Lecture 1. What is discrete mathematics?
Lecture 2. Basic concepts of combinatorics
Lecture 3. The 12-fold way of combinatorics
Lecture 4. Pascal's triangle and the binomial theorem
Lecture 5. Advanced combinatorics
Lecture 6. The principle of inclusion-exclusion
inductive, geometric, combinatorial
Lecture 8. Linear recurrences and Fibonacci Numbers
Lecture 9. Gateway to number theory
Lecture 10. The structure of numbers
Lecture 11. Two principles
Lecture 13. Enormous exponents and card shuffling
Lecture 14. Fermat's "little" theorem and prime testing
Lecture 16. The birth of graph theory
matrices and Markov Chains
Lecture 18. Social networks and stable marriages
Lecture 19. Tournaments and King Chickens
Lecture 20. Weighted graphs and minimum spanning trees
when can a graph be untangles?
Lecture 22. Coloring graphs and maps
Lecture 23. Shortest paths and algorithm complexity
Lecture 24. The magic of discrete mathematics.
Part 1: Disc 1. Lecture 1. What is discrete mathematics? ; Lecture 2. Basic concepts of combinatorics ; Lecture 3. The 12-fold way of combinatorics ; Lecture 4. Pascal's triangle and the binomial theorem ; Lecture 5. Advanced combinatorics: Multichoosing ; Lecture 6. The principle of inclusion-exclusion --
Disc 2. Lecture 7. Proofs: Inductive, geometric, combinatorial ; Lecture 8. Linear recurrences and Fibonacci Numbers ; Lecture 9. Gateway to number theory: Divisibility ; Lecture 10. The structure of numbers ; Lecture 11. Two principles: Pigeonholes and parity ; 12. Modular arithmetic: The math of remainders.
Part 2: Disc 3. Lecture 13. Enormous exponents and card shuffling ; Lecture 14. Fermat's "little" theorem and prime testing ; Lecture 15. Open secrets: Public key cryptography ; Lecture 16. The birth of graph theory ; Lecture 17. Ways to walk: Matrices and Markov chains ; Lecture 18. Social networks and stable marriages --
Disc 4. Lecture 19. Tournaments and King Chickens ; Lecture 20. Weighted graphs and minimum spanning trees ; Lecture 21. Planarity: When can a graph be untangled? ; Lecture 22. Coloring graphs and maps ; Lecture 23. Shortest paths and algorithm complexity ; Lecture 24. The magic of discrete mathematics.