Discrete mathematics : an open introduction

Format:

Book

Author/Creator:

Levin, Oscar, author.

Language:

English

Subjects (All):

Mathematics--Textbooks.

Mathematics.

Physical Description:

1 online resource

Edition:

3rd Edition

Place of Publication:

Greeley, CO Oscar Levin [2016]

Language Note:

In English.

Summary:

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.

Contents:

0 Introduction and Preliminaries 1

0.1 What is Discrete Mathematics?

0.2 Mathematical Statements

0.3 Sets

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

1.7 Chapter Summary

2 Sequences

2.1 Definitions

2.2 Arithmetic and Geometric Sequences

2.3 Polynomial Fitting

2.4 Solving Recurrence Relations

2.5 Induction

2.6 Chapter Summary

3 Symbolic Logic and Proofs

3.1 Propositional Logic

3.2 Proofs

3.3 Chapter Summary

4 Graph Theory

4.1 Definitions

4.2 Trees

4.3 Planar Graphs

4.4 Coloring

4.5 Euler Paths and Circuits

4.6 Matching in Bipartite Graphs

4.7 Chapter Summary

5 Additional Topics

5.1 Generating Functions

5.2 Introduction to Number Theory

Notes:

Description based on print resource