STUDY ADVICE: Math 20B

The quarter system: over before you know it.

By now many of you know that the 10 week quarter goes by very fast. This means that you need to make every effort to follow the material on a regular basis. If you are having trouble with the material, seek help from the professor or TA's early. It is very difficult to catch up once you start slacking off, particularly in a math class. But you know that already...

 

Prerequisite skills.

Derivatives: You need to know your derivatives backward and forward for this class. This is meant literally, not just as a figure of speech. Really, you need to be so fluent in taking derivatives that you can work backwards: given a certain  simple function you should be able to find a function whose derivative it is. 

        Trigonometry: You need to know your basic trig identities at the level where given, say, (cos x)^2, you should be able to 

instantly recite all the trig identities involving this expression. You also need to know by heart the values of all the trig functions at 0, p/6, p/4, p/3, p/2, 2p/3, 5p/6, p, etc.

 

Check your work.

The nice thing about this class is that you can check your work. Not sure if the anti-derivative you found is correct? Take its derivative and see if you get what you started out with! This is a good habit to get into in general. Whether you work in industry or pursue further studies after your graduation, you'll find that you'll win more respect from your colleagues if you check your work before presenting it to others.

A word on word problems...

Many students hate word problems. It seems easier to just dive into a calculation: at least you know what you're supposed to calculate. I agree: in fact it is so much easier to do plain computations that computers can do them much faster than we can say "calculate"! Word problems is what we need humans for! The word problems in this class will introduce you to the process of taking a real life situation, translating it into a mathematical framework, and using mathematical techniques to solve it. Being good at this type of thing will go a long way in giving you job security once you graduate.

 

Group study: benefits and pitfalls to watch for.

You are encouraged to discuss your problem solutions with other people in the class. There are many scenarios in which this is helpful: the two or three of you together may be able to solve a problem that neither one of you could solve alone, or if one of you thinks (s)he has a solution to a problem, the person may discover some holes in his or her argument and, in the process, discover the areas where (s)he needs improvement. Sometimes you may even discover your own mistake just by trying to phrase a question. Once you graduate from UCSD, it is very likely that you will find yourself in a situation where you have to collaborate with other people. Studying in a group can help with getting you initiated into this way of working.

 

However, you should watch out for some potential pitfalls that sometimes befall group study. Be sure  that you are contributing to the problem solving. If someone else is doing most of the work and you get credit for it, you may feel you got a "free ride" in the short term, but this type of partnership will not do much to raise your confidence and performance levels during the exams. If you find that this is happening, change study groups. Groups of two to three people of roughly comparable abilities frequently work well.

The key to success: practice solving problems.

No matter what the math class is, the best way to prepare for the exam is to do lots of problems. That means being able to do all the homework problems with the solutions closed (as opposed to just being able to understand the solution) and working additional problems. Doing this will give help you remember the key concepts in the class, give you practice in applying them, and help you increase the speed of problem solving so that you can better deal with the time constraint of an exam. Your confidence level will also be raised by the experience you'll gain in tackling problems.

 

Maximizing the benefits of sections and office hours: come prepared with questions.

It can be very tempting to come to section in a passive state of mind and let whatever takes place during the hour wash over you. Try not to fall into that temptation. Come to section with questions about problems or the class material. This will make section more interesting for you, and you will get more out of it. The same goes for office hours. While you will gain something from hearing other people's questions and answers to them, you will gain more by formulating your own questions.