How to Study Mathematics (2017) • Hacker News Board

Re: How to Study Mathematics (2017)

#31

Post by dorchadas » Sun, Mar 21, 2021, 2:30 AM UTC

TrackerFF wrote: post #29

My only real critique of academic books, was that the exercises varied A LOT in difficulty. Some books had exercises that seemed to assume that the reader had been a honors student, and thus able to pre-process/setting up the problem with intricate identities and what not, before coming to the part where you apply some theorem. Now - no big problem if you worked with very keen math students, and they'd show you that,…

I've also found it way too easy to just convince myself I know the material and move on without actually doing any problems when I was self-studying. Thankfully I came across a Discord server that is run by a math PhD where he assigns problems and corrects proof for self-learners. Best thing that has ever happened to me in learning maths, and I have since finished several undergraduate textbooks and am working on upper undergraduate/graduate ones currently, with problems assigned from him and guidance/proof critiques.

All of this to say, is it's really necessary to have guidance with it, and to make sure you actually do problems, not just convince yourself that you know the material.

Re: How to Study Mathematics (2017)

#32

Post by dorchadas » Sun, Mar 21, 2021, 2:31 AM UTC

benrbray wrote: post #30

jdlyga wrote: post #2

I would love to get back and really learn math. I was really interested back in High School with Geometry and Algebra. But my interested totally burned out with poorly taught and punishing Calculus classes in College.

For abstract algebra self-study, I highly recommend "A Book of Abstract Algebra" by Charles Pinter. Each chapter starts with a few definitions and examples, and the rest of the chapter is a series of exercises meant to help you discover algebraic concepts for yourself.

This is what I started with, then I moved on to Dummit and Foote. It really did help as a build up.

Re: How to Study Mathematics (2017)

#33

Post by gtpedrosa » Sun, Mar 21, 2021, 2:37 AM UTC

dorchadas wrote: post #31

TrackerFF wrote: post #29

My only real critique of academic books, was that the exercises varied A LOT in difficulty. Some books had exercises that seemed to assume that the reader had been a honors student, and thus able to pre-process/setting up the problem with intricate identities and what not, before coming to the part where you apply some theorem. Now - no big problem if you worked with very keen math students, and they'd show you that,…

I've also found it way too easy to just convince myself I know the material and move on without actually doing any problems when I was self-studying. Thankfully I came across a Discord server that is run by a math PhD where he assigns problems and corrects proof for self-learners. Best thing that has ever happened to me in learning maths, and I have since finished several undergraduate textbooks and am working on upp…

Hey, this Discord server seems to be a valuable resource. Do you mind sharing where to find it? I would love to try to get a deeper dive into some math subjects sometime in near future.

Re: How to Study Mathematics (2017)

#34

Post by tunesmith » Sun, Mar 21, 2021, 2:42 AM UTC

dorchadas wrote: post #31

TrackerFF wrote: post #29

My only real critique of academic books, was that the exercises varied A LOT in difficulty. Some books had exercises that seemed to assume that the reader had been a honors student, and thus able to pre-process/setting up the problem with intricate identities and what not, before coming to the part where you apply some theorem. Now - no big problem if you worked with very keen math students, and they'd show you that,…

I've also found it way too easy to just convince myself I know the material and move on without actually doing any problems when I was self-studying. Thankfully I came across a Discord server that is run by a math PhD where he assigns problems and corrects proof for self-learners. Best thing that has ever happened to me in learning maths, and I have since finished several undergraduate textbooks and am working on upp…

I'm interested in more information about that Discord server.

Re: How to Study Mathematics (2017)

#35

Post by tunesmith » Sun, Mar 21, 2021, 2:44 AM UTC

Are there any resources for taking a self-assessment to know what to learn next as a self-studier?

Re: How to Study Mathematics (2017)

#36

Post by ectopod » Sun, Mar 21, 2021, 2:46 AM UTC

baby wrote: post #26

alisonkisk wrote: post #24

Earlier quoted context omitted.

Doing the assigned work is good way to learn the material. Most teachers know better than most students what is need to do to succeed in the class.

When you spend most of your time in class, when do you have the time to do the assigned work? That’s what I struggled with.

How much class did you have? My first year at university had three hours of tutorials and ten hours of optional lectures per week. Subsequent years had less. There was plenty of time.

Re: How to Study Mathematics (2017)

#37

Post by lumost » Sun, Mar 21, 2021, 3:14 AM UTC

TrackerFF wrote: post #29

My only real critique of academic books, was that the exercises varied A LOT in difficulty. Some books had exercises that seemed to assume that the reader had been a honors student, and thus able to pre-process/setting up the problem with intricate identities and what not, before coming to the part where you apply some theorem. Now - no big problem if you worked with very keen math students, and they'd show you that,…

The missing piece is often the solution book which can be difficult to come by.

like leetcode and other problem assesors, you learn a lot by trying, failing, and getting an explanation of where it went wrong.

Would be pretty useful to have an online platform for worked textbook problems from arbitrary textbooks.

Re: How to Study Mathematics (2017)

#38

Post by dorchadas » Sun, Mar 21, 2021, 3:43 AM UTC

gtpedrosa wrote: post #33

dorchadas wrote: post #31

Earlier quoted context omitted.

I've also found it way too easy to just convince myself I know the material and move on without actually doing any problems when I was self-studying. Thankfully I came across a Discord server that is run by a math PhD where he assigns problems and corrects proof for self-learners. Best thing that has ever happened to me in learning maths, and I have since finished several undergraduate textbooks and am working on upp…

Hey, this Discord server seems to be a valuable resource. Do you mind sharing where to find it? I would love to try to get a deeper dive into some math subjects sometime in near future.

I found it from someone on /r/math. I don't feel like I can share the link myself, but he does check there and r/learnmath regularly.

Re: How to Study Mathematics (2017)

#39

Post by dorchadas » Sun, Mar 21, 2021, 3:44 AM UTC

tunesmith wrote: post #34

dorchadas wrote: post #31

Earlier quoted context omitted.

I've also found it way too easy to just convince myself I know the material and move on without actually doing any problems when I was self-studying. Thankfully I came across a Discord server that is run by a math PhD where he assigns problems and corrects proof for self-learners. Best thing that has ever happened to me in learning maths, and I have since finished several undergraduate textbooks and am working on upp…

I'm interested in more information about that Discord server.

See my reply to the sister comment.

Re: How to Study Mathematics (2017)

#40

Post by codeproject » Sun, Mar 21, 2021, 3:46 AM UTC

There is one trick to master mathematics: Proactive. you can't be lazy. You have to ask question relentlessly. Always ask question, always find an example.