter 1

     

    2. Logic

    2.1. Statements

    2.2. The Negation of a Statement

    2.3. The Disjunction and Conjunction of Statements

    2.4. The Implication

    2.5. More On Implications

    2.6. The Biconditional

    2.7. Tautologies and Contradictions

    2.8. Logical Equivalence

    2.9. Some Fundamental Properties of Logical Equivalence

    2.10. Quantified Statements

    2.11. Characterizations of Statements

    Exercises for Chapter 2

     

    3. Direct Proof and Proof by Contrapositive

    3.1. Trivial and Vacuous Proofs

    3.2. Direct Proofs

    3.3. Proof by Contrapositive

    3.4. Proof by Cases

    3.5. Proof Evaluations

    Exercises for Chapter 3

     

    4. More on Direct Proof and Proof by Contrapositive

    4.1. Proofs Involving Divisibility of Integers

    4.2. Proofs Involving Congruence of Integers

    4.3. Proofs Involving Real Numbers

    4.4. Proofs Involving Sets

    4.5. Fundamental Properties of Set Operations

    4.6. Proofs Involving Cartesian Products of Sets

    Exercises for Chapter 4

     

    5. Existence and Proof by Contradiction

    5.1. Counterexamples

    5.2. Proof by Contradiction

    5.3. A Review of Three Proof Techniques

    5.4. Existence Proofs

    5.5. Disproving Existence Statements

    Exercises for Chapter 5

     

    6. Mathematical Induction

    6.1 The Principle of Mathematical Induction

    6.2 A More General Principle of Mathematical Induction

    6.3 Proof By Minimum Counterexample

    6.4 The Strong Principle of Mathematical Induction

    Exercises for Chapter 6

     

    7. Prove or Disprove

    7.1 Conjectures in Mathematics

    7.2 Revisiting Quantified Statements

    7.3 Testing Statements

    Exercises for Chapter 7

     

    8. Equivalence Relations

    8.1 Relations

    8.2 Properties of Relations

    8.3 Equivalence Relations

    8.4 Properties of Equivalence Classes

    8.5 Congruence Modulo n

    8.6 The Integers Modulo n

    Exercises for Chapter 8

     

    9. Functions

    9.1 The Definition of Function

    9.2 The Set of All Functions from A to B

    9.3 One-to-one and Onto Functions

    9.4 Bijective Functions

    9.5 Composition of Functions

    9.6 Inverse Functions

    9.7 Permutations

    Exercises for Chapter 9

     

    10. Cardinalities of Sets

    10.1 Numerically Equivalent Sets

    10.2 Denumerable Sets

    10.3 Uncountable Sets

    10.4 Comparing Cardinalities of Sets

    10.5 The Schröder-Bernstein Theorem

    Exercises for Chapter 10

     

    11. Proofs in Number Theory

    11.1 Divisibility Properties of Integers

    11.2 The Division Algorithm

    11.3 Greatest Common Divisors

    11.4 The Euclidean Algorithm

    11.5 Relatively Prime Integers

    11.6 The Fundamental Theorem of Arithmetic

    11.7 Concepts Involving Sums of Divisors

    Exercises for Chapter 11

     

    12. Proofs in Calculus

    12.1 Limits of Sequences

    12.2 Infinite Series

    12.3 Limits of Functions

    12.4 Fundamental Properties of Limits of Functions

    12.5 Continuity

    12.6 Differentiability

    Exercises for Chapter 12

     

    13. Proofs in Group Theory

    1