Discrete Mathematics (Classic Version)

An ever-increasing percentage of mathematic applications involve discrete rather than continuous models. Driving this trend is the integration of the computer into virtually every aspect of modern society. Intended for a one-semester introductory course, the strong algorithmic emphasis of Discrete Mathematics is independent of a specific programming language, allowing students to concentrate on foundational problem-solving and analytical skills. Instructors get the topical breadth and organizational flexibility to tailor the course to the level and interests of their students.

(Each Chapter concludes with "Historical Notes," "Supplementary Exercises," "Computer Projects," and "Suggested Readings.").

1: An Introduction to Combinatorial Problems and Techniques

Section 1.1 The Time to Complete a Project

Section 1.2 A Matching Problem

Section 1.3 A Knapsack Problem

Section 1.4 Algorithms and Their Efficiency

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

2: Sets, Relations, and Functions

Section 2.1 Set Operations

Section 2.2 Equivalence Relations

Section 2.3_ Partial Ordering Relations

Section 2.4 Functions

Section 2.5 Mathematical Induction

Section 2.6 Applications

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

3: Coding Theory

Section 3.1 Congruence

Section 3.2 The Euclidean Algorithm and Diophantine Equations

Section 3.3 The RSA Method

Section 3.4 Error-Detecting and Error-Correcting Codes

Section 3.5 Matrix Codes

Section 3.6 Matrix Codes That Correct All Single-Digit Errors

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

4: Graphs

Section 4.1 Graphs and Their Representations

Section 4.2 Paths and Circuits

Section 4.3 Shortest Paths and Distance

Section 4.4 Coloring a Graph

Section 4.5 Directed Graphs and Multigraphs

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

5: Trees

Section 5.1 Properties of Trees

Section 5.2 Spanning Trees

Section 5.3 Depth-First Search

Section 5.4 Rooted Trees

Section 5.5 Binary Trees and Traversals

Section 5.6 Optimal Binary Trees and Binary Search Trees

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

6: Matching

Section 6.1 Systems of Distinct Representatives

Section 6.2 Matchings in Graphs

Section 6.3 A Matching Algorithm

Section 6.4 Applications of the Algorithm

Section 6.5 The Hungarian Method

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

7: Network Flows

Section 7.1 Flows and Cuts

Section 7.2 A Flow Augmentation Algorithm

Section 7.3 The Max-Flow Min-Cut Theorem

Section 7.4 Flows and Matchings

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

8: Counting Techniques

Section 8.1 Pascal’s Triangle and the Binomial Theorem

Section 8.3 Permutations and Combinations

Section 8.4 Arrangements and Selections with Repetitions

Section 8.5 Probability

Section 8.6* The Principle of Inclusion-Exclusion

Section 8.7* Generating Permutations and r -Combinations

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

9: Recurrence Relations and Generating Functions

Section 9.1 Recurrence Relations

Section 9.2 The Method of Iteration

Section 9.3 Linear Difference Equations with Constant Coefficients

Section 9.4* Analyzing the Efficiency of Algorithms with Recurrence Relations

Section 9.5 Counting with Generating Functions

Section 9.6 The Algebra of Generating Functions

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

10: Combinatorial Circuits and Finite State Machines

Section 10.1 Logical Gates

Section 10.2 Creating Combinatorial Circuits

Section 10.3 Karnaugh Maps

Section 10.4 Finite State Machines

Historical Notes

Supplementary Exercises

Computer Projects

Suggested Readings

Section A.1 Statements and Connectives

Section A.2 Logical Equivalence

Section A.3 Methods of Proof

Historical Notes

Supplementary Exercises

Suggested Readings

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