Discrete Mathematics 2Nd Ed.

Biggs

Published by Oxford University Press, 2013
ISBN 10: 019871369X / ISBN 13: 9780198713692
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Title: Discrete Mathematics 2Nd Ed.
Publisher: Oxford University Press
Publication Date: 2013
Binding: Paperback
Book Condition: Used; Good

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Book Description Oxford University Press, 2015. Softcover. Book Condition: New. 5th or later edition. Contents: Part 1 Foundations 1. Statements and Proofs 1.1 Some Mathematical Statements 1.2 How to do Mathematics 1.3 Compound Statements 1.4 Existential Statements 1.5 Universal Statements 1.6 Proof Techniques 1.7 Miscellaneous Exercises 2. Set Notation 2.1 Sets of Objects and Numbers 2.2 Subsets 2.3 Union and Intersection 2.4 Miscellaneous 3. The logical Framework 3.1 logical Operations: not or, and 3.2 if- then 3.4 The converse Statement 3.5 The Contrapositive Statement 3.6 Universal and Existential Quantifiers 3.7 Miscellaneous Exercises 4. Natural Numbers 4.1 The `law of Algebra 4.2 Putting the Natural Numbers in Order 4.3 The Principle of Induction 4.5 Recursive Definitions 4.6 Other forms of the Principle of Induction 4.7 Greatest and least Members 4.8 How a Conjecture Becomes a Theorem 4.9 Miscellaneous Exercises 5 Function 5.1 The Concept of a Function 5.2 Surjections, Injections 5.3 Composition of Functions 5.4 Bijections and Inverse Functions 5.5 Miscellaneous Exercises 6 How to Count 6.1 Counting as a Bijection 6.2 The Size of a Set 6.3 A Counting Problem 6.4 some Applications of the Pigeonhole Principle 6.5 Infinite Sets 6.6 Strange Properties of Infinite Sets 6.7 Miscellaneous Exercises 7. Integers 7.1 Negative Numbers 7.2 Equivalence Relations 7.3 Classification 7.4 Construction of the Integers 7.5 Properties of the Integers 7.6 Bounded Subsets of Z 7.7 Miscellaneous Exercise 8. Divisibility and Prime Numbers 8.1 Divisibility 8.2 Quotient and Remainder 8.3 Representation of Integers 8.4 The Greatest Common Divisor 8.5 Prime Numbers 8.6 Existence and Uniqueness of Prime Factorization 8.7 Miscellaneous Exercises 9. Fractions and Real Numbers 9.1 Construction and Properties of Rational Numbers 9.2 Density of Fractions 9.3 Decimal Representations of Fractions 9.4 Real Numbers 9.5 Approximations for Real Numbers 9.6 The Greatest lower Bound Property 9.7 The real Numbers are More Plentiful then the Rationals 9.8 Miscellaneous Exercises Part II. Techniques 10 Principles of Counting 10.1 the Addition Principle 10.2 Counting Sets of Pairs 10.3 Euler`s function 10.4 functions, Word, and Selections 10.5 Injections as Ordered Selections Without Repetition 10.6 Permutations 10.7 Miscellaneous Exercises 11.Subsets and Designs 12 Partition, Classification, and Distribution 13. Modular Arithmetic 14. Algorithms and their Efficiency 15. Graphs 16. trees, Sorting, and Searching 17. Bipartite graphs and Matching 18. digraphs, Networks, and Flows 19. recursive Techinques 20 Groups 21 groups of Permutations 22. rings, Fields, and Polynimials 23. Finite Fields and Some Applications 24. Error- Correcting Codes 25. Generating Functions 26. Partitions of a Positive Integer 27. symmetry and Counting 18. Printed Pages: 440. Bookseller Inventory # 98391

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Book Description Oxford University Press, 2015. Softcover. Book Condition: New. 5th or later edition. Contents: Part 1 Foundations 1. Statements and Proofs 1.1 Some Mathematical Statements 1.2 How to do Mathematics 1.3 Compound Statements 1.4 Existential Statements 1.5 Universal Statements 1.6 Proof Techniques 1.7 Miscellaneous Exercises 2. Set Notation 2.1 Sets of Objects and Numbers 2.2 Subsets 2.3 Union and Intersection 2.4 Miscellaneous 3. The logical Framework 3.1 logical Operations: not or, and 3.2 if- then 3.4 The converse Statement 3.5 The Contrapositive Statement 3.6 Universal and Existential Quantifiers 3.7 Miscellaneous Exercises 4. Natural Numbers 4.1 The `law of Algebra 4.2 Putting the Natural Numbers in Order 4.3 The Principle of Induction 4.5 Recursive Definitions 4.6 Other forms of the Principle of Induction 4.7 Greatest and least Members 4.8 How a Conjecture Becomes a Theorem 4.9 Miscellaneous Exercises 5 Function 5.1 The Concept of a Function 5.2 Surjections, Injections 5.3 Composition of Functions 5.4 Bijections and Inverse Functions 5.5 Miscellaneous Exercises 6 How to Count 6.1 Counting as a Bijection 6.2 The Size of a Set 6.3 A Counting Problem 6.4 some Applications of the Pigeonhole Principle 6.5 Infinite Sets 6.6 Strange Properties of Infinite Sets 6.7 Miscellaneous Exercises 7. Integers 7.1 Negative Numbers 7.2 Equivalence Relations 7.3 Classification 7.4 Construction of the Integers 7.5 Properties of the Integers 7.6 Bounded Subsets of Z 7.7 Miscellaneous Exercise 8. Divisibility and Prime Numbers 8.1 Divisibility 8.2 Quotient and Remainder 8.3 Representation of Integers 8.4 The Greatest Common Divisor 8.5 Prime Numbers 8.6 Existence and Uniqueness of Prime Factorization 8.7 Miscellaneous Exercises 9. Fractions and Real Numbers 9.1 Construction and Properties of Rational Numbers 9.2 Density of Fractions 9.3 Decimal Representations of Fractions 9.4 Real Numbers 9.5 Approximations for Real Numbers 9.6 The Greatest lower Bound Property 9.7 The real Numbers are More Plentiful then the Rationals 9.8 Miscellaneous Exercises Part II. Techniques 10 Principles of Counting 10.1 the Addition Principle 10.2 Counting Sets of Pairs 10.3 Euler`s function 10.4 functions, Word, and Selections 10.5 Injections as Ordered Selections Without Repetition 10.6 Permutations 10.7 Miscellaneous Exercises 11.Subsets and Designs 12 Partition, Classification, and Distribution 13. Modular Arithmetic 14. Algorithms and their Efficiency 15. Graphs 16. trees, Sorting, and Searching 17. Bipartite graphs and Matching 18. digraphs, Networks, and Flows 19. recursive Techinques 20 Groups 21 groups of Permutations 22. rings, Fields, and Polynimials 23. Finite Fields and Some Applications 24. Error- Correcting Codes 25. Generating Functions 26. Partitions of a Positive Integer 27. symmetry and Counting 18. Printed Pages: 440. Bookseller Inventory # 98391

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