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Discrete Mathematics de Oscar Levin

Discrete Mathematics

Autor Oscar Levin
en Limba Engleză Paperback

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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Specificații

ISBN-13: 9781534970748
ISBN-10: 1534970746
Pagini: 342
Dimensiuni: 152 x 229 x 18 mm
Greutate: 0.46 kg

Cuprins

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. 

Notă biografică

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. 

Descriere

Descriere de la o altă ediție sau format:
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.