Discrete Mathematics

Boolean Algebra and Logic Gates

Model logical circuits and Boolean algebra with code-driven truth tables.

Truth Tables and SAT

Build truth tables and explore satisfiability in logic formulas.

Finite State Machines

Simulate finite state machines to model sequential logic and transitions.

// Unit 2: Set Theory and Relations

Sets and Power Set Explosion

Explore set operations and the exponential growth of power sets.

Relations as Matrices

Represent relations with adjacency matrices and analyze their properties.

Hashing and Pigeonhole

Explore hashing concepts and the pigeonhole principle in discrete structures.

// Unit 3: Combinatorics and Complexity

Traveling Salesperson

Model TSP heuristics and examine computational complexity.

Recurrence and DP Fibonacci

Compare recurrence versus dynamic programming through Fibonacci computations.

Big-O Sort Race

Benchmark sorting algorithms to understand runtime behavior.

// Unit 4: Graph Theory

Adjacency Matrices and BFS

Implement BFS on graphs and examine adjacency matrix representations.

Dijkstra’s Algorithm

Compute shortest paths on weighted graphs with Dijkstra’s algorithm.

Minimum Spanning Trees

Find MSTs and compare Prim’s and Kruskal’s algorithm behaviors.

// Unit 5: Number Theory and Cryptography

Sieve and Ulam Spiral

Generate prime sieves and visualize primes with the Ulam spiral.

Euclidean Algorithm and Inverses

Compute modular inverses and gcds with the Euclidean algorithm.

RSA Encryption

Implement RSA key generation and explore public-key cryptography.