Research

# Teaching

## Spring 2015: Math 241 BDB

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 grateful to have been awarded the Brahana TA award for 2014. I have appeared on the List of Teachers Ranked as Excellent in Fall '09, Spring '10, Fall '11, Fall '12, Spring '13, and Spring '14.

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?"

• If I mark a question with a tilde (~), I mean that what you've written is not technically correct but is close enough for me to not take off points. It will frequently occur in a question with many parts: if you answer the first part incorrectly, the subsequent parts are graded as though your first answer were correct. (Note that if your incorrect answer to the first part makes the subsequent parts significantly easier, this may not apply.)
• The bulk of the points in a question comes from the work that we are currently dealing with in the course. An algebra error will count less than not taking the derivative correctly.

#### Sample teaching materials:

• 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.
• 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).