This semester I am teaching 18.211, a course in combinatorial analysis. Here is a link to some of the most recent courses I have taught.

**Course 18.211: Combinatorial Analysis (MIT, Fall 2021)**

**Class Meetings:** Mondays/Wednesdays/Fridays 11-12pm; Room: 4-163

**Instructor:** Felix Gotti

**Office Hours:** TBA

**Official Textbook:** "A Walk Through Combinatorics" by Miklos Bona (any edition will be suitable for this course)

**Further (Non-Required) Recommended Books:**

- "Enumerative Combinatorics" (Vol. I) by Richard Stanley
- "Algebraic Combinatorics: Walks, Trees, Tableaux, and More" by Richard Stanley
- "Modern Graph Theory" by Béla Bollobás

- Lecture 1 [W 09/08]. Pigeonhole Principle
- Lecture 2 [F 09/10]. Mathematical Induction
- Lecture 3 [M 09/13]. Elementary Counting
- Lecture 4 [W 09/15]. Binomial and Multinomial Theorems
- Lecture 5 [F 09/17]. Inversions of Permutations, q-Factorial, and q-Binomials
- Lecture 6 [M 09/20]. Compositions
- Lecture 7 [W 09/22]. Set Partitions, Stirling Numbers of the Second Kind (PS 1 is due.)
- Lecture 8 [F 09/24]. Integer Partitions I
- Lecture 9 [M 09/27]. Integer Partitions II
- Lecture 10 [W 09/29]. Midterm I (Lectures 1-9)

- Lecture 11 [F 10/01]. Permutations: Cycle Type
- Lecture 12 [M 10/04]. Permutations: Stirling Numbers of the First Kind
- Lecture 13 [W 10/06]. The Sieve Formula
- Lecture 14 [F 10/08]. The Problem of Derangements
- Holiday [M 10/11]. Indigenous Peoples Day
- Lecture 15 [W 10/13]. Generating Functions I: Recurrences and Examples (PS 2 is due.)
- Lecture 16 [F 10/15]. Generating Functions II: Products and Catalan Numbers
- Lecture 17 [M 10/18]. Generating Functions III: Compositions
- Lecture 18 [W 10/20]. Exponential Generating Functions I: Recurrences and Products
- Lecture 19 [F 10/22]. Exponential Generating Functions II: The Exponential Formula
- Lecture 20 [M 10/25]. Midterm II (Lectures 11-19)

- Lecture 21 [W 10/27]. Intro to Graph Theory (PS 3 is due.)
- Lecture 22 [F 10/29]. Eulearian Trails and Hamiltonian Cycles
- Lecture 23 [M 11/01]. Connectedness and Trees
- Lecture 24 [W 11/03]. More on Trees: The Cayley's Formula
- Lecture 25 [F 11/05]. Spanning Trees of Graphs
- Lecture 26 [M 11/08]. Kruskal's Algorithm and Matroids (PS 4 is due.)
- Lecture 27 [W 11/10]. Graph and Matrices: The Matrix-Tree Theorem
- Lecture 28 [F 11/12]. Midterm III (Lectures 21-27)

- Lecture 29 [M 11/15]. Matching in Graphs I: Bipartite Graphs
- Lecture 30 [W 11/17]. Matching in Graphs II: Hall's Marriage Theorem
- Lecture 31 [F 11/29]. Graphs Coloring I: k-Coloring and Brooks' Theorem
- Lecture 32 [M 11/22]. Graph Coloring II: Tutte's Theorem (PS 5 is due.)
- Lecture 33 [W 11/24]. Planarity I: Euler's Formula and Kuratowski's Theorem
- Holiday [F 11/26]. Institute Holiday
- Lecture 34 [M 11/29]. Planarity II: Polytopes
- Lecture 35 [W 12/01]. Ramsey Theory
- Lecture 36 [F 12/03]. Midterm IV (Lectures 29-35)
- Lecture 37 [M 12/06]. Intro to Posets and Lattices
- Lecture 38 [W 12/08]. The Möbius Inversion Formula (PS 6 is due.)

- Problem Set 1
- Problem Set 2
- Problem Set 3
- Problem Set 4
- Problem Set 5
- Problem Set 6