Felix Gotti

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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

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

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 (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 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]. Generating Functions II (PS 2 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 II (Lectures 11-19)
Lecture 21 [W 10/27]. Intro to Graph and Eulerian Trails
Lecture 22 [F 10/29]. Hamiltonian Graphs (PS 3 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 (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]. 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 (PS 5 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 (PS 6 is due.)

Problem Sets

Midterms

Current Grades:

Here are the current grades.

Felix Gotti

MIT-NSF Postdoctoral Fellow

This page was last updated in August 2021.

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