Teaching
Below there are links to the material of some of the most recent courses I have taught.
Most Recent Courses
This is the most recent course I have taught.
Course 18.211: Combinatorial Analysis (MIT, Fall 2021)
- Class Meetings: Mondays/Wednesdays/Fridays 11-12pm; Room: 4-163
- Instructor: Felix Gotti
- Graders: Joseph Heerens and Daniil Kliuev
- Office Hours: Wednesdays 6:30-8pm (via Zoom)
- 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
More information about this course can be found in its Syllabus.
Tentative Schedule of Topics
- 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 (PS1 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 I: Disjoint Cycle Decomposition
- Lecture 12 [M 10/04]. Permutations II: Stirling Numbers of the First Kind
- Lecture 13 [W 10/06]. Permutation III: Descents and Eulerian Numbers
- Lecture 14 [F 10/08]. The Sieve Method and Applications
- Holiday [M 10/11]. Indigenous Peoples Day
- Lecture 15 [W 10/13]. Generating Functions I
- Lecture 16 [F 10/15]. Lecture 16 link; Generating Functions II (PS2 is due.)
- Lecture 17 [M 10/18]. Generating Functions III
- Lecture 18 [W 10/20]. Exponential Generating Functions I
- Lecture 19 [F 10/22]. Exponential Generating Functions II
- Lecture 20 [M 10/25]. Midterm I (Lectures 11–19)
- Lecture 21 [W 10/27]. Intro to Graph and Eulerian Trails
- Lecture 22 [F 10/29]. Hamiltonian Graphs (PS3 is due.)
- Lecture 23 [M 11/01]. Intro to Trees
- Lecture 24 [W 11/03]. The Cayley’s Theorem
- Lecture 25 [F 11/05]. The Cayley’s Theorem (continuation)
- Lecture 26 [M 11/08]. Spanning Trees and Kruskal’s Algorithm (PS4 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]. Bipartite Graphs
- Lecture 30 [W 11/17]. Perfect Matchings and Hall’s Theorem
- Lecture 31 [F 11/19]. Coloring I: Chromatic Numbers and Polynomials
- Lecture 32 [M 11/22]. Coloring II: Brooks’ Theorem (PS5 is due.)
- Lecture 33 [W 11/24]. Planarity: Euler’s Formula and Kuratowski’s Theorem
- Holiday [F 11/26]. Institute Holiday
- Lecture 34 [M 11/29]. Polytopes and Platonic Solids
- Lecture 35 [W 12/01]. Intro to Posets
- Lecture 36 [F 12/03]. Midterm IV (Lectures 29–35)
- Lecture 37 [M 12/06]. Intro to Lattices
- Lecture 38 [W 12/08]. Incidence Algebras and Möbius Inversion Formula (PS6 is due.)
Problem Sets
Problem Sets
- Problem Set 1
- Problem Set 1 (with solutions)
- Problem Set 2
- Problem Set 2 (with solutions)
- Problem Set 3
- Problem Set 3 (with solutions)
- Problem Set 4
- Problem Set 4 (with solutions)
- Problem Set 5
- Problem Set 5 (with solutions)
- Problem Set 6
- Problem Set 6 (with solutions)
- Bonus Problem Set
Midterms
Current Grades
Here are the current grades.