Current Teaching / Tutoring

I am currently (Spring 2018)  a Teaching Assistant for Math 3B at University California, Santa Barbara.
I am also a private tutor and happy to help with most undergraduate math courses.

Past Teaching

My past teaching experiences include:

​Fall 2011: TA for Math 1031 at University of Minnesota
Spring 2012: TA for Math 1031 at University of Minnesota
Fall 2012: TA for Math 1031 at University of Minnesota
Spring 2013: TA for Math 1031 at University of Minnesota

Summer 2014: TA for Math 4A at University of California, Santa Barbara.
Fall 2014: TA for Math 4A at University of California, Santa Barbara.
Winter 2015: TA for Math 3B at University of California, Santa Barbara.
Spring 2015: TA for Math 3B at University of California, Santa Barbara.
Summer 2015: Instructor for Math 3B, University of California Santa Barbara.
Fall 2015: TA for Math 3B at University of California, Santa Barbara.
Winter 2016: TA for Math 3B at University of California, Santa Barbara.
Summer 2016: Instructor for Math 3B, University of California, Santa Barbara.
Fall 2016: TA For Math 4A at University of California, Santa Barbara.
Winter 2016: TA For Math 108A, University of California, Santa Barbara.
Fall 2017: TA For Math 6A, University of California, Santa Barbara.
Winter 2018: TA for Math 3B, University of California, Santa Barbara.

Science Fair 

As a highschool student I was heavily involved in the science fair: competing at the state, national and international levels.   The national competition, Junior Science and Humanities Symposium (JSHS) gave me early experience giving conference-style research talks, and I am very happy to be able to give back as an adult.

Expository Writings

Experience tutoring various levels of mathematics over the years has led me to think a lot about the different ways new ideas can be presented.  As I myself am rather geometrically inclined, I've collected some of the more interesting geometric perspectives that I have come across or thought up below; the topics covered range from grade school through undergraduate mathematics.

Multiplication - Geometrically

Taking a geometric viewpoint with respect to basic arithmetic and algebra allows us to visualize factoring, foiling and the proof of the quadratic formula.

The Pythagorean Theorem

A very visual argument for the pythagorean theorem, one you can replicate yourself with a scissors and some paper!

Geometric Series

​Geometric series are the simplest introduction to the idea of adding up infinitely many things.  Here we will discuss the potential pitfalls of infinite addition, and work through a couple of really clever examples which will help us expose a general pattern for what happens when we want to compute sums of the form $1+x+x^2+\cdots$.

Exponentials: Discrete and Real

Exponential functions are everywhere, and with them comes the mysterious number $e$.  Here we will discuss what it means to raise numbers to powers, and how we extend that process to a function on the real line which has fundamental applications to the study of growth.

Exponentials: Imaginary

(COMING SOON)
​What does it mean to raise a number to an imaginary power?  No longer can we just extrapolate from the idea of "repeated multiplication" - we need other means to decide what this means.  Here we look at a couple of justifications for Euler's formula: $e^{ix}=\cos(x)+i\sin(x)$.

Fundamentals of Calculus

(COMING SOON)
Calculus is all about slopes and area: and so by its nature is a very visual field.  Here we talk about the geometric meaning behind the linearity of the derivative and integral, and explain pictorially the fundamental theorem of calculus.

The Gradient & LINE INTEGRALS

(COMING SOON)
The gradient from multivariable calculus is a generalization of the derivative for functions from $\mathbb{R}^n\to\mathbb{R}.  And along with this notion of derivative there is a corresponding version of the fundamental theorem of calculus.  Here we discuss one way to concretely understand the gradient through the analogy of slopes on a mountain range.

Divergence & Curl

Divergence and curl are two generalizations of the idea of derivative to higher dimensions: but instead of measuring changes of functions they measure changes in vector fields.  The curl of a vector field measures the "infintesimal circulation" and the divergence the "infintesimal expansion": these ideas will be made precise here.

Stoke's & Gauss' Theorems

(COMING SOON)
​The integral theorems of Stokes and Gauss (the latter also known as the Divergence theorem) are two further analogs of the fundamental theorem for the two new types of derivatives defined above.  Here we shall give heuristic arguments for their validity.​

FOURIER SERIES / TRANSFORM

Fourier series (and the associated Fourier transform) are extremely powerful tools for solving problems in mathematics and the sciences - here we discuss the linear algebra behind the scary looking formulas involved.​

Convolution

Convolution is a process by which two functions are combined by integrating against each other in an (seemingly) complicated way.  This operation is actually rather natural however - here we will talk through heuristic arguments that lead us to construct this operation for ourselves.