Course Notes

I keep notes on many courses and seminars I have been a part of. There are sure to be some errors, both cosmetic and mathematical, so if you find any, please contact me at ajkobinmath (at) gmail (dot) com. Comments and questions are also welcome!

• Abelian Varieties (Virginia, Fall 2019 - Spring 2020 / Emory, Summer 2022)

• Abstract Algebra (Wake Forest, Fall 2013 - Spring 2014)

• Algebraic Geometry of Curves (Virginia, Fall 2016)

• Algebraic Number Theory (Virginia, Spring 2016)

• Algebraic Stacks (Virginia, Spring 2017 - Spring 2020)

• Algebraic Topology (Virginia, Spring - Fall 2016)

• Analysis of Banach Spaces (Wake Forest, Spring 2014)

• Analytic Number Theory (Wake Forest, Fall 2013)

• Arithmetic Fundamental Group (Virginia, Spring 2017)

• Class Field Theory (Wake Forest, Fall 2013 - Spring 2015)

• Commutative Algebra (Virginia, Spring 2016 & 2019)

• Complex Analysis (Wake Forest, Fall 2010)

• Complex Surfaces (in progress)

• Derived Categories (in progress)

• Differential Geometry (Wake Forest, Spring 2015)

• Differential Topology (Virginia, Fall 2015)

• Elementary Number Theory (Wake Forest, Spring 2013 / Emory, Fall 2022 & 2023)

• Étale Cohomology (in progress)

• Étale Theory (Virginia, Fall 2018 - Spring 2019)

• Fibre Bundles (Virginia, Spring 2017 & 2018)

• Galois Cohomology (in progress)

• General Topology (Wake Forest, Fall 2013 - Spring 2014)

• Generalized Jacobians (Virginia, Fall 2016 - Spring 2017)

• Homological Algebra (Wake Forest, Fall 2014 / Virginia, Spring 2017)

• Homotopy Theory (Virginia, Fall 2017)

• Hyperbolic Geometry (in progress)

• L-Functions and Modular Forms (Virginia, Fall 2017 - Spring 2018)

• Lie Groups (Virginia, Fall 2015 & Spring 2018)

• Linear Algebra I (Emory, Fall 2021)

• Linear Algebra II (Wake Forest, Fall 2014 / UC Santa Cruz, Spring 2021)

• Measure Theory (Virginia, Spring 2016)

• Modular Forms (Virginia, Fall 2019)

• Noncommutative Algebra (Virginia, Fall 2015)

• Numerical Methods (Wake Forest, Fall 2014)

• Probabilistic Measure Theory (Wake Forest, Spring 2015)

• Real Analysis (Wake Forest, Fall 2012)

• Representation Theory (Wake Forest, Fall 2014)

• Sheaf Cohomology (Virginia, Fall 2018)

• Short Course on Schemes (Virginia, Summer 2017)

Although my philosophy is that 'all math is connected', I have grouped many of the above notes by area for ease of cross-referencing. These larger files are available below. 

• Algebra

• Algebraic Geometry

• Analysis

• Number Theory

• Topology

Thanks to Matt Feller, George Seelinger, Richard Vradenburgh and many others for noticing errors!