Felix Gotti

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

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 (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

• 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

• Midterm 1 (with solutions)
• Midterm 2 (with solutions)
• Midterm 3 (with solutions)
• Midterm 4 (with solutions)

Current Grades:

Here are the current grades.