3 ms·

if it's something you're self-studying, don't be afraid to put something down and pick it up later. There are topics and materials that I completely failed to u

if it's something you're self-studying, don't be afraid to put something down and pick it up later. There are topics and materials that I completely failed to understand the first time I encountered them, but months or years later they were easy to understand. Of course, if your goal is to get good grades in specific courses which have exams on specific dates, then this isn't very useful advice. Some other advice: - don't underestimate the value of memorization when it comes to definitions and important theorems. - do lots of practice problems which are like those on the exams (obviously) - as much as possible, find peers to study with and talk with. it's easy to fool yourself into thinking you understand something, but when you try to talk about it with a real person, the holes in your knowledge are revealed pretty quickly. - if you can't do that, try to explain the concepts and ideas you're learning to an imaginary friend. - you might be able to find lecture notes or slides online from the actual versions of classes taught at your institution. I agree you should ask the professors for materials to look at, or at least try to focus on the materials and courses actually taught at your institution. This is the path of least resistance and will probably make it easier to stay motivated too.

currymj 6y ago
oh, also -- the advice to skim early chapters is generally good. In general, don't be afraid to skip past things you don't understand, as long as you have some way of testing that you are learning everything you need in the end (via peers and practice problems). Sometimes there are seemingly-extraneous details that can only make sense after you see how they are used later in the text, and sometimes confusing stuff ends up not being very important.
hypersurface 6y ago
The end goal is of course, a grade; however I will have to take supplementary exams. Although past papers are available, there is a degree of ‘aptitude testing’ involved which is strictly mathematical but still difficult to prepare for directly. Nevertheless practice problems are good for that and I will be doing a lot. You are right, the advice to skip/quickly pass the first chapters [thank you lurker137] is good. I think this is something I have known subconsciously but I will try to keep aware. Same for those who have suggested seeking further material. > as much as possible, find peers to study with and talk with This is good advice. Thank you.
- thomashobohm 6y ago
  In terms of aptitude testing, going through some books like "How to Prove It" and working on rigorous proofs-based material (perhaps an introductory analysis book with lots of diagrams) will be helpful. As will brushing up on geometry-lots of people memorize a lot of geometry in middle school/high school, do well in their class, and forget it. Geometric concepts continue to appear throughout math and having a deep grasp of them is super helpful for your first "rigorous" math classes, where the secret to finishing a proof often lies in visualizing or drawing it correctly.

currymj 6y ago

oh, also -- the advice to skim early chapters is generally good. In general, don't be afraid to skip past things you don't understand, as long as you have some way of testing that you are learning everything you need in the end (via peers and practice problems). Sometimes there are seemingly-extraneous details that can only make sense after you see how they are used later in the text, and sometimes confusing stuff ends up not being very important.

hypersurface 6y ago

The end goal is of course, a grade; however I will have to take supplementary exams. Although past papers are available, there is a degree of ‘aptitude testing’ involved which is strictly mathematical but still difficult to prepare for directly. Nevertheless practice problems are good for that and I will be doing a lot. You are right, the advice to skip/quickly pass the first chapters [thank you lurker137] is good. I think this is something I have known subconsciously but I will try to keep aware. Same for those who have suggested seeking further material. > as much as possible, find peers to study with and talk with This is good advice. Thank you.

thomashobohm 6y ago
In terms of aptitude testing, going through some books like "How to Prove It" and working on rigorous proofs-based material (perhaps an introductory analysis book with lots of diagrams) will be helpful. As will brushing up on geometry-lots of people memorize a lot of geometry in middle school/high school, do well in their class, and forget it. Geometric concepts continue to appear throughout math and having a deep grasp of them is super helpful for your first "rigorous" math classes, where the secret to finishing a proof often lies in visualizing or drawing it correctly.