Ross M. Richardson: Teaching

Current Teaching (Winter '07)

Damn straight.

Last Current Teaching (Spring '07)

Math 152 (Applicable Mathematics and Computing)

• Instructor: Fan Chung Graham
• Course Page: Math 152 Page
• TA Page: Math 152 TA Page
• Discussion Session I Teach:
  
  • Th 4-4:50, 5-5:50, Center 203
• Office Hours:
  • W 12-12:50, Th 11:30a-12:15p, AP&M 6436
  • By appointment, scheduled via email

Prior Teaching

• Fall '03:Math 20A, Calculus for Scientists and Engineers
• Winter '04:Math 20C, Calculus for Scientists and Engineers
• Spring '04:Math 20C, Calculus for Scientists and Engineers
• Fall '04:Math 20D, Introduction to Differential Equations
• Fall '05:Math 103A, Applied Modern Algebra
• Winter '06:Math 103B, Applied Modern Algebra
• Spring '06:Math 140B, Mathematical Analysis
• Fall '06:Math 140A, Mathematical Analysis
• Fall '06:Math 120A, Complex Analysis
• Fall '06:Learning Seminar, Harmonic Methods in Combinatorics
• Spring '07:Learning Seminar, Asymptotic Methods in Combinatorics and Probability

About Homework

So it happens that in a large university, we ask students to hand in well written homeworks which are clearly formatted, written in clean mathematical English, and consistent with standard mathematical convention. I know, it sounds downright humorous when put so plainly. In any case, it is clear that we often don't demonstrate how a student should go about this task, having read little to no mathematical literature and equipped with only the basic writing skills expected of any entering UC student. Thus, I have posted the following references to some examples which make clear what is expected. If you are a student, I urge you to take the time to examine these links.

• Harvey Mudd College Homework Site
• Student's Guide to Good Problems

Ross' Surefire Tips for Suceeding in Math

• Do your homework! Seriously, mathematics is a creative endeavor which involves thinking deeply about why things work. The only way to gain such understanding is to buckle down and tackle problems. Don't kid yourself; if you haven't sat down and really thought about the problems, you haven't learned anything. If you find yourself spending lots of time memorizing, you're not doing mathematics.
• Ask Questions. This includes asking your professor questions, your TA, your fellow students, and most importantly yourself. To learn math you must constantly ask questions and try to answer them, thus prompting more questions. Asking others adds new ideas, as well as forces you to better understand your problem.
• Avoid Solution Manuals. There's no better way to convince yourself that you've learned something and actually have learned nothing than to read solution manuals. Checking your solution (e.g. comparing against the number in the back of the book) is valuable so long as it causes you to reconsider a problem you've gotten wrong; copying a written solution has almost no value. As a further note, most “Student Solution Manuals” are reprinted solution manuals meant for your teachers. Hence, they are written as solution sketches, missing many details and concepts which are necessary for a complete solution.
• Spend enough time to understand. It is amazing how much repeated exposure to mathematics helps understanding. Don't cheat yourself; spend time solving problems and making completely clear any concept which seems mysterious. In other disciplines, memorization and bullshit will get you a long way - you'll find this is not true in mathematics.
• They're problems, not exercises. My last point is philosophical. When you are asked to do homework, approach your homework as a set of problems to be solved by understanding how they work and how you can get to your conclusion. We learn only when we are confronted with a challenge, think about how it works, and understand our solution when we (hopefully) come up with it. If you are not solving problems but just moving symbols around in immitation of something you've been taught, you will learn very little. Real life is a series of challenging problems—those who have done nothing but exercises will find themselves hardpressed to meet the challenge.

Previous Handouts/Materials

• Handout on Continuity -- Math 140 PDF.
• Normal Subgroups and Homomorphisms, a lecture for 103A. PDF.
• Three lectures on Probabilistic Methods, given at Nankai University. Part introduction, part research. Go here.
• While taking the graduate topology sequence at UCSD I, and others, created a large number of useful summaries of the material. It is located here for purpituity.

References

• Mathematics Pronunciation Guide. Mathematics is an international discipline with a long history of funny names and words. Thankfully, someone has created a reference.
• Radio Announcers Pronunciation Guide. More generally, here are some tips for the correct pronunciation or correct anglicized pronunciation of European names.
• Earliest Known Uses of Some of the Words of Mathematics. Check out the entry on “nabla”.
• A Not So Short Guide to LaTeX. There are many ways to start typesetting mathematics using TeX/LaTeX, and none of them are entirely clear. This is probably a good place to look first.
• Mac OS X TeX/LaTeX Web Site and MikTeX. These are really the places to get your TeX/LaTeX distributions for Mac OS X and Windows, respectively.
• Vim Editor. If you have to do any text editing on a regular basis, you should learn Vim. There is an especially nice Vim LaTeX package available.

This file last modified 09/06/07