Discrete Mathematics: An Open Introduction, Fourth Edition 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, especially those who intend to teach middle and high school mathematics. The book began as a set of notes for the Discrete Mathematics course at the University of Northern Colorado. This course serves both as a survey of the topics in discrete math and as the “bridge” course for math majors.
Features
- Uses problem-oriented and inquiry-based methods to teach the concepts.
- Suitable for undergraduates in mathematics and computer science.
New to the 4th edition
- Large scale restructuring.
- Contains more than 750 exercises and examples.
- New sections on probability, relations, and discrete structures and their proofs.
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.
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. Pascals 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.
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.
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