500 exercises over 10 weeks is 50 a week, or 10 a day. This leaves you weekends free, and you get the final weeks (typically 5) of the semester left for all those projects that are due at the end of the semester but you can't start early. 500 a day is too much, but you should be able to do 50-100 problems a day in your study time. And others report that when you do this you get good at doing math and so it takes less time.
Sadly I didn't do that. I graduated and do okay, but I encourage everyone to do better than me. As I get close to retirement I need a few people who are still working to build things (and medical treatments) that makes my life better (and in turn take some of that money I saved up over the years for your own life)
Pugh's exercises aren't trivial calculations, they're the proof kind of exercise. If you manage to do 10 a day consistently and still have time for your other courses, congrats.
I also don't think that people who develop new medical treatments necessarily did all the exercises in a pure maths textbook. Being able to prove that continuous functions on a compact set are uniformly continuous probably won't help you fight cancer.
Re:How to Study Mathematics
by StefanBatory on Monday December 02, 2024 @03:02PM
(#42299803)
Also, it's very unlikely that Calculus will be the only subject you're taking. Other subjects require homework too.
On the other hand, I second the suggestion to engage more deeply with the subject material itself: Modify assumptions and see what happens. Can certain proofs be simplified? Try to reconstruct proofs by only memorising certain key details. Try to draw a mental map of a subject and how the different theorems and definitions relate together. Try to implement some proofs in an automated theorem prover, if that's your thing.