Courses at New College

• Fall 2024:
  • Advanced Linear Algebra
  • Mathematical Thinking: Patterns, Puzzles, and Exploration
• Spring 2024:
  • Real Analysis II
  • Discrete Mathematics
• Fall 2023:
  • Real Analysis I
  • Mathematical Thinking: Patterns, Puzzles, and Exploration
• Spring 2023:
  • Calculus With Theory II
  • Writing in Mathematics
• Fall 2022:
  • Calculus With Theory I
  • Mathematical Thinking: Patterns, Puzzles, and Exploration
• Spring 2022:
  • Real Analysis II
  • Discrete Mathematics
• Fall 2021:
  • Real Analysis I
  • Mathematical Thinking: Patterns, Puzzles, and Exploration
• Spring 2021:
  • Complex Analysis
  • Writing in Mathematics
• Fall 2020:
  • Calculus III
  • Mathematical Thinking: Patterns, Puzzles, and Exploration
• Spring 2020:
  • PDE
  • Writing in Mathematics
• Fall 2019: On leave
• Spring 2019:
  • Distribution Theory
  • Writing in Mathematics
• Fall 2018:
  • Calculus III
  • Complex Analysis
• Spring 2018:
  • PDE
  • Real Analysis II
• Fall 2017:
  • Calculus III
  • Real Analysis
• Spring 2017:
  • Advanced Linear Algebra
  • Complex Analysis
• Fall 2016:
  • Calculus III
  • Functional Analysis

New College thesis class for LaTeX

For New College students who wish to write their thesis in LaTeX, I have written a class file which will give you all the proper formatting. Feel free to reach out to me with questions about how to use these.

• ncfthesis project page on GitHub, including documentation. A direct link to the class file is here.

Courses at Northeastern

• Spring 2016:
  • Math 7376, Topics in Differential Geometry: Analysis on Compact Manifolds.
• Fall 2015:
  • Math 2321, Calculus 3
  • Math 3150, Real Analysis
• Spring 2015:
  • Math 2321, Calculus 3
• Fall 2014:
  • Math 3150, Real Analysis
• Spring 2014:
  • Math 2321, Calculus 3
• Fall 2013:
  • Math 3150, Real Analysis

Courses at Brown

• Spring 2013:
  • Math 540, Honors Linear Algebra
  • Math 1530, Abstract Algebra
• Fall 2012:
  • Math 1110, Differential Equations
• Spring 2012:
  • Math 2420, Algebraic Topology
• Fall 2011:
  • Math 1580, Mathematical Cryptography
  • Math 170, Advanced Placement Calculus
• Spring 2011:
  • Math 540, Honors Linear Algebra
• Fall 2010:
  • Math 350, Honors Vector Calculus

Notes from various classes

• Linear Analysis on Compact Manifolds. Notes on elliptic theory on compact manifolds, including spectral theory, heat kernels, Weyl asymptotics, and a proof of the Atiyah-Singer index theorem by heat kernel methods.
• Products in homology and cohomology via acyclic models. Mostly following Bredon’s Topology and Geometry, and used to supplement Hatcher’s Algebraic Topology.
• Ext, Tor and the universal coefficient theorem. Used to supplement Hatcher.
• Bundles, classifying spaces and characteristic classes. Emphasizes the role of principal bundles and associated bundles in the classification of vector bundles, and contains a homotopy theoretic definition of Steifel-Whitney and Chern classes.
• Jordan canonical form. Filipov’s brief, elementary proof of Jordan form for real and complex matrices.
• Row reduction and its many uses. Used to supplement Axler’s Linear Algebra Done Right.

Old MIT review packets

• 18.02A review covering the second half (IAP portion) of 18.02A, 2009.
• 18.03 final exam review, last edited 2010.