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An undergraduate text like Pugh's Real Mathematical Analysis can have over 500 exercises. Trying to do them all on top of your regular workload seems excessive,

An undergraduate text like Pugh's Real Mathematical Analysis can have over 500 exercises. Trying to do them all on top of your regular workload seems excessive, unless maybe it's an area you really want to specialise in. I also tend to find certain kinds of exercises boring because they appear terribly unmotivated. 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.

bluGill 2y ago
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)
- Tainnor 2y ago
  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.
- StefanBatory 2y ago
  Also, it's very unlikely that Calculus will be the only subject you're taking. Other subjects require homework too.

bluGill 2y ago

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)

Tainnor 2y ago
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.
StefanBatory 2y ago
Also, it's very unlikely that Calculus will be the only subject you're taking. Other subjects require homework too.