Faculty materials
Lesson keys
Statements, Propositions and Truth Values
Unit 01 · Lesson 01
Logical Connectives and Compound Statements
Unit 01 · Lesson 02
Truth Tables and Semantic Evaluation
Unit 01 · Lesson 03
Logical Equivalence and Algebra of Propositions
Unit 01 · Lesson 04
Implication, Converse, Inverse and Contrapositive
Unit 01 · Lesson 05
Predicates, Quantifiers and Negation
Unit 01 · Lesson 06
Rules of Inference, Valid Arguments and Fallacies
Unit 01 · Lesson 07
Set Language, Membership and Subsets
Unit 02 · Lesson 01
Set Operations and Identities
Unit 02 · Lesson 02
Power Sets, Cartesian Products and Tuples
Unit 02 · Lesson 03
Functions, Domains, Codomains and Ranges
Unit 02 · Lesson 04
Injective, Surjective and Bijective Functions
Unit 02 · Lesson 05
Relations and Their Properties
Unit 02 · Lesson 06
Equivalence Relations, Partitions, Orders and Cardinality
Unit 02 · Lesson 07
Definitions, Theorems and the Anatomy of Proof
Unit 03 · Lesson 01
Direct Proof and Constructive Reasoning
Unit 03 · Lesson 02
Proof by Contraposition
Unit 03 · Lesson 03
Proof by Contradiction and Counterexample
Unit 03 · Lesson 04
Proof by Cases, Existence and Uniqueness
Unit 03 · Lesson 05
Mathematical, Strong and Structural Induction
Unit 03 · Lesson 06
Recursive Definitions, Invariants and Termination
Unit 03 · Lesson 07
Divisibility and the Division Algorithm
Unit 04 · Lesson 01
Greatest Common Divisors and the Euclidean Algorithm
Unit 04 · Lesson 02
Prime Numbers and Unique Factorization
Unit 04 · Lesson 03
Congruence and Modular Arithmetic
Unit 04 · Lesson 04
Modular Inverses and Linear Congruences
Unit 04 · Lesson 05
Chinese Remainder Theorem and Fast Exponentiation
Unit 04 · Lesson 06
RSA Foundations, Hashing and Check Digits
Unit 04 · Lesson 07
Sum and Product Rules
Unit 05 · Lesson 01
Permutations and Ordered Arrangements
Unit 05 · Lesson 02
Combinations and Binomial Coefficients
Unit 05 · Lesson 03
Multisets and Combinations with Repetition
Unit 05 · Lesson 04
Pigeonhole Principle and Extremal Guarantees
Unit 05 · Lesson 05
Inclusion–Exclusion and Overlapping Constraints
Unit 05 · Lesson 06
Combinatorial Proofs and Binomial Identities
Unit 05 · Lesson 07
Sequences and Recursive Definitions
Unit 06 · Lesson 01
Modelling with Recurrence Relations
Unit 06 · Lesson 02
Iteration, Substitution and First-Order Recurrences
Unit 06 · Lesson 03
Linear Homogeneous Recurrences and Characteristic Roots
Unit 06 · Lesson 04
Nonhomogeneous Recurrences and Particular Solutions
Unit 06 · Lesson 05
Divide-and-Conquer Recurrences and Growth
Unit 06 · Lesson 06
Generating Functions and Recurrence Verification
Unit 06 · Lesson 07
Finite Sample Spaces and Event Algebra
Unit 07 · Lesson 01
Conditional Probability and Bayes Reasoning
Unit 07 · Lesson 02
Independence and Repeated Trials
Unit 07 · Lesson 03
Discrete Random Variables and Expected Value
Unit 07 · Lesson 04
Variance, Indicators and Linearity of Expectation
Unit 07 · Lesson 05
Binomial and Geometric Distributions
Unit 07 · Lesson 06
Randomized Algorithms and the Probabilistic Method
Unit 07 · Lesson 07
Graph Models, Terminology and Representations
Unit 08 · Lesson 01
Degree, Handshaking and Structural Accounting
Unit 08 · Lesson 02
Walks, Trails, Paths and Cycles
Unit 08 · Lesson 03
Connectivity, Components and Cut Structure
Unit 08 · Lesson 04
Euler Trails and Circuits
Unit 08 · Lesson 05
Hamiltonian Paths, Cycles and Computational Difficulty
Unit 08 · Lesson 06
Breadth-First and Depth-First Traversal
Unit 08 · Lesson 07
Trees and Equivalent Characterizations
Unit 09 · Lesson 01
Rooted Trees, Levels and Traversals
Unit 09 · Lesson 02
Binary, Search and Expression Trees
Unit 09 · Lesson 03
Spanning Trees and Network Redundancy
Unit 09 · Lesson 04
Kruskal and Prim Minimum-Spanning Algorithms
Unit 09 · Lesson 05
Tree Encodings, Prüfer Sequences and Counting
Unit 09 · Lesson 06
Structural Induction and Recursive Tree Algorithms
Unit 09 · Lesson 07
Shortest Paths and Dijkstra’s Algorithm
Unit 10 · Lesson 01
Directed Acyclic Graphs and Topological Ordering
Unit 10 · Lesson 02
Graph Coloring and Scheduling Constraints
Unit 10 · Lesson 03
Bipartite Graphs and Matchings
Unit 10 · Lesson 04
Hall’s Theorem and Augmenting Paths
Unit 10 · Lesson 05
Network Flow and Max-Flow Min-Cut
Unit 10 · Lesson 06
Planar Graphs, Euler’s Formula and Algorithmic Verification
Unit 10 · Lesson 07
Boolean Algebra and Duality
Unit 11 · Lesson 01
Logic Gates and Combinational Circuits
Unit 11 · Lesson 02
Normal Forms and Karnaugh-Map Minimization
Unit 11 · Lesson 03
Finite-State Machines and Transition Tables
Unit 11 · Lesson 04
Deterministic and Nondeterministic Automata
Unit 11 · Lesson 05
Regular Languages and Pattern Recognition
Unit 11 · Lesson 06
State Invariants, Protocol Verification and Model-Checking Foundations
Unit 11 · Lesson 07
Growth of Functions and Asymptotic Notation
Unit 12 · Lesson 01
Summations and Loop Analysis
Unit 12 · Lesson 02
Recurrences in Algorithm Analysis
Unit 12 · Lesson 03
Algorithm Correctness with Preconditions, Postconditions and Invariants
Unit 12 · Lesson 04
Countability and Diagonal Reasoning
Unit 12 · Lesson 05
Decidability, Recognizability and Reductions
Unit 12 · Lesson 06
P, NP and NP-Completeness Foundations
Unit 12 · Lesson 07
Set and Logic Models in Databases and Queries
Unit 13 · Lesson 01
Coding Theory and Hamming Distance
Unit 13 · Lesson 02
Parity, Check Codes and Error Correction
Unit 13 · Lesson 03
Constraint Satisfaction and SAT
Unit 13 · Lesson 04
Network Analysis, Centrality and Community Structure
Unit 13 · Lesson 05
Security, Privacy and Combinatorial Risk
Unit 13 · Lesson 06
Capstone Design: Model, Proof and Algorithm
Unit 13 · Lesson 07
Technical Report, Demonstration and Oral Defense
Unit 13 · Lesson 08