Oscar Levin

Discrete Mathematics (eBook, PDF)

An Open Introduction

• Format: PDF

Produktbeschreibung

This book aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math and computer science majors. This course serves both as a survey of the topics in discrete math and as the "bridge" course for math majors.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 480
• Erscheinungstermin: 15. Februar 2025
• Englisch
• ISBN-13: 9781040305850
• Artikelnr.: 73214462

Autorenporträt

Oscar Levin is a professor at the University of Northern Colorado. He has taught mathematics and computer science at the college level for over 15 years and has won multiple teaching awards. His research studies the interaction between logic and graph theory, and he is an active developer on the PreTeXt project, an open-source authoring system for writing accessible scholarly documents. He earned his Ph.D. in mathematical logic from the University of Connecticut in 2009.

Outside of the classroom, Oscar enjoys entertaining his two brilliant daughters with jaw-dropping magic tricks and hilarious Dad jokes, hiking with his amazing wife, and coming in second-to-last in local pinball tournaments.

Inhaltsangabe

0. Introduction and Preliminaries. 0.1. What is Discrete Mathematics?. 0.2.
Discrete Structures. 1. Logic and Proofs. 1.1. Mathematical Statements.
1.2. Implications. 1.3. Rules of Logic. 1.4. Proofs. 1.5. Proofs about
Discrete Structures. 1.6. Chapter Summary. 2. Graph Theory. 2.1. Problems
and Definitions. 2.2. Trees. 2.3. Planar Graphs. 2.4. Euler Trails and
Circuits. 2.5. Coloring. 2.6. Relations and Graphs. 2.7. Matching in
Bipartite Graphs. 2.8. Chapter Summary. 3. Counting. 3.1. Pascal's
Arithmetical Triangle. 3.2. Combining Outcomes. 3.3. Non-Disjoint Outcomes.
3.4. Combinations and Permutations. 3.5. Counting Multisets. 3.6.
Combinatorial Proofs. 3.7. Applications to Probability. 3.8. Advanced
Counting Using PIE. 3.9. Chapter Summary. 4. Sequences. 4.1. Describing
Sequences. 4.2. Rate of Growth. 4.3. Polynomial Sequences. 4.4. Exponential
Sequences. 4.5. Proof by Induction. 4.6. Strong Induction. 4.7. Chapter
Summary. 5. Discrete Structures Revisited. 5.1. Sets. 5.2. Functions. 6.
Additional Topics. 6.1. Generating Functions. 6.2. Introduction to Number
Theory.