An Introduction to Discrete Mathematics offers an engaging and accessible introduction to discrete mathematics for beginning undergraduate students across a wide range of application areas, from mathematics to statistics, operations research, business, engineering, and the sciences. It provides solid foundation in precise proof writing methods, with early chapters introducing set theory and logic that are followed by deductive and inductive proof techniques, number theory, counting principles, permutations and combinations, probability of events, random variables, graphs, and weighted graphs.
The book illustrates fundamental concepts in discrete mathematics with clear and precise definitions that are paired with examples and counter-examples as applied in combinatorics, discrete probability, and graph theory. Chapters include student exercises to enhance learning, and a solutions manual and example questions are available for instructors on a companion website.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. A Sherlock Holmes fable - p. v 7. Preface - p. xi 8. Part 1: Foundations - p. xii 9. Chapter 1: Number system - p. 3 10. Chapter 2: Logic and deduction - p. 9 11. Chapter 3: Sets, functions, sequences, sums - p. 31 12. Chapter 4: Induction, recursion - p. 69 13. Chapter 5: Elementary number theory - p. 87 14. Part 2: Combinatorics - p. 106 15. Chapter 6: Basic principles of counting - p. 109 16. Chapter 7: Permutations and combinations - p. 125 17. Chapter 8: Further topics in counting - p. 141 18. Part 3: Discrete probability - p. 159 19. Chapter 9: Probability of events - p. 163 20. Chapter 10: Random variables - p. 201 21. Part 4: Graphs and networks - p. 229 22. Chapter 11: Graphs - p. 233 23. Chapter 12: Weighted graphs - p. 287 24. Answers to selected problems - p. 313 25. Index - p. 329
An Introduction to Discrete Mathematics offers an engaging and accessible introduction to discrete mathematics for beginning undergraduate students across a wide range of application areas, from mathematics to statistics, operations research, business, engineering, and the sciences. It provides solid foundation in precise proof writing methods, with early chapters introducing set theory and logic that are followed by deductive and inductive proof techniques, number theory, counting principles, permutations and combinations, probability of events, random variables, graphs, and weighted graphs.
The book illustrates fundamental concepts in discrete mathematics with clear and precise definitions that are paired with examples and counter-examples as applied in combinatorics, discrete probability, and graph theory. Chapters include student exercises to enhance learning, and a solutions manual and example questions are available for instructors on a companion website.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. A Sherlock Holmes fable - p. v 7. Preface - p. xi 8. Part 1: Foundations - p. xii 9. Chapter 1: Number system - p. 3 10. Chapter 2: Logic and deduction - p. 9 11. Chapter 3: Sets, functions, sequences, sums - p. 31 12. Chapter 4: Induction, recursion - p. 69 13. Chapter 5: Elementary number theory - p. 87 14. Part 2: Combinatorics - p. 106 15. Chapter 6: Basic principles of counting - p. 109 16. Chapter 7: Permutations and combinations - p. 125 17. Chapter 8: Further topics in counting - p. 141 18. Part 3: Discrete probability - p. 159 19. Chapter 9: Probability of events - p. 163 20. Chapter 10: Random variables - p. 201 21. Part 4: Graphs and networks - p. 229 22. Chapter 11: Graphs - p. 233 23. Chapter 12: Weighted graphs - p. 287 24. Answers to selected problems - p. 313 25. Index - p. 329
