suggetions about how to improve

Hi everyone,

You may feel crushed after the first midterm. Indeed, it was too little time and problems are hard (or at least, no so familiar). The test was meant to be hard, and serves as a wake-up call. And here are some suggestions to improve.

In general, math is about understanding and explain your understanding to others, in a precise and clear way. It has nothing to do with memorizing formula. The general procedure of learning is the following

  1. Learn the definition. Definition specifies what we want to study, it introduces a concept, a property etc. It is distilled from many examples and fuzzy intuitions, so it is impossible to know a defininition without going through examples and intuition. It is not just memorizing that few lines.
  2. Play with the examples and counterexamples. Examples are very important for understanding. Learning requires doing rather than just watching, as in any sport.
  3. About proofs. A major part of math (if not all), is to make sure what we claim is true. We start from the ground, and build things up. A proof of a theorem trys to answer one question “why do you think this is true?”. Try to answer that question yourself first, before looking at how the proof is written.

That was the traditional definition-example-proposition cycles. They are the goals that we are aiming for. But how to get there? If there is one answer, then it is about:

asking questions

I am sure most of us has doubts or confusions when learning something new. Just as driving in a new neighborhood, or touring in a new city, even equipped with google map, you can get lost. Sure, it is not easy to have interaction among peers, making friends in classes, form study groups, etc. However, we can still do something in the purely online setup.