How to learn Undergraduate Mathematics by self-study as the college lectures are not clear enough

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I am an Electrical Engineering undergraduate student. I have just joined college, so I am currently a freshman. I wish to pursue Masters in Mathematics after graduation. In order to be competent enough for Masters course, I need to study Mathematics on my own.

I have read answers related to my question but none of them seem to address my query. My questions are:

  1. Should I learn from books or from videos available on Internet (such as MIT OCW)? Also mention the resources which I should follow.

  2. As a student, I find many topics like Calculus intriguing and I am curious to dive deep into learning them. On the other hand, I feel unmotivated to learn some topics like Statistics. How should I deal with such topics?

  3. Which roadmap should I follow? I tried OSSU Mathematics curicullum but it didn't seem to fit in.

  4. How much time should I invest in solving problems? Personally, I like to solve real-world problems. I want to know whether mathematical geniuses are nurtured by intuitive thinking or problem-solving. I also want to know what makes them exceptionally good at math – discipline or curiosity.

Thank you in advance.

Best Answer

I recommend books.

It is important to find the right book for you, on any given topic in Math. A book that is right for someone else may not be right for you.

Generically, you want a book that offers many, many exercises for you to solve. My experience has been that about $20\%$ of my learning takes place by studying the text of the Math book, and about $80\%$ of my learning occurs when I tackle the exercises.

In effect, the exercises represent applications of the text, that force you to really understand the text. MathSE can then be a great tool for posting those exercises that you are unable to solve. You merely have to follow the protocol in this article.

As for finding the right texts, my first choice would be to seek out a working Math professor, at your school, rather than someone with an Engineering PHD, or (for example) the chairman of the Math department, or (for example) a Math teaching assistant.

You want someone in the business of being directly responsible (to a limited extent) for the student's learning.

A reasonable secondary approach is to review MathSE postings that are tagged book-recommendation or reference-request. You can couple this with an examination of the book reviews on a site like Amazon.com.

Then, the final issue is which Math topics to attack, and in what order. Here, I would (again) go straight to a working Math professor, explain the problem, and let him suggest the Math topics, and the order in which they should be tackled.

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