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Discrete Mathematics

Kenneth A. Ross and Charles R. Wright
Publisher: 
Prentice Hall
Publication Date: 
2002
Number of Pages: 
640
Format: 
Hardcover
Edition: 
5
Price: 
122.20
ISBN: 
0130652474
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

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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.

 

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