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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

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

Creative Commons License

Creative Commons Attribution-NonCommercial 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

Discrete Math for Computer Science

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