Some tips on how to do well in this class

Mathematics is often said to be a very difficult subject, being abstract, logical, conceptual and sometimes difficult to understand. It is the purpose of this article to address these difficulties, and more importantly how to resolve them.

Mathematics is an abstract subject because it is based so heavily on fundamental principles. These principles are often simple once you understand them properly, but if one is careless about these principles one easily got confused. What's worse is that mathematical knowledge and skills are things that has to be built up from bottom up. One cannot start at the middle and expect to pick up what they need by going back as they proceed, unlike most other subjects. Therefore it is of utmost importance to understand these fundamental principles one by one with patience, and gradually build up your body of mathematical knowledge.

I guess for non-math majors, what is important here is the experience to deal with abstract things and to develop skills in logical reasoning. Below we will see how one could get the most out of this course.

1. On understanding the subject matter, and how to spend your time more effectively

I think the best way to understand thoroughly what was taught in class is to think it through on your own. That means you close the book and write out the main definitions, theorems and techniques that were covered that day. You may realize that you will miss out a few important things, or even find it hard to begin writting anything. It's alright, just go to read the book again, mentally identify what was important there, and close the book again and try writing down the details. After a while you realize you have understood the subject matter. This is best done after each lecture, and this way you also get to prepare notes of your own for your future revision.

In my opinion, this is even more important in doing exercises. This is because of the fundamental role that principles (or what people call theorems) play in the subject. It is the understanding of these principles themselves that are important, not the examples. The examples only serves to help you understand the underlying principles, and they are not the main focus of study for their own sake. It is very useful to keep in mind simple concrete examples, but that alone cannot replace a careful study of the fundamental principles.

Also, when you write, it is a very good practice to always write rigourously and with clarity. So contrary to some common belief, language skills, like how to express oneself without ambiguity, are very important in the study of mathematics. For example, when you state a theorem, it is important to get everything right: a typical theorem consists of two parts, namely the conditions and the conclusions. The former is the circumstance under which the theorem applies; the latter is what it can say in such a condition. Make sure that you know the difference, and that you don't confuse the conditions of a theorem with its conclusions. This is a very important training in logical reasoning (for instance, you will find this practice very useful if one day you want to go to graduate schools and needs to take the analytical writing exam of the GRE).

2. Homeworks - How am I supposed to solve 30 problems each week?!

First of all, be assured that you are not asked to do them all - do them only if you think you want to consolidate what you have learned by doing a few more exercises. Secondly, there are many ways to "do" a homework problem: since you are not actually writing up the solutions anyway, the best way to proceed might be the following. You first read the question carefully, mentally identify what the problem is really about and how you are supposed to solve the problem, and if possible identify the main difficulties in solving the problem. Then you carry out some computations on a scratch paper, until you are confident that you can finish off the rest to get the answer. The answer is not even important; what is important is the thinking process when you tried to solve the problem.

You are also suggested to begin working on the homework problems as soon as possible. This is to give yourself more time to finish them, and more importantly a chance to figure out earlier what you might have missed in class and what you may have difficulty understanding. Now homeworks are being assigned on Fridays, in hope that you will have time to work on them for at least a little bit during the weekend. You are also encouraged to come to our office hours and make good use of the review sessions.

3. Where to get help

There are of course the office hours and the review sessions, where you can freely ask questions concerning homework and the course materials. I will try my best to answer all your questions.

As far as I know, help is also available on the 3rd floor of Frist Campus Center in the evenings that targets 100 level math courses. That could also potentially be a very useful resource.

There are old mid-terms and exams online (hard copies available on the 1st floor entrance of Fine Hall), which you may find useful when you are preparing for the exams.

Remember that this can be a difficult course for non-math majors, and that quite a lot of effort on your part is expected. However, your effort shall be well paid off - I am committed to work with you to make sure that this happens.