Oscar Levin

Discrete Mathematics

An Open Introduction

• Broschiertes Buch

Produktbeschreibung

Note: This is the 3rd edition. If you need the 2nd edition for a course you are taking, it can be found as a "other format" on amazon, or by searching its isbn: 1534970746 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 470 exercises, including 275 with solutions and over 100 with hints. 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. This third edition brings improved exposition, a new section on trees, and a bunch of new and improved exercises. For a complete list of changes, and to view the free electronic version of the text, visit the book's website at discrete.openmathbooks.org

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Produktdetails

• Verlag: Amazon Digital Services LLC - Kdp
• Seitenzahl: 410
• Erscheinungstermin: 31. Dezember 2018
• Englisch
• Abmessung: 254mm x 181mm x 25mm
• Gewicht: 708g
• ISBN-13: 9781792901690
• ISBN-10: 1792901690
• Artikelnr.: 56011324

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.