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Discrete Mathematics
This text aims to give an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math majors, especially those who intend to teach middle and high school mathematics. A difference between this text and most other discrete math books is that this book is intended to be used in a class taught using problem oriented or inquiry based methods.
- Author
- Oscar Levin
- Publisher
- University of Northern Colorado
- Source
- LibreTexts
- License
- CC BY-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 42 sections
- 0: Introduction and Preliminaries
- 0.1: What is Discrete Mathematics
- 0.2: Mathematical Statements
- 0.3: Sets
- 0.4: Functions
- 0.E: Introduction and Preliminaries (Exercises)
- 1: Counting
- 1.1: Additive and Multiplicative Principles
- 1.2: Binomial Coefficients
- 1.3: Combinations and Permutations
- 1.4: Combinatorial Proofs
- 1.5: Stars and Bars
- 1.6: Advanced Counting Using PIE
- 1.E: Counting (Exercises)
- 1.S: Counting (Summary)
- 2: Sequences
- 2.1: Definitions
- 2.2: Arithmetic and Geometric Sequences
- 2.3: Polynomial Fitting
- 2.4: Solving Recurrence Relations
- 2.5: Induction
- 2.E: Sequences (Exercises)
- 2.S: Sequences (Summary)
- 3: Symbolic Logic and Proofs
- 3.0: Prelude to Symbolic Logic and Proofs
- 3.1: Propositional Logic
- 3.2: Proofs
- 3.E: Symbolic Logic and Proofs (Exercises)
- 3.S: Symbolic Logic and Proofs (Summary)
- 4: Graph Theory
- 4.0: Prelude to Graph Theory
- 4.1: Definitions
- 4.2: Planar Graphs
- 4.3: Coloring
- 4.4: Euler Paths and Circuits
- 4.5: Matching in Bipartite Graphs
- 4.E: Graph Theory (Exercises)
- 4.S: Graph Theory (Summary)
- 5: Additional Topics
- 5.1: Generating Functions
- 5.2: Introduction to Number Theory
- 5.E: Additional Topics (Exercises)