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How to Study Mathematics (2017)

math.uh.edu

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Re: How to Study Mathematics (2017)

#71
post #22

I dropped out of my maths degree after struggling for six years (!) at university - I had fallen too far behind. I can't just blame my part-time jobs for that. Especially early on I often dismissed problems and assignments that I felt I wouldn‘t be able to tackle in terms of time or intellect. This wasn‘t what the successful students did. They took on every problem with determination and focus. No matter how hopeless…

I had this problem and noticed it among others too. I think part of the problem is that in High School (and many times in undergrad, at least the beginning) you could get away with not doing the homework/studying/etc. So while you have the intelligence for the material you never learned the work ethic associated with achieving at the higher levels (and studying didn't force the material into long term memory as well). Sometimes I wonder how things would be different if these people learned an (academic[0]) work ethic early on.

[0] I stress academic here because at least in my case I was working a lot during undergrad. 40+hrs/week while in JC and 30+ when I transferred to a uni. But succeeding in those areas aren't the same as academic work ethic and I do want to acknowledge people that just ran out of energy.

Re: How to Study Mathematics (2017)

#72

I am going to be honest, these kind of articles are useless. 1. Make sure you understand the concepts 2. Mark what you dont know clearly 3. Write down what you know 4. Use 3 to find out 2. Oh gee, thanks! This is a more realistic approach. 1. Have a reasonable amount of mathematical talent 2. Study materials appropriate to your current level and mathematical maturity. 3. Work hard at it. 4. Ask for help when you are…

What does mathematical talent mean? I was bang average at high school algebra(computation) but untouchable at geometry/trig. At uni linear algebra was a breeze but Calculus II was a nightmare. What does mathematical talent mean?

" Grothendieck's mathematical education changed radically by his arrival, in 1949, to the Cartan seminar hosted at the *Ecole Normale Superieure". As Grothendieck himself confessed(reference), he had not heard by then about topological spaces, groups, rings,modules, homology!!. The astounding capacity of Grothendieck is revealed in the giant mathematical leap achieved between his naive ignorance in 1949(in Paris) and his spectacular technical nous in 1953(in Nancy). At that year he finished his doctoral thesis about "nuclear spaces" and had become according to Schwartz in "the number one worldwide specialist" in the theory topological vector spaces.According to Dieudonne, Grothendieck was author by then of a life work "only comparable to Banach's"

A rough translation from https://www.pesmm.org.mx/Serie%20Cursos_archivos/smm2018Curs...

Either you believe there is no such thing as mathematical talent and you and me are in the same caliber of Grothendieck or you have to accept there are people with inborn qualities to excel way above the average human in that area. Same for Kasparov in chess, Mozart in Music, Jordan in BB. Blank-slatism will be the death of western societies.

Re: How to Study Mathematics (2017)

#73
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Re: How to Study Mathematics (2017)

#74

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 don't know if you're still gonna see this, but message u/micromss on Reddit for it.

Re: How to Study Mathematics (2017)

#75

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.

I don't know if you're still gonna see this, but message u/micromss on Reddit for it.

Re: How to Study Mathematics (2017)

#76
post #5

Also, use computers! I use SAGE extensively to get a feeling for lots of mathematical objects! 1. Grobner bases: http://bollu.github.io/computing-equivalent-gate-sets-using-... 2. Localization: https://github.com/bollu/bollu.github.io/blob/8cd335687ff3ef... 3. More broadly, an answer on math.stackexchange on how to debug math: https://math.stackexchange.com/questions/1769475/how-to-debu... 4. (WIP) continued fraction…

Sage is a remarkable project. For Grobner bases it relies on the Singular computer algebra system. I cringe every time I'm at a talk where someone credits Sage when they should have cited Singular. It's hard work writing a system like Singular, and not an obvious path to glory, so this stings.

I am sorry. I shall reference Singular in the future whenever I discuss SAGE. Thank you for your fantastic work on Singular :)
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