These tips have been collected through the years from professors, past and present. You can also check out the Learning How To Learn Coursera for other general tips.
The material takes some time to sink in. You’ll be able to pick up the nuances if you’ve already got a gist of what will be covered.
In a conceptual class such as this, it is particularly important to maintain a steady effort throughout the semester, rather than hope to cram just before homework deadlines or exams. This is because it takes time and practice for the ideas to sink in. Make sure you allocate a sufficient number of hours every week to the class, including enough time for reading and understanding the material as well as for doing assignments. (As a rough guide, you should expect to do at least one hour of reading and two hours of problem solving for each hour of lecture.) Even though this class does not have any major projects, you should plan to spend as much time on it as on any of your other technical classes.
The homeworks are explicitly designed to help you to learn the material as you go along. Although the numerical weight of the homeworks is not huge, we work hard to make them instructive and interesting. Do read the sample solutions, even for the problems on which you received full points. You may well learn a different way of looking at the problem, and you may also benefit from emulating the style of the solutions. (In science, people learn a lot from emulating the approach of more experienced scientists.) Even for those in the “no-homework” option, we highly encourage you to attempt the homeworks and review the solutions.
Our best advice is to read through the homework problems as soon as they are available and let them percolate in your brain. Think through possible approaches while you are waiting in line, or stuck in an elevator. Sleeping on a problem, or taking a walk has often helped people to come up with a creative approach to it. Definitely do not wait until the night before it is due to start working on the homework.
The professors and TAs hold office hours expressly to help you. It is often surprising how many students do not take advantage of this service. You are free to attend as many office hours as you wish (you are not constrained just to use the office hours of your section TA). You will also likely get more out of an office hour if you have spent a little time in advance thinking about the questions you have, and formulating them precisely. (In fact, this process can often lead you to a solution yourself!)
Discussion sections are not auxiliary lectures. They are an opportunity for interactive learning, through guided group problem solving and other activities. The success of a discussion section depends largely on the willingness of students to participate actively in it. As with office hours, the better prepared you are for the discussion, the more you are likely to get out of it.
As stated above, you are welcome to form small groups (two to four people) to work together on homeworks and on understanding the class material on a regular basis. In addition to being fun, this can save you a lot of time by generating ideas quickly and preventing you from getting hung up on some point or other. Of course, it is your responsibility to ensure that you contribute actively to the group; passive listening will likely not help you much. And recall the caveat above that you must write up your solutions on your own. Homework parties are an alternative vehicle for working with others in a nice atmosphere and can be a good place to find a group to work with regularly.
As the semester proceeds, many of you will no doubt feel the urge to ‘daydream’ during lectures or to skip them altogether, on the grounds that you can catch up by reading the lecture notes. If you follow this strategy, you should be aware that reading mathematics is NOT the same as reading a novel or a news article: each page of mathematics needs to be read many times before it is fully understood, and needs to be backed up by examples and discussion. Following the material in class should save you several readings; even just watching it go by without fully understanding it makes your later reading easier. And you also get the benefit of student questions, examples, etc. Exactly how you handle lectures is up to you. One strategy is to print out the lecture notes in advance, bring them to lecture, and add a few additional notes during class.