MA101
Discrete Mathematics
The mathematics of the discrete and finite: logic, sets, relations, and proof — the formal language of computer science.
10 modules · 40 lessons · Practice after every lesson
Syllabus
Module 1
Propositional Logic
- Propositions and Connectives
- Truth Tables and Logical Equivalence
- Implication, Converse, and Contrapositive
- Normal Forms and Satisfiability
Module 2
Predicate Logic and Quantifiers
- Predicates and Domains
- Universal and Existential Quantification
- Negating Quantified Statements
- Nested Quantifiers and Formal Translation
Module 3
Proof Foundations
- Definitions, Theorems, and Counterexamples
- Direct Proof
- Proof by Contrapositive
- Proof by Contradiction
Module 4
Induction and Recursive Reasoning
- Weak Mathematical Induction
- Strong Induction
- Structural Induction
- Recursive Definitions and Well-Foundedness
Module 5
Sets, Functions, and Relations
- Set Operations and Identities
- Cartesian Products and Power Sets
- Functions, Images, and Inverses
- Relations and Their Properties
Module 6
Equivalence and Order
- Equivalence Relations and Partitions
- Partial Orders and Hasse Diagrams
- Total Orders and Lexicographic Order
- Closures of Relations
Module 7
Counting
- Sum and Product Rules
- Permutations and Combinations
- Binomial Coefficients and Identities
- Pigeonhole Principle and Double Counting
Module 8
Advanced Counting
- Inclusion–Exclusion
- Recurrence Relations
- Generating Functions: An Introduction
- Counting with Symmetry and Constraints
Module 9
Graphs and Trees
- Graph Definitions and Representations
- Paths, Connectivity, and Cycles
- Trees and Spanning Trees
- Graph Coloring, Matchings, and Planarity
Module 10
Number Theory for Computing
- Divisibility and the Euclidean Algorithm
- Modular Arithmetic
- Prime Numbers and Unique Factorization
- Congruences, Inverses, and Chinese Remainders
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