Teaching

Below there are links to the material of some of the most recent courses I have taught.

Most Recent Courses

NoteMIT, 18.211: Combinatorial Analysis (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.

NoteMIT, IAP 2021: Ideal Theory and Prüfer Domains (Spring 2021)

Hours: Mondays/Wednesdays/Fridays 4-5pm (via Zoom)

Textbook: We will follow the structure of Gilmer’s book “Multiplicative Ideal Theory”

Lecture Notes

• Preliminaries on Rings and Modules
• Lecture 1: Localization
• Lecture 2: Prime and Maximal Ideals
• Lecture 3: Radical and Primary Ideals
• Lecture 4: Primary Decompositions
• Lecture 5: One-dimensional Noetherian Rings
• Lecture 6: Krull’s Theorems
• Lecture 7: Integral Extensions I (Basic Properties)
• Lecture 8: Integral Extensions II (Spectral Theorems)
• Lecture 9: Fractional Ideals
• Lecture 10: Valuation Domains I (Characterizations)
• Lecture 11: Valuation Domains II (Overrings and Integral Closures)
• Lecture 12: Discrete Valuation Rings
• Lecture 13: Dedekind Domains
• Lecture 14: Prüfer Domains I (Characterizations)
• Lecture 15: Prüfer Domains II (Overrings)
• Lecture 16: Almost Dedekind Domains
• Lecture 17: Integer-Valued Polynomials I (The Spectrum)
• Lecture 18: Integer-Valued Polynomials II (Prüferness)

NoteMIT, 18.02: Multivariable Calculus (Fall 2020)

Recitations: Tuesdays/Thursdays 11-12pm and 1-3pm (via Zoom)

Office Hours: Thursdays 7-10pm (via Zoom)

NoteMATH 53: Multivariable Calculus (UC Berkeley, Summer 2018)

Office Hours: Tuesday 5pm–6pm and Thursday 6pm–7pm

Textbook: Single Variable Calculus (8th Edition) by J. Stewart

Discussion Problems

• R3 Geometry, Inner Product, and Cross Product
  Sections 12.1–12.4
• Lines and Planes
  Section 12.5
• Cylinders and Quadric Surfaces
  Section 12.6
• Vector Functions
  Sections 13.1–13.4
• Limit and Continuity
  Sections 14.1, 14.2
• Partial Derivatives
  Sections 14.3, 14.4
• The Chain Rule
  Section 14.5
• Directional Derivatives and the Gradient Vector
  Section 14.6
• Maxima, Minima, and Lagrange Multipliers
  Sections 14.7, 14.8
• Double Integrals
  Sections 15.1, 15.2, 15.4, 15.5
• Triple Integrals
  Section 15.6
• Polar and Cylindrical Coordinates
  Sections 15.3, 15.7
• Spherical Coordinates
  Section 15.8
• General Changes of Coordinates
  Section 15.9
• Line Integrals and Green’s Theorem
  Sections 16.1–16.4
• Surface Integrals and Flux
  Sections 16.5–16.7
• Stokes’ Theorem and Divergence Theorem
  Sections 16.8, 16.9

NoteMATH 1B: Single Variable Calculus II (UC Berkeley, Spring 2017)

Office Hours: Monday and Wednesday 6pm–7pm

Textbook: Single Variable Calculus (8th Edition) by J. Stewart

Discussion Problems

• Section 7.1: Integration by Parts
• Section 7.2: Trigonometric Integrals
• Section 7.3: Trigonometric Substitution
• Section 7.4: Integration of Rational Functions by Partial Fractions
• Section 7.5: Strategy for Integration
• Section 7.7: Approximate Integration
• Section 7.8: Improper Integrals
• Section 8.1: Arc Length
• Section 8.2: Area of a Surface of Revolution
• Section 11.1: Sequences
• Section 11.2: Series
• Section 11.3: The Integral Test
• Section 11.4: The Comparison Tests
• Section 11.5: Alternating Series
• Section 11.6: Absolute Convergence; Ratio and Root Tests
• Section 11.7: Strategy for Testing Series
• Section 11.8: Power Series
• Section 11.9: Representations of Functions as Power Series
• Section 11.10: Taylor and Maclaurin Series
• Section 11.11: Applications of Taylor Series and Taylor Polynomials
• Section 9.3: Separable Differential Equations
• Section 9.4: Models for Population Growth
• Section 9.5: Linear Differential Equations
• Section 17.1: Homogeneous Second-Order Differential Equations
• Section 17.2: Nonhomogeneous Second-Order Differential Equations
• Section 17.4: Series Solutions of Differential Equations

Quizzes

• Mock Quiz 1 (with solutions)
• Quiz 1 (with solutions)
• Mock Quiz 2 (with solutions)
• Quiz 2 (with solutions)
• Mock Quiz 3 (without solutions)
• Quiz 3 (with solutions)

Exams

• Final Practice Exam (with solutions)

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

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

Current Grades

Here are the current grades.