Synopses & Reviews
- Even more examples - Designed to motivate and illustrate the mathematical ideas as they are developed. - Allows the instructor to spend time on selected topics in class and assign reading to fill out the presentation. - Exercise sets - Include a complete range of problems, building smoothly from easy examples to more challenging uses of the methods and extensions of the ideas. - Develops abstract understanding and gives practice with proofs.
Synopsis
Key Benefit: This book presents a sound mathematical treatment that increases smoothly in sophistication. Key Topics: The book presents utility-grade discrete math tools so that any reader can understand them, use them, and move on to more advanced mathematical topics. Market: A handy reference for computer scientists.
Table of Contents
1. Sets, Sequences, and Functions.
Some Warm-up Questions. Factors and Multiples. Office Hours 1.2. Some Special Sets. Set Operations. Functions. Sequences. Properties of Functions. Office Hours 1.7. Supplementary Exercises.
2. Elementary Logic.
Informal Introduction. Propositional Calculus. Getting Started with Proofs. Methods of Proof. Office Hours 2.4. Logic in Proofs. Analysis of Arguments. Supplementary Exercises.
3. Relations.
Relations. Digraphs and Graphs. Matrices. Equivalence Relations and Partitions. The Division Algorithm and Integers Mod p. Supplementary Exercises.
4. Induction and Recursion.
Loop Invariants. Mathematical Induction. Office Hours 4.2. Big-Oh Notation. Recursive Definitions. Recurrence Relations. More Induction. The Euclidean Algorithm. Supplementary Exercises.
5. Counting.
Basic Counting Techniques. Elementary Probability. Inclusion-Exclusion and Binomial Methods. Counting and Partitions. Office Hours 5.4. Pigeon-Hole Principle. Supplementary Exercises.
6. Introduction to Graphs and Trees.
Graphs. Edge Traversal Problems. Trees. Rooted Trees. Vertex Traversal Problems. Minimum Spanning Trees. Supplementary Exercises.
7. Recursion, Trees and Algorithms.
General Recursion. Recursive Algorithms. Depth-First Search Algorithms. Polish Notation. Weighted Trees. Supplementary Exercises.
8. Digraphs.
Digraphs Revisited. Weighted Digraphs and Scheduling Networks. Office Hours 8.2. Digraph Algorithms. Supplementary Exercises.
9. Discrete Probability.
Independence in Probability. Random Variables. Expectation and Standard Deviation. Probability Distributions. Supplementary Exercises.
10. Boolean Algebra.
Boolean Algebras. Boolean Expressions. Logic Networks. Karnaugh Maps. Isomorphisms of Boolean Algebras. Supplementary Exercises.
11. More on Relations.
Partially Ordered Sets. Special Orderings. Multiplication of Matrices. Properties of General Relations. Closures of Relations. Supplementary Exercises.
12. Algebraic Structures.
Groups Acting on Sets. Fixed Points and Subgroups. Counting Orbits. Group Homomorphisms. Semigroups. Other Algebraic Systems. Supplementary Exercises.
13. Predicate Calculus and Infinite Sets.
Quantifiers and Predicates. Elementary Predicate Calculus. Infinite Sets. Supplementary Exercises.
Dictionary.