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I'm currently self-studying mathematics according to a modified version of this program: http://verbit.ru/Job/HSE/Curriculum/all.txt (it's in Russian).

Since I'm also working full-time, I'm able to devote about 5 hours every day 6-7 days a week.

My question is -- would you suggest studying 1 subject at a time doing a 1.5-2 month sprint, or going through 3 subjects at the same time in 6-7 months? I'm wondering what other strategies worked for people in the past. I tend to do 1 day, 1 week, and 1 month review after I read something to make sure I understand it, but doing that with more than one subject at a time is proving problematic as concepts often intertwine and I don't feel like I'm getting enough focus on a particular thing.

My background is actually in pure math (a decade ago), but I've been working in industry (speech recognition) for a while now, and suddenly have a desire to re-visit and re-learn my math skills.

Thanks!

Note: the program presented in Russian is roughly as follows (I do not own this program nor am I promoting it. Just seemed advanced and interesting enough.)

Semester 1

Metric geometry and topology

Fundamentals of algebra and linear algebra

Analysis: limits, sequences, and smooth functions of one variable

Fundamentals of set theory

Semester 2

Linear algebra (Jordan normal form, Hermitian symmetric spaces)

Measure theory, Lebesgue integration

General topology, fundamental group, covering spaces

Algebra: presentation of finite groups and Galois theory

Analysis on R^n and definition of manifolds (atlases, sheaves, and homeomorphism to subspaces in R^n)

Semester 3

Analysis on manifolds

Fundamentals of commutative algebra

Measure theory and fundamentals of complex analysis

Lie algebras, differential equation (via phase portraits mostly)

Semester 4

Complex analysis

Algebraic topology

Differential geometry (Riemannian manifolds)

Lie groups and Lie algebras

PS. Mathoverflow noted that my question will be better posted here.

mzv
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  • Well although I am a student currently and I can assure you as much as it sounds good doing one subject at a time it's not the thing you should be doing, I prefer doing 2-3 subjects doing same time for longer period, it maybe take long time but in long run it'l benefit you, the reason is if you do one subject at one time then when you pickup next subject you'll forget your previous concepts of the former subject and it'll be hard for you to revise so much stuff at once. If you'll take everything with you slow and steady it'll be better and you'll have much control over your all subjects. – Iti Shree Apr 25 '17 at 01:16
  • Very interesting, thank you for your answer. If I may ask, what revision strategies do you usually use to keep your knowledge of the subject fresh? – mzv Apr 25 '17 at 01:18
  • I usually practice sample test since it contains every type of questions and I quickly realize my weak areas and start working on them also it saves my time, revising notes won't help you as much as doing real test (I've done that mistake) and answering question like on these sites, it'll help you learn stuff that too new methods if you answer questions on online sites. And giving real time tests. – Iti Shree Apr 25 '17 at 01:26
  • But you should regularly revise notes to clear up concepts along with giving tests. – Iti Shree Apr 25 '17 at 01:26
  • Studying math while working full time has really convinced me there's no need to follow a preset course. If you have a family and a job (me!) there is no time. I've solved it by getting a bunch of books and using them for self study. With diligence I have cleared up a lot of the misunderstandings (on lack of understanding) I had after taking abstract algebra and complex analysis as an undergrad. – JMJ Apr 25 '17 at 01:36
  • @ALB Wow, I admire your devotion, it must have required a lot of diligence given you have a family. Did you focus on one subject at a time? – mzv Apr 25 '17 at 01:45
  • I basically use mornings of the weekends to study. I pick a book out of my stack I want to read that day and I spend a few hours with the book, pencil and paper, working out all the results as I read. I tend to find I go through phases --right now it's abstract algebra-- but I don't force myself to study a particular subject because I do this for fun. – JMJ Apr 25 '17 at 01:57

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