Fedya Manin

Teaching

In 2025--26, I will be teaching:

• MAT 464/1342, Riemannian geometry (a cross-listed undergraduate/masters level course)
• MAT 367, Differential geometry (an undergraduate course on manifolds, vector bundles, etc.)

At Toronto, I have taught:

• MAT 464/1342, Riemannian geometry (a cross-listed undergraduate/masters level course)
• MAT 1351, Topics in Homotopy Theory: Rational homotopy theory with geometric applications (a graduate topics course)

At UCSB, I taught:

• CCS Math 120 TC, Topological combinatorics (a class in the College of Creative Studies based on Matoušek's book Using the Borsuk–Ulam theorem, Spring 2024)
• Math 227C, Topics in geometric and algebraic topology (this topics course focused on the geometry of nilpotent groups, Spring 2024)
• Math 221B, Homotopy theory (a graduate course focusing on the fundamental group, Ch. 0 and 1 of Hatcher's textbook, Winter 2024)
• Math 113, Non-Euclidean geometry (Fall 2023)
• Math 227C, Topics in geometric and algebraic topology (this topics course focused on quasi-isometry invariants in geometric group theory, Spring 2022)
• CCS Math 120SY, Symmetry (Winter 2022)

  This was an IBL course of my own design. The students were mainly advanced first-years who had taken an introduction to proofs, but no proof-based linear algebra or analysis courses. It focused on symmetry groups, i.e. groups acting by isometries on metric spaces, starting with isometries of the Euclidean plane. Feel free to contact me if you would like to see the course materials and my thoughts about how to do it better next time.
• Math 221A, (graduate point-set) Topology (Fall 2021)
• CCS Math 128 (an introduction to proof-based math in the College of Creative Studies, Fall 2021)
• Math 147A, Introduction to differential geometry (undergraduate curves and surfaces, Spring 2021)
• Math 232B, Algebraic topology (a graduate course focusing on cohomology, Spring 2021)
• Math 227A, Topics in geometric and algebraic topology (this topics course focused on rational homotopy and its applications in the world of manifolds, Fall 2020)
• Math 108B, Advanced linear algebra (focusing on diagonalization, Jordan form, and inner product spaces, Spring 2020)
• Math 111B, Abstract algebra (undergraduate ring and module theory, Winter 2020)
• Math 232A, Algebraic topology (a graduate course focusing on homology, Ch. 2 of Hatcher's textbook, Fall 2019 and Fall 2022)

• MATH 4507, Geometry (a flipped-classroom course focusing on Euclidean, spherical, and hyperbolic geometry, Spring 2019)
• MATH 2255, Ordinary Differential Equations and Applications (Fall 2018)
• MATH 2568, Linear algebra (Spring 2018, two sections)

• MAT 137, Calculus! (2015–2016 and 2016–2017).

• MATH 152–153, Calculus II and III (2014–2015)
• MATH 196, Linear algebra (Winter 2014 and Spring 2012)
• MATH 195, Mathematical methods for the social sciences (a multivariable calculus class; Fall 2013, Winter 2013, Fall 2012)
• MATH 131–132, Elementary functions and calculus I and II (2011–2012)