I love to teach. As an instructor, I set high standards, and then commit myself to serving you with whatever means necessary to help you meet those standards.

You can see a some of the videos I have made. More are available on my YouTube channel, at iTunes U, or in my Coursera course, Sequences and Series.

My office is in room MW658, in the Math Tower.

This semester, I will be holding office hours on Mondays at 4:10pm and Fridays at 1pm, or by appointment.

M2O2C2 is an invitation to think carefully about how one thing changing affects something else. What is the "derivative" of a function of many variables? How can a curved object be approximated by a flat plane? What does the chain rule look like when many things are affecting many other things? How do we find an input which maximizes a function of many variables?

This is a course in multivariable differential calculus, but we will also introduce a ton of linear algebra. The result is a course targeted at a student who has seen a bit of calculus and is willing to learn about matrices and vectors to provide the best possible vantage point from which to understand derivatives of functions of many variables.

Sequences and Series will challenge us to think very carefully about "infinity." What does it mean to add up an unending list of numbers? How can an infinite task result in a finite answer? These questions lead us to some very deep conceptsâ€”but also to some powerful computational tools which are used not only in math but in many quantitative disciplines.

This course is a first introduction to sequences, infinite series, convergence tests, and Taylor series. It is suitable for someone who has seen just a bit of calculus before.

Calculus is about the very large, the very small, and how things change. The surprise is that something seemingly so abstract ends up explaining the real world. Calculus plays a starring role in the biological, physical, and social sciences. This online course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems.

This course introduces topological and metric spaces, continuous maps, convergence, connectedness, and compactness, as well as some combinatorial, geometric, and algebraic techniques in knot theory and knot invariants.

Calculus is among the greatest achievements of humankind; this fast-moving course explores single variable calculus in depth.

This is a beginning graduate course in complex analysis; as such, we study analysis (e.g., the rigorous foundations of calculus) as it applies to functions of a complex variable. The resulting theory is strikingly beautiful.

This course is the first in the differential branch of the core topology and geometry curriculum of the Ph.D. program and provides a basic introduction to smooth manifolds.

At the Ross Mathematics Program, I taught a seminar for the more advanced students on piecewise-linear topology.

I taught Math 153 at the University of Chicago, during the Fall Quarter of 2008–2009.

This is a very fast-moving multivariable calculus course.

This is a very fast-moving multivariable calculus course.

Math 758 is the last in the standard algebraic topology sequence and provides beginning graduate students with an in-depth study of cohomology theory, assuming a working knowledge of homology theory.

For more than two millenia, humans have been discovering mathematical truths via an axiomatic, deductive method—proof. This course, drawing on examples from number theory and set theory, invites you to join this tradition.

I taught Math 204 and Math 205 at the University of Chicago, during the Winter and Spring Quarters of 2008–2009. These were taught in an inquiry-based format.

I taught Math 195 at the University of Chicago, during the Summer of 2009.

During Fall Quarter of 2006-2007, I organized an undergraduate seminar on Lie groups; the students gave short talks after having read through Frank Adams' book *Lectures on Lie Groups*.

I taught Math 133 at the University of Chicago, during the Spring Quarter of 2005–2006.

I taught Math 131 at the University of Chicago, during the Fall Quarter of 2005–2006.

Between Fall 2005 and Spring 2009, I visited Chicago Public Schools, where I taught elementary and middle school students in small groups and whole-classroom settings, and assisted Chicago public school teachers with pedagogy and their own study of mathematics.

I taught Math 132 at the University of Chicago, during the Winter Quarter of 2005–2006.