Discrete Mathematics: An Open Introduction Y91XFCEVHQ
| URI | m2://res/Y91XFCEVHQ |
|---|---|
| Kind | textbook |
| Creators | Oscar Levin |
| Scope | deferred (no test decides the record, and the classifier has no model) |
Expressions
e1: edition, 3rd edition
Contents
- chapter 1: Introduction and Preliminaries
- section 1.1: What is Discrete Mathematics?
- section 1.2: Mathematical Statements
- subsection 1.2.1: Atomic and Molecular Statements
- subsection 1.2.2: Implications
- subsection 1.2.3: Predicates and Quantifiers
- section 1.3: Sets
- subsection 1.3.1: Notation
- subsection 1.3.2: Relationships Between Sets
- subsection 1.3.3: Operations On Sets
- subsection 1.3.4: Venn Diagrams
- section 1.4: Functions
- subsection 1.4.1: Describing Functions
- subsection 1.4.2: Surjections, Injections, and Bijections
- subsection 1.4.3: Image and Inverse Image
- chapter 2: Counting
- section 2.1: Additive and Multiplicative Principles
- subsection 2.1.1: Counting With Sets
- subsection 2.1.2: Principle of Inclusion/Exclusion
- section 2.2: Binomial Coefficients
- subsection 2.2.1: Subsets
- subsection 2.2.2: Bit Strings
- subsection 2.2.3: Lattice Paths
- subsection 2.2.4: Binomial Coefficients
- subsection 2.2.5: Pascal's Triangle
- section 2.3: Combinations and Permutations
- section 2.4: Combinatorial Proofs
- subsection 2.4.1: Patterns in Pascal's Triangle
- subsection 2.4.2: More Proofs
- section 2.5: Stars and Bars
- section 2.6: Advanced Counting Using PIE
- subsection 2.6.1: Counting Derangements
- subsection 2.6.2: Counting Functions
- section 2.7: Chapter Summary
- chapter 3: Sequences
- section 3.1: Describing Sequences
- section 3.2: Arithmetic and Geometric Sequences
- subsection 3.2.1: Sums of Arithmetic and Geometric Sequences
- section 3.3: Polynomial Fitting
- section 3.4: Solving Recurrence Relations
- subsection 3.4.1: The Characteristic Root Technique
- section 3.5: Induction
- subsection 3.5.1: Stamps
- subsection 3.5.2: Formalizing Proofs
- subsection 3.5.3: Examples
- subsection 3.5.4: Strong Induction
- section 3.6: Chapter Summary
- chapter 4: Symbolic Logic and Proofs
- section 4.1: Propositional Logic
- subsection 4.1.1: Truth Tables
- subsection 4.1.2: Logical Equivalence
- subsection 4.1.3: Deductions
- subsection 4.1.4: Beyond Propositions
- section 4.2: Proofs
- subsection 4.2.1: Direct Proof
- subsection 4.2.2: Proof by Contrapositive
- subsection 4.2.3: Proof by Contradiction
- subsection 4.2.4: Proof by (counter) Example
- subsection 4.2.5: Proof by Cases
- section 4.3: Chapter Summary
- chapter 5: Graph Theory
- section 5.1: Definitions
- section 5.2: Trees
- subsection 5.2.1: Properties of Trees
- subsection 5.2.2: Rooted Trees
- subsection 5.2.3: Spanning Trees
- section 5.3: Planar Graphs
- subsection 5.3.1: Non-planar Graphs
- subsection 5.3.2: Polyhedra
- section 5.4: Coloring
- subsection 5.4.1: Coloring in General
- subsection 5.4.2: Coloring Edges
- section 5.5: Euler Paths and Circuits
- subsection 5.5.1: Hamilton Paths
- section 5.6: Matching in Bipartite Graphs
- section 5.7: Chapter Summary
- chapter 6: Additional Topics
- section 6.1: Generating Functions
- subsection 6.1.1: Building Generating Functions
- subsection 6.1.2: Differencing
- subsection 6.1.3: Multiplication and Partial Sums
- subsection 6.1.4: Solving Recurrence Relations with Generating Functions
- section 6.2: Introduction to Number Theory
- subsection 6.2.1: Divisibility
- subsection 6.2.2: Remainder Classes
- subsection 6.2.3: Properties of Congruence
- subsection 6.2.4: Solving Congruences
- subsection 6.2.5: Solving Linear Diophantine Equations
- appendix A: List of Symbols
Catalogue records
- levin_dmoi: levin_dmoi (work)