# Courses at New College

- Spring 2019:
- Fall 2018:
- Spring 2018:
- Fall 2017:
- Spring 2017:
- Fall 2016:
- 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.cls is the class file for formatting.
- template.tex and template.bib are an example/template thesis and bibliography database.

# Courses at Northeastern

- Spring 2016:
- Math 7376, Topics in Differential Geometry: Analysis on Compact Manifolds.

- Fall 2015:
- 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:
- Fall 2012:
- Math 1110, Differential Equations

- Spring 2012:
- Math 2420, Algebraic Topology

- Fall 2011:
- 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.