Spring 2026
This semester, I will be teaching Math 102 and Math 232 (Honors Multivariable Calculus).
If you are interested in taking Math 232, you should send me an email. You are welcome to attend lectures as a guest before the add/drop deadline, and you should also talk to me before/after class to be added to the course Canvas page.
Math 102: Calculus II
You can find the course syllabus here.
What tools do we have to calculate an integral like $\int_0^1 xe^{-x^2} \ dx$ or $\int_0^1 e^{-x^2} \ dx$?
When your calculator tells you that the value of $\int_0^1 e^{-x^2} \ dx \approx 0.746824$, how do you know it’s correct? How accurate is your calculator? Is it possible for an infinite region to have finite area? Can we calculate the area of a fractal?
You’ve previously seen in Math 101 that calculus is an important and powerful tool that allows us to describe the physical world around us. In Math 102, we will push the notion of integration to its utmost limits. In this class, we will build our toolbox for integration; we will study the behavior of the infinite, and we will learn how to quantify how accurate our approximations are.
In this course, you will develop the critical thinking and questioning skills needed to answer these complex questions. Moreover, you will become fluent in precisely communicating your ideas through the mathematical language of calculus.
Math 232: Honors Multivariable Calculus
You can find the course syllabus here.
How can we describe the physical world mathematically? What changes, and what stays the same when we move from single variable calculus to multivariable calculus? What does it mean to take a derivative of a multivariable function? What does it mean to integrate a multivariable function? What regions can we integrate over? How can we generalize the Fundamental Theorem of Calculus?
Multivariable calculus is the mathematical language that allows us to describe the geometry of the physical world around us, such as the motion of planets in orbit, the path of steepest ascent through the hills of Los Angeles, or how to calculate the amount of electricity flowing along a curve or through a surface. In this course, you will develop the reasoning and questioning skills needed to explore these geometric concepts and apply them to real-life situations. Moreover, you will become fluent in communicating your ideas through the mathematical language of multivariable calculus.
The course MATH 232 differs from MATH 212 in that it covers the topics of multivariable calculus with more mathematical rigor (e.g. proofs). That is, in addition to learning how to perform standard computations, we will also learn how to grapple with and prove statements about complex mathematical concepts. Moreover, this course builds the foundation for more advanced topics, such as real analysis, complex analysis, and differential geometry. This course differs from MATH 222 in that we will not discuss general manifolds (only curves and surfaces), nor differential forms.
This course is recommended for students interested in learning about advanced mathematics.