Oscar Levin

Discrete Mathematics

An Open Introduction

• Broschiertes Buch

Produktbeschreibung

This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions. Update: as of July 2017, this 2nd edition has been updated, correcting numerous typos and a few mathematical errors. Pagination is almost identical to the earlier printing of the 2nd edition. For a list of changes, see the book's website: http://discretetext.oscarlevin.com

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Produktdetails

• Verlag: 12th Media Services
• Seitenzahl: 246
• Erscheinungstermin: 16. August 2016
• Englisch
• Abmessung: 280mm x 216mm x 14mm
• Gewicht: 629g
• ISBN-13: 9781680921861
• ISBN-10: 168092186X
• Artikelnr.: 51445228

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.