As a professor in the math department at Cal Poly, one of my primary jobs is teaching mathematics. Most quarters, that means teaching two sections of calculus and one higher-level course. It also means working with students outside of the classroom, generally in the form of senior projects and independent studies.

## Courses I Teach

Winter 2018

## Math 141: Calculus I

Calculus is often described as the mathematical study of change, analogous to how geometry is the mathematical study of shape. It can also be viewed as the study of approximations and limits. The first two-thirds of this course focuses on differential calculus, which concerns rates of change. The last third of the course focuses on integral calculus, which concerns the accumulation of quantities. These two ideas are connected by the Fundamental Theorem of Calculus, which essentially says that the two processes are mutual inverses. Derivatives and integrals have proven incredibly useful in many fields of study, and we will see many examples of their applications.

“I have so many ideas that may perhaps be of some use in time if others more penetrating than I go deeply into them someday and join the beauty of their minds to the labour of mine.”

## Math 344: Linear Analysis II

In this second quarter in differential equations, we make the transition from the simple guess-and-check method of solving differential equations to the more advanced theory of transforms. We begin with naively searching for series solutions to differential equations, which for periodic functions leads naturally to Fourier series. In attempting to extend the techniques of Fourier series to non-periodic functions we will discover the Fourier transform and the related Laplace transform. These tools offer a powerful new approach to solving differential equations, completely transforming the original differential equation into something else entirely.

“Ce que nous connaissons est peu de chose, ce que nous ignorons est immense. [What we know is not much. What we do not know is immense.]”

Previously

## Math 141

### Calculus I

The first in a three-quarter sequence in single-variable calculus. This course focuses mainly on the derivative, although the definite integral is introduced near the end.

**Prerequisite: **Placement exams or appropriate coursework.

*Teaching Winter 2017*

## Math 142

### Calculus II

The second in a three-quarter sequence in single-variable calculus. This course focuses mainly on the integral, including both techniques and applications of integration.

**Prerequisite: **Math 141 with a grade of C- or better.

*Last taught Winter 2016*

## Math 143

### Calculus III

The third in a three-quarter sequence in single-variable calculus. This course focuses largely on series, but also introduces vectors, vector-valued functions, and parametric curves.

**Prerequisite: **Math 142 with a grade of C- or better.

*Last taught Spring 2016*

## Math 206

### Linear Algebra I

The first in a three-quarter sequence in linear algebra. This courses focuses real vector spaces, beginning with systems of linear equations and eventually working up through eigenvalues and eigenvectors.

**Prerequisite: **Math 143.

*Last taught Fall 2015*

## Math 241

### Calculus IV

An introduction to multi-variable calculus. This course covers both the differential aspect (e.g., partial derivatives) and the integration aspect (e.g., line and surface integrals).

**Prerequisite: **Math 143.

*Last taught Winter 2017*

## Math 244

### Linear Analysis I

A hybrid course that melds ordinary differential equations and linear algebra. The main focus is solving differential equations, and the linear algebra is developed as needed.

**Prerequisite: **Math 143.

*Last taught Fall 2017*

## Math 306

### Linear Algebra II

The second in a three-quarter sequence in linear algebra. This course focuses on the properties of abstract linear transformations and vector spaces.

**Prerequisites: **Math 241, 248, and either 206 or 244.

*Last taught Spring 2014*

## Math 341

### Theory of Numbers

An introduction to elementary number theory. This course largely focuses on modular arithmetic, culminating in Gauss’ law of quadratic reciprocity.

**Prerequisite:** Math 248 (C- or better).

*Last taught Fall 2016*

## Math 344

### Linear Analysis II

The second quarter in a hybrid course in differential equations and linear algebra. This course focuses on solving differential equations using Laplace and Fourier transforms, and power series methods.

**Prerequisite: **Math 206 and Math 242, or Math 241 and Math 244.

*Teaching Winter 2017*

## Math 351

### Typesetting with LaTeX

An introduction to the LaTeX typesetting language, which most modern mathematicians use to typeset their work. Each week focuses on a new typesetting topic.

**Prerequisite:** Junior standing.

*Last taught Winter 2013*

## Math 370

### Putnam Exam Seminar

An exploration of common problem-solving techniques, generally aimed at preparing students for the yearly Putnam Exam. Each week focuses on a specific technique.

**Prerequisite:** None.

*Last taught Fall 2014*

## Math 408

### Complex Analysis I

The first in a two-quarter sequence in complex analysis. This course begins with an introduction to complex functions and then proceeds to develop a theory of calculus for such functions.

**Prerequisite:** Math 242, or Math 241 and Math 244.

*Last taught Fall 2014*

## Math 409

### Complex Analysis II

The second in a two-quarter sequence in complex analysis. This course continues the study of complex functions, which may include advanced topics in contour integration, conformal maps, and other similar topics.

**Prerequisite:** Math 408.

*Last taught Winter 2015*

## Math 481

### Abstract Algebra I

The first in a two-quarter sequence in modern (abstract) algebra. This course focuses mainly on groups and the maps between them, but may also include the beginnings of ring theory.

**Prerequisite:** Math 306 or 341.

*Last taught Winter 2016*

## Math 482

### Abstract Algebra II

The second in a two-quarter sequence in modern (abstract) algebra. This course focuses mainly on rings, but may also include the beginnings of field theory.

**Prerequisite:** Math 481.

*Last taught Spring 2016*

## Math 560

### Field Theory

This graduate course focuses on Galois theory, the intimate connection between fields and groups that led to the first proof of the “insolvability of the quintic.”

**Prerequisite:** Passing score on algebra qual.

*Last taught Spring 2017*

# Outside the Classroom

Learning (Math) by Doing (Math)

## Senior Projects I’ve Advised

## Popular Topics for Independent Study

# Algebraic Geometry

# Category Theory

### “Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.”

### “We now come to two (sets of) facts I wish I had learned as a child, as they would have saved me lots of grief. They encapsulate what is best and worst of abstract nonsense.”

Excerpt from *The Rising Sea: Foundations of Algebraic Geometry*.