Currently teaching

In Fall 2017 I am teaching Math 019: Fundamentals of Calculus I.

Applying to graduate schools and REUs, and getting letters of recommendation

On December 6, I gave a presentation to the UVM Math Club on applying to graduate schools and REUs, and getting strong letters of recommendation. Here is a page collecting the links I presented.

Teaching materials

Over the years I have created some teaching-related materials.

  • At Stanford I worked on developing what was then Stanford's Precalculus Resource Portal, developed under the supervision of Rafe Mazzeo. The aim of this project was to become a comprehensive website collecting every precalculus resource offered by Stanford across all departments and organizations. Since I left, the project has moved to Stanford's Canvas site, where it is only available to Stanford students.
    The only parts still publicly available (as of this writing) are a collection of YouTube videos on various precalculus topics that I wrote and recorded myself. A subset of these form a structured online mini-course on trigonometry, which is also still available, and contains videos I recorded, supplementary videos from Khan Academy, and exercises selected from Khan Academy so that students can practice the skills they have just learned.
    As part of my work on the Stanford Precalculus Resource Portal, I also created in 2013 an online precalculus learning tool which is based on the software ALEKS. That is unfortunately no longer available but I would be happy to share my insights if anyone is interested in doing something similar.
    The website and its materials were created with the financial support of the Vice-Provost for Undergraduate Education at Stanford University.
  • At UW-Madison I wrote handout on designing course policies. This document accompanied my hour-long workshop at the Fall 2009 Letters and Science Teaching Assistant Training Program on the same subject. It was created with the financial support of the College of Letters and Science at the University of Wisconsin in Madison.
  • At UW-Madison I also wrote study skills handout for students taking calculus. Half of the material is specific to UW-Madison, but the rest applies to any math class an undergraduate might take. This document was created with the financial support of the Wisconsin Emerging Scholars Program at the University of Wisconsin in Madison.

Past teaching


In the past I have taught:

Math 255: Elementary Number Theory (Spring 2016). All course materials were posted on Blackboard.
Math 124: Linear Algebra (Fall 2016)
Math 255: Elementary Number Theory (Spring 2017)

At Stanford

For three years I was one of the instructors and coordinators for the first-year univariate calculus sequence Math 19 (fall), Math 20 (winter) and Math 21 (spring).

Stanford maintains and archives the course websites for all courses I have taught there, except for Math 20 in Winter 2014 because it was archived incorrectly on our end.

Math 19 Math 20 Math 21
Math 19, Fall 2012 Math 20, Winter 2013 Math 21, Spring 2013
Math 19, Fall 2013 This page is unavailable Math 21, Spring 2014
Math 19, Fall 2014 Math 20, Winter 2015 Math 21, Spring 2015

At UW-Madison

Between 2010 and 2012, at UW-Madison I was the TA coordinator and instructor for Math 101: Intermediate Algebra for four semesters, in addition to sitting on the Pre-Calculus Sequence Redesign Committee from 2009 to 2012 (where in particular we redesigned Math 101). In Spring and Fall 2010 we used the software ALEKS. In Fall 2011 and Spring 2012 we used the software MyMathLab, which is the software we ended up settling on for the pre-calculus portion of WisCEL. In the middle, in Spring 2011, we used the software Hawkes, and I worked with it a little bit, even though I was not an instructor.

In Spring 2011 I was the instructor for Math 130: Mathematics for Teaching: Numbers and Operations, Lecture 2. Here is the syllabus for the class, and below are all of the worksheets, homework sets, and various handouts from that semester.

Worksheets   Homework
Worksheet 1 (1.1-1.2) Worksheet 2 (1.3-1.4) Homework 1
Worksheet 3 (1.5-1.6) Worksheet 4 (1.6-2.1) Homework 2
Worksheet 5 (2.2-2.3) Worksheet 6 (3.1-3.2) Homework 3
Worksheet 7 (3.3-3.4) Worksheet 8 (3.4-3.5) Homework 4
Worksheet 9 (3.6) (Review 1) Homework 5
(Exam 1) Worksheet 10 (4.1) Homework 6
Worksheet 11 (4.2-4.3) Worksheet 12 (5.1-5.2) Homework 7
Worksheet 13 (5.3-5.4) Worksheet 14 (5.3-5.4) Homework 8
Worksheet 15 (5.5) Worksheet 16 (6.1-6.2) Homework 9
Worksheet 17 (6.3) Worksheet 18 (6.4) Homework 10
(No Worksheet) (Review 2) Homework 11
(Exam 2) Worksheet 19 (7.1) Homework 12
Worksheet 20 (7.2-7.3) Worksheet 21 (7.4) Homework 13
(No Worksheet) (No Worksheet) Homework 14
(No Worksheet) (Review) Homework 15
Practice Exam 1 as well as the solutions to it.
A review document for Exam 1.
A proof of the Divisibility Test for 4, with extra fun activities.
The last question of Exam 2.
Practice Exam 2 as well as the solutions to it.
A review document for Exam 2.
What would be Practice Exam 3, if there were an Exam 3, as well as the solutions to it.
What would be a review document for Exam 3, if there were an Exam 3.
A Study Guide for the Final.
A blank copy of Exam 1 and a blank copy of Exam 2.

In Fall 2009 I was a TA for Doctor Wei's Lecture of Math 213: Calculus and Introduction to Differential Equations, Sections 303 and 304.

The syllabus for the class.
How to graph without a calculator
Some double integrals from section 9.6
Quiz 8 from the Thursday section, has an Euler's method problem on it.
Four sets of problems to do to study for the final.
Some notes on series and telescoping sums, and the answers to the questions in it.
Solutions to question 2 of the Tuesday students' Quiz 10.
Solutions to question 2 of Quiz 11.
A blank copy of the mock final I wrote, and solutions for it.

In Spring 2009 I was a TA for Professor Smith's Lecture of Math 320: Linear Algebra and Differential Equations, Sections 321 and 322.

Quiz solutions
Quiz 1
Quiz 2
Quiz 3
Quiz 4
Quiz 5
Quiz 6
Quiz 7
The syllabus for the class.
Some worked out problems from Sections 1.2 and 1.3.
A few facts about Taylor series expansions.
Here is an Excel file showing how to implement the various Euler schemes in Excel, along with a pdf file explaining what is happening.
An alternative solution to the first problem of the first midterm.
Solutions to a problem from Section 4.5.
An excellent reference on nth roots and roots of polynomials.
Solutions to selected problems from Homework 3.
A summary of the general solution of an Euler equation.
A series of questions exploring concepts from linear algebra.
The sections we have covered from Boyce and DiPrima.
Problem 26 from Section 7.3 (or what to do with complex eigenvalues).

I also was a TA for Math 171: Calculus with Algebra and Trigonometry I in Fall 2006, the WES (Wisconsin Emerging Scholars) section of Math 234: Calculus - Functions of Several Variables in Spring 2007, Math 213: Calculus and Introduction to Differential Equations in Fall 2007, Math 217: Calculus with Algebra and Trigonometry II in Spring 2008, and the WES section of Math 234: Calculus - Functions of Several Variables in Fall 2008, but that was all before I had a website.