Teaching

Information about my current and past courses is available below. I make most of my course materials publicly available, in case they are useful to anyone at Amherst or elsewhere. Please notify me of any broken links or other issues, and feel free to contact me to request any materials not posted on these pages.

Spring 2024

Math 385 — Mathematical Logic

What, exactly, is a proof? This course begins with a precise definition specifying what counts as a mathematical proof. This definition makes it possible to ...

Math 281 — Combinatorics

This course emphasizes enumerative combinatorics, a classical subject in mathematics related to the theory of counting. Problems in this area often pertain t...

Fall 2023

Math 111 — Introduction to the Calculus

This course concerns the two central idea of calculus: the derivative and the integral.

Spring 2023

Math 252 — Mathematics of Public-Key Cryptography

This course concerns the mathematical problems underlying public-key ciphers and digital signatures, as well as algorithms to solve them. Topics include disc...

Math 121 — Intermediate Calculus

This course is focused on integration techniques, series, and parametric/polar equations.

Spring 2022

Math 271 — Linear Algebra

This course concerns the core theory of linear algebra, with specific attention to the theoretical development necessary for pure mathematics. The primary ob...

Math 252 — Mathematics of Public-Key Cryptography

This course concerns the mathematical problems underlying public-key ciphers and digital signatures, as well as algorithms to solve them. Topics include disc...

Spring 2020

Math 252 — Mathematics of Public-Key Cryptography

This course concerns the mathematical problems underlying public-key ciphers and digital signatures, as well as algorithms to solve them. Topics include disc...

Math 220 — Mathematical Reasoning and Proof

This course serves as an introduction to mathematical reasoning and pays particular attention to helping students learn how to write proofs. The topics cover...

Fall 2019

Math 350 — Groups, Rings, and Fields

This course is an introduction to abstract algebra, a central pillar of modern mathematics that concerns generalizations of the familiar addition and multipl...

Math 272 — Linear Algebra with Applications

This course concerns the core theory of linear algebra, with specific attention to applications.

Spring 2019

Math 272 — Linear Algebra with Applications

This course concerns the core theory of linear algebra, with specific attention to applications.

Math 252 — Mathematics of Public-Key Cryptography

This course concerns the mathematical problems underlying public-key ciphers and digital signatures, as well as algorithms to solve them. Topics include disc...

Fall 2018

Math 350 — Groups, Rings, and Fields

This course is an introduction to abstract algebra, a central pillar of modern mathematics that concerns generalizations of the familiar addition and multipl...

Math 105 — Calculus with Algebra

This course covers the first major topics of calculs: limits and derivatives. Alongside the calculus material, the course provides continual review of concep...

Spring 2018

Math 272 — Linear Algebra with Applications

This course concerns the core theory of linear algebra, with specific attention to applications.

Math 121 — Intermediate Calculus

This course is focused on integration techniques, series, and parametric/polar equations.

Fall 2017

Math 272 — Linear Algebra with Applications

This course concerns the core theory of linear algebra, with specific attention to applications.

Math 111 — Introduction to the Calculus

This course concerns the two central idea of calculus: the derivative and the integral.

Spring 2017

Math 206 — Algebraic Geometry II (at Brown)

This course will cover the methods, key examples, and technical foundations of modern algebraic geometry. It is a continuation of Math 205 from the fall. The...

Fall 2016

Math 205 — Algebraic Geometry I (at Brown)

This course will cover the methods, key examples, and technical foundations of modern algebraic geometry. The course will aim to both present examples and me...

Math 158 — Cryptography (at Brown)

This course concerns the mathematical problems underlying public-key ciphers and digital signatures, as well as algorithms to solve them. Topics include disc...

Spring 2016

Math 206 — Algebraic Geometry II (at Brown)

We will discuss sheaf cohomology in detail, and then cover the basic theory and some special topics in the theory of algebraic curves.

Fall 2015

Math 158 — Cryptography (at Brown)

This course will focus on the mathematics of public-key cryptography. This subject presents an appealing introduction to several topics from both mathematics...

Spring 2015

Math 9 — Calculus I (at Brown)

Students will learn to understand, evaluate, and apply limits and derivatives of functions, as well as the basics of antidifferentiation and integration.

Math 42 — Introduction to Number Theory (at Brown)

This course introduces the basic ideas of number theory. It is aimed at non-majors and has no prerequisites.

Fall 2014

Math 19 — Calculus 2 for Physics and Engineering (at Brown)

A second-semester course in calculus, geared towards students interested in physics and engineering.

Fall 2013

Math 1A — Introduction to Calculus (at Harvard)

Fall 2011

Math 1B — Calculus, Series, and Differential Equations (at Harvard)