- Office Hours: T 11:30 - 12:30 pm, Th 5:30 - 6:30 pm
- Thursday 2:00 - 2:50 pm via Zoom
- Attend lecture and discussion. The ideas in the course all build on each other -- things done earlier in the course will remain relevant throughout.
- If you're confused, raise your hand! If you do not understand something in lecture or discussion, ask for clarification. Often times if you are confused, so are your peers!
- Go to office hours. You don't need to have a specific question in mind to attend. In the case you feel so confused that you can't articulate what you are confused about, that is exactly what office hours are for!
- Work through proofs and examples in the textbook. The techniques that are used to prove theorems in the textbook are often times the same techniques you will use to prove results in your homework. Carefully read through the proofs in the textbook to make sure you not only are understanding the material, but to look for useful ideas for solving problems. If you have time, try to prove the result yourself first!
- Focus on the big ideas. It's easy to get caught up in and lost in technical details. Summarize the ideas used in a proof and write up a sketch to get a feeling for what ideas are important.
- Convince yourself of what you are trying to prove. If you just can't seem to prove a result, do a sanity check and look for a counter-example. If you can't find one, the failed process of trying to "break" a result might give you additional insight into why it should be true.
- Work through special cases. If you're stuck on a problem, work through easier special cases to try and get a feeling for how it might be proved in general. For example, if you need to prove a result about nxn matrices, try the case n = 2 or n = 3 first.
- Start your homework/exam studying early. Math is skill that requires practice. Think about how you would prepare to run a marathon. This isn't something that will happen without any training, and certainly preparing the day before won't make any difference. Just like training, learning math is a proccess that happens over time. A concept that is confusing one day might become clearer the next while your brain is working in the background.
- Feeling stuck is normal. Math is hard, and the most learning happens when you are bashing your head against a wall. When you solve a problem you have been stuck on for a long time, you get a much deeper understanding than just looking up a solution.
- Write drafts of solutions. The point of a proof is not just to be logically correct, but to communicate clearly that it is so. After solving a problem, go back and try to improve the clarity of your writing. Your argument should ideally be understandable to your peers!