discrete-structures

• PDFs of homework problems from ZyBooks's Discrete Mathematics.
• From Discrete Computational Structures (CS2071) class, taught by Nitin Nitin at the University of Cincinnati.

Topics

Logic (Ch1).pdf

• Chapter 1.1     Propositions and logical operations
• Chapter 1.2     Evaluating compound propositions
• Chapter 1.3     Conditional statements
• Chapter 1.4     Logical equivalence
• Chapter 1.5     Laws of propositional logic
• Chapter 1.6     Predicates and quantifiers
• Chapter 1.7     Quantified statements
• Chapter 1.8     De Morgan's Law for quantified statements
• Chapter 1.9     Nested quantifiers
• Chapter 1.10   More nested quantified statements
• Chapter 1.11   Logic reasoning
• Chapter 1.12   Rules of inference with propositions
• Chapter 1.13   Rules of inference with quantifiers

Proofs (Ch2).pdf

• Chapter 2.1     Mathematical definitions
• Chapter 2.2     Introduction to proofs
• Chapter 2.3     Best practices and common errors in proofs
• Chapter 2.4     Writing direct proofs
• Chapter 2.5     Proof by contrapositive
• Chapter 2.6     Proof by contradiction
• Chapter 2.7     Proof by cases

Sets (Ch3).pdf

• Chapter 3.5     Set identities
• Chapter 3.6     Cartesian products
• Chapter 3.7     Partitions

Functions (Ch4).pdf

• Chapter 4.5     Composition of functions
• Chapter 4.6     Logarithm and exponents

Relations & Digraphs (Ch6).pdf

• Chapter 6.4     Composition of relations
• Chapter 6.5     Graph power and transitive closure
• Chapter 6.6     Matrix multiplication and graph powers
• Chapter 6.7     Partial orders
• Chapter 6.8     Strict orders and directed acyclic graphs
• Chapter 6.9     Equivalence relations

Computation (Ch7).pdf

• Chapter 7.4     Finite state machines
• Chapter 7.5     Turing machines

Induction & Recursion (Ch8).pdf

• Chapter 8.3     Summations
• Chapter 8.4     Mathematical induction
• Chapter 8.5     More inductive proofs
• Chapter 8.6     Strong induction
• Chapter 8.8     Recursive definitions
• Chapter 8.9     Structural induction
• Chapter 8.10   Recursive algorithms
• Chapter 8.11   Induction and recursive algorithms

Integer Properties (Ch9).pdf

• Chapter 9.1     Division algorithm
• Chapter 9.2     Modular arithmetic
• Chapter 9.3     Prime factorizations
• Chapter 9.8     Introduction to cryptography

Introduction to Counting (Ch10).pdf

• Chapter 10.12 Counting problem examples

Advanced Counting (Ch11).pdf

• Chapter 11.3   The pigeonhole principle