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Applied Discrete Structures [Doer] - mklabgr - 06-10-2026
Applied Discrete Structures
Authors: Alan Doerr & Kenneth Levasseur
Latest version: Version 3.14, June 2026
Original print publication: 2012
Publisher: Lulu.com / open-textbook edition maintained by the authors
ISBN: 978-1-105-55929-7
Applied Discrete Structures is a broad introduction to discrete mathematics that emphasizes the structures underlying mathematical and computational problems, rather than treating the subject as a loose collection of techniques. The first half develops foundational material such as sets, combinatorics, logic, proof methods, relations, functions, probability, recursion and recurrence relations, graph theory, and trees. The later chapters move into more algebraic territory, covering monoids, groups, modular arithmetic, vector spaces, Boolean algebra, automata, coding theory, rings, fields, and polynomial structures. The current edition contains 16 chapters, with two new probability sections added to Chapter 7 in the 2026 update.
A strong feature of the book is the way it connects pure mathematics with computation. Topics such as the Euclidean algorithm, binary search, sorting, graph traversal, spanning-tree algorithms, coding theory, and finite-state machines appear alongside the underlying proofs and algebra. Many sections include SageMath material, and the book is accompanied by interactive resources, videos, active-learning assignments, and approximately 1,000 exercises, with answers or solutions available for selected problems. This makes it particularly useful for mathematics, computer-science, and STEM students who want to see how abstract concepts translate into algorithms and computational models.
Main topics
- Foundations: sets, logic, quantifiers, induction and proof techniques
- Combinatorics: permutations, combinations and the binomial theorem
- Relations and functions, including equivalence relations and partial orders
- Recursion and recurrence relations, including generating functions
- Graph theory: connectivity, BFS, Eulerian/Hamiltonian graphs, coloring, networks and optimization
- Trees: spanning trees, Prim's and Kruskal's algorithms, binary trees
- Number theory: GCD, the Euclidean algorithm and modular arithmetic
- Abstract algebra: monoids, groups, quotient groups, homomorphisms, rings and fields
- Computer-science connections: automata, Boolean algebra, switching theory and coding theory.
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