Doerr A., Levasseur K. Applied Discrete Structures

3rd. ed. (ver. 6) — University of Massachusetts Lowell, 2019. — 567 p.Applied Discrete Structures is designed for use in a university course in discrete mathematics spanning up two semesters. Its original design was for computer science majors to be introduced to the mathematical topics that are useful in computer science. It can also serve the same purpose for mathematics majors, providing a firrst exposure to many essential topics. Many of the concepts introduced in this text are illustrated using SageMath code. SageMath (sagemath.org) is a free, open source, software system for advanced mathematics. Sage can be used either on your own computer, a local server, or on SageMathCloud (https://cloud.sagemath.com/).
Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative.Set Theory.
Combinatorics.
Logic.
More on Sets.
Introduction to Matrix Algebra.
Relations.
Functions.
Recursion and Recurrence Relations.
Graph Theory.
Trees.
Algebraic Structures.
More Matrix Algebra.
Boolean Algebra.
Monoids and Automata.
Group Theory and Applications.
An Introduction to Rings and Fields.
A Algorithms.
B Python and SageMath.
C Determinants.
D Hints and Solutions to Selected Exercises.
E Notation.