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Description
Discrete Mathematics and its Applications is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, expansive discussion, and detailed exercise sets. These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students.
Publication Date
3-2025
Recommended Citation
Kamran Habibkhani, Houman, "Discrete Math for Computer Science" (2025). Pacific Open Texts. 31.
https://scholarlycommons.pacific.edu/open-textbooks/31
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Notice:
Video recordings of each chapter can be found here:
Chapter 1: Proposition, Logical operations, and conditional statements
Chapter 2: Logical equivalence: Laws of propositional logic
Chapter 3: Predicates and quantifiers: Quantified statements
Chapter 4: Logical reasoning: Rules of inference
Chapter 5: Direct proofs: Proofs by contrapositive
Chapter 6: Proofs by contradiction: Proofs by cases
Chapter 7: Sets and subsets: Set of sets
Chapter 8: Union and intersection and complement: Set identities
Chapter 9: Cartesian products
Chapter 10: Definition of functions: Properties of functions
Chapter 11: Inverse of a function: Composition of functions
Chapter 12: Introduction to binary relations
Chapter 13: Sequences: Recurrence relations
Chapter 14: Summations
Chapter 15: Mathematical induction
Chapter 16: Recursive definitions: Recursive algorithms (no video)
Chapter 17: The division algorithm: Modular arithmetic (no video)
Chapter 18: Prime factorization: gcd and Euclid’s algorithm
Chapter 19: Number representation
Chapter 20: Sum and product rules
Chapter 21: Counting permutations and subsets
Chapter 22: Counting by complement: Permutations with repetitions: Inclusion/exclusion principle
Chapter 23: Probability of an event
Chapter 24: Unions and complements of events
Chapter 25: Conditional probability and independence
Chapter 26: Introduction to graphs: Graph representations
Chapter 27: Paths and cycles: Graph connectivity
Chapter 28: Introduction to trees: Properties of trees
Chapter 29: Tree traversals: Spanning trees