Teaching
Course Pages
I believe the best way to learn mathematics is to understand the "pictures" behind the subject. I try to convey these ideas, and hopefully by understanding them my students will have a deep knowledge that they can draw upon to help recall even the more computational aspects. (This is not to say that intuition should replace rigor. But rigorous definitions follow good ideas.)
I am happy to have been awarded the Brahana TA award for 2014 by the Mathematics department at U Illinois Urbana-Champaign. I appeared on the List of Teachers Ranked as Excellent at UIUC in Fall '09, Spring '10, Fall '11, Fall '12, Spring '13, Spring '14, and Spring '15.
See the bottom of this page for some selected teaching materials I have developed. Or look through the Archive of my course webpages.
Students: I will do my best to help you learn. But learning is not a passive process. Especially at higher levels of difficulty, a student must actively participate by reading appropriate texts, studying notes, and attempting problems. Paul Halmos wrote about mathematics:
"Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?"
Sample teaching materials:
- Fall17 Calc3 exam solutions.
- Fall17 Calc3 worksheet, introducing a non-differentiable multivariate function.
- Spring17 Discrete exam solutions.
- π Day 2015 event materials.
- Spring11 Merit worksheet 16; fun with word problems.
- Fall11 Merit worksheet 10; problems 1 and 2 were in response to some student misunderstanding of symmetry in related problems on the previous worksheet.
- Fall11 Merit worksheet 19; after some standard practice problems, students find the well-known Euler formula, and then move on to a nice (if a bit convoluted) application problem.
- Fall11 Merit worksheet 20; filled with fun nonstandard problems.
- Spring13 C&M exam 2 solutions; this is fairly representative of one of my 1-hour exams (just keep in mind that C&M sometimes takes nonstandard approaches and notation).
- Mathematica notebook for Lagrange's method as part of a solution (interactive notebook if you have Mathematica or its CDF player, or noninteractive (and poorly formatted) pdf); the descriptions of the method in the existing notebooks only dealt with applications with a constraint equality, but I feel constraint inequalities are an important aspect.
- Mathematica notebook for examples of the PageRank algorithm (notebook or pdf; see also the second example's worksheet).
Last modified 19 November, 2017.