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Oscar Levin

Discrete Mathematics: An Open Introduction

A first course in discrete mathematics: counting, sequences, symbolic logic and proof, and graph theory, plus a closing pair of sections on generating functions and number theory. Investigate-first problems — knights and knaves, rook paths, Rubik's cube distributions — motivate each technique before it is formalized.

Discrete Mathematics: An Open Introduction

134 exercises25 sections
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Sections
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Introduction and Preliminaries

22
Mathematical Statements5
Sets6
Functions11

Counting

10
Additive and Multiplicative Principles1
Combinatorial Proofs3
Stars and Bars1
Advanced Counting Using PIE1
Chapter Summary4

Sequences

32
Describing Sequences7
Arithmetic and Geometric Sequences1
Polynomial Fitting5
Solving Recurrence Relations4
Induction12
Chapter Summary3

Symbolic Logic and Proofs

15
Propositional Logic4
Proofs3
Chapter Summary8

Graph Theory

35
Definitions3
Trees4
Planar Graphs5
Coloring3
Euler Paths and Circuits1
Chapter Summary19

Additional Topics

20
Generating Functions11
Introduction to Number Theory9

Adapted from Discrete Mathematics: An Open Introduction © 2013–2019 Oscar Levin. Licensed under CC BY-SA 4.0. Source: Discrete Mathematics: An Open Introduction. Imported at revision 1e2e26b.