(There is also a web page on Courseworks.)

Time: Th 2:30-4:00
Place: Math 507
Office hours: Thursday, 10:30-11:30 and by appointment, in Math 625.

Textbook: None.

Some relevant reading:

Course Goals.

The goal of this course is to prepare mathematics graduate students to teach at Columbia. This is done mainly through practice teaching (prepared mini-lectures) and discussion / feedback on them, although there are also a number of other assignments. In addition to the mini-lectures, we will discuss:

Mini-Lecture Schedule


This course has no prerequisites. It is required of all first-year graduate students in the mathematics department. Other students should talk with the instructor before taking the course.



Homework 40%
In-class mini-lectures 40%
Class participation (not including presentations) 20%

More than two unexcused absences will mean automatically failing the class.


Except as noted, you are welcome to discuss out-of-class work with your classmates, but you must write the versions you turn in by yourself.

You are also generally welcome to use any resources you like. However, any resource you use for written work must be cited. This includes electronic resources (including Wikipedia and Google) and human resources (including your classmates). Failure to cite sources constitutes academic misconduct.

Students with disabilities

Students with disabilities requiring special accommodation should contact Office of Disability Services (ODS) promptly to discuss appropriate arrangements.


Syllabus and schedule.

Except as noted, each day three students will give 20 minute prepared mini-lectures, which we will then discuss. (You will hand me a copy of your lecture notes before giving the lecture, and I will give feedback on those, too.) Some days we will discuss additional topics.

Date Material
9/04 Overview of the seminar and goals. Teaching observations. Discussion of mini-lectures. Creating a webpage on the math server. Discussion of teaching at Columbia versus other institutions. (No mini-lectures.)

Discussion of teaching observations. 3 mini-lectures.

[Last day to add a class is 9/12]

9/16 (Tuesday)
2:30 p.m.

Special meeting: introduction to disability services at Columbia.
9/18 3 mini-lectures.
9/25 Making a course webpage and syllabus. Exam and homework grading. 2 mini-lectures.

3 mini-lectures.

[Last day to drop a class is 10/07]

10/09 4 mini-lectures.
10/16 Discussion of teaching observations. 3 mini-lectures.

Policies: students with disabilities, conflict of interest, sexual harassment, academic misconduct.

3 mini-lecture.

10/30 Exam writing 1: goals, sample exams. 2 mini-lectures.
11/06 3 mini-lectures
11/13 Exam writing 2: discussion. 2 mini-lectures.
11/20 3 mini-lectures
11/27 Thanksgiving holiday -- no class
12/04 3 mini-lectures, review.



  1. (Due September 11) Class observation 1. Observe one of the faculty teaching Calculus 1 - 3. (Sign up for which class you will observe, so we do not have too many people observing a given class.) Fill out the evaluation form I (currently) use when observing graduate student classes. Pay particular attention to the level of the course and how the lecturer gets students involved.
  2. (Due September 18) Personal webpage. Create a brief personal webpage for yourself on the math department server. (It should have your name and contact
  3. information. Optionally, include your research interests, your current/past teaching responsibilities (probably none), your picture, and/or your CV.) E-mail me a link to the webpage.
  4. (Due September 25) Exam and homework grading. I will pass out some sample exam questions to grade on September 18. Grade them, by yourself, for us to discuss on September 25.
  5. (Due October 9) Course webpage and policy handout. Create a course webpage, day-by-day syllabus, and policy handout for an imaginary Calculus 1 course to be taught in the Fall Semester of 2015. (We will have discussed by what should be on the webpage and handout.) Turn in the physical copy of the handout and e-mail me a link to the course webpage.
  6. (Due October 16) Class observation 2. Same as observation 1, but observe a different faculty member and course.
  7. (Due November 6) Exam writing. Write an in-class (1 hour and 15 minute) midterm exam over the first 5 weeks of Calculus 1. You will turn in the exam, I will read them, and then we will discuss them in class. This assignment should be done on your own, without discussing it with your classmates.
  8. (Due December 4) Evaluation form for this class, including carefully thought out comments on what parts you found most helpful and what parts you thought could be improved.