As the title, I concern about what is the best way to learn mathematics. I've asked some of the professors in my university.

  • Some said that I should intuitively understand mathematical concepts and theorems (i.e. understand the geometrical intuition or the idea of the concepts and the theorems)

  • Some said that I should just study the concepts and theorems, try to prove them using mathematical formulas, or try to understand the mathematical formulas and reasoning in the proof

  • Some said that I should study the concepts and theorems just to know where to find them when I need some reference

Which is the right way for me to learn mathematics ?

P.s: my major is machine learning


closed as primarily opinion-based by José Carlos Santos, Masacroso, Yves Daoust, Brahadeesh, Andrés E. Caicedo Dec 3 '18 at 15:55

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ this is a tough question, and similar to the general question, how does one learn best, or what is the best day rythm, I think there is no clear way, you need to figure out yourself. For me it is always like playing and trying to understand. $\endgroup$ – Enkidu Dec 3 '18 at 15:44
  • 1
    $\begingroup$ All questions with "best" in the title are meaningless. "Right way" isn't much better. $\endgroup$ – Yves Daoust Dec 3 '18 at 15:46
  • 2
    $\begingroup$ You are not on the right site, try Mathematics Educators. $\endgroup$ – Yves Daoust Dec 3 '18 at 15:47

This is much too vague a question and will probably be closed. That said, I will try to help.

First, there is no "best way". What works for someone else may not work for you. So you have to experiment with several ways and learn how you learn best.

I think that is rather like "machine learning", where the goal is to teach a machine to figure something out with guided experiments rather than by telling it something. Here you are the machine and the subject is mathematics.

Since you are more interested in the applications of some mathematics, not in the mathematics for its own sake, I suggest that when you encounter it in your work you try to understand what it says in that context rather than focus on starting from fundamentals and proving theorems.

  • $\begingroup$ In Machine Learning, they usually require employees to be good at math and have completed some graduate program. So if I want to have a Master or PhD degree in Machine Learning. Which is the right way, in your opinion ? Or can you just tell me your way of studying math ? $\endgroup$ – HOANG GIANG Dec 3 '18 at 16:40
  • $\begingroup$ My way won't help you. For machine learning you will surely need at least linear algebra and probability - those are second or third year courses for undergraduates. If you find that material very very difficult you may not be able to work in machine learning. $\endgroup$ – Ethan Bolker Dec 3 '18 at 17:17
  • $\begingroup$ I've finished Linear Algebra course and Probability & Statistics course in my university without problems. But I still concern about the right way to study math, especially advanced math (e.g. information theory, optimization, etc). Hope that you can share your way so that I can try it out ? $\endgroup$ – HOANG GIANG Dec 3 '18 at 17:25

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