MATH 4190 - Discrete Mathematical Structures

Week One

Tue May 12 — Lecture 1: Propositional Logic and Truth Tables
Slides | Videos
Read and exercises: Rosen, Sections 1.1, 1.2, 1.3.

Wed May 13 — Lecture 2: Predicate Logic
Slides | Videos
Read and exercises: Rosen, Sections 1.4, 1.5.

Thu May 14 — Lecture 3: Proofs
Slides | Videos
Read and exercises: Rosen, Sections 1.6, 1.7, 1.8.

Fri May 15 — Lecture 4: Basic Set Theory
Slides | Videos
Read and exercises: Rosen, Sections 2.1, 2.2.

Week Two

Mon May 18 — Lecture 5: Functions
Slides | Videos
Read and exercises: Rosen, Section 2.3.

Tue May 19 — Lecture 6: Counting
Slides | Videos
Read and exercises: Rosen, Sections 6.1, 6.3.

Wed May 20 — Lecture 7: More Counting
Slides | Videos
Read and exercises: Rosen, Sections 6.4, 6.5.

Thu May 21 — Lecture 8: Pigeonhole Principle & Induction
Slides | Videos
Read and exercises: Rosen, Sections 6.2, 5.1, 5.2.

Fri May 22 — Lecture 9: Recurrence Relations
Slides | Videos
Read and exercises: Rosen, Sections 2.4, 8.1, 8.2.

Week Three

Wed May 27 — Lecture 10: Divide and Conquer
Slides | Videos
Read and exercises: Rosen, Sections 3.2, 3.3, and 8.3.

Thu May 28 — Lecture 11: Generating Functions
Slides | Videos
Read and exercises: Rosen, Section 8.4.
Also read and do exercises: Wilf, Generatingfunctionology (free!), Chapter 1 and Sections 2.1–2.2.

Fri May 29 — Lecture 12: More Generating Functions
Slides | Videos
Read and exercises: Rosen, Section 8.4.
Also read and do exercises: Wilf, Generatingfunctionology (free!), Chapter 1 and Sections 2.1–2.2.

Week Four

Mon June 1 — Lecture 13: Even More Generating Functions
Slides | Videos
Read and exercises: Rosen, Section 8.4.
Also read and do exercises: Wilf, Generatingfunctionology (free!), Chapter 1 and Sections 2.1–2.2.

Tue June 2 — Lecture 14: Probability Theory
Slides | Videos
Read and exercises: Rosen, Sections 7.1 and 7.2.

Wed June 3 — Lecture 15: More Probability
Slides | Videos
Read and exercises: Rosen, Section 7.4.

Thu June 4 — Lecture 16: Expectations and Gambling
Slides | Videos
Read and exercises: Rosen, Sections 7.2 and 7.3.

Fri June 5 — Lecture 17: Variance
Slides | Videos
Read and exercises: Rosen, Sections 7.3 and 7.4.

Week Five

Mon June 8 — Lecture 18: Basic Number Theory
Slides | Videos
Read and exercises: Rosen, Sections 4.1 and 4.3.

Tue June 9 — Lecture 19: Modular Arithmetic
Slides | Videos
Read and exercises: Rosen, Sections 4.1 and 4.3.

Wed June 10 — Lecture 20: Solving Congruences
Slides | Videos
Read and exercises: Rosen, Section 4.4.

Fri June 12 — Lecture 21: Classical Cryptography
Slides | Videos
Read and exercises: Rosen, Section 4.6.

Week Six

Mon June 15 — Lecture 22: Modern Cryptography
Slides | Videos
Read and exercises: Rosen, Section 4.6.
Additional recommended source: Trappe and Washington, Introduction to Cryptography with Coding Theory, Chapters 6 on block ciphers, 8 on AES, 9 on RSA, and 13 on digital signatures.

Tue June 16 — Lecture 23: Secret Sharing
Slides | Videos
Read and exercises: Trappe and Washington, Introduction to Cryptography with Coding Theory, Chapter 12 on secret sharing.