Hi There I am new to Mathematics Educators so please bear with me if my question is not up to mark?

I am interested in mathematics and have gotten comfortable with basic proofs with Daniel J Velleman's How to Prove it and am currently working through Sheldon Axler Linear Algebra Done Right.

I was wondering given my level of Mathematical-Maturity whether it would be wise to study Linear Algebra, Number Theory, and Abstract Algebra concurrently and if so can you recommend some references? Thank you!

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    $\begingroup$ Do you have any specific goals in mind? For example, do you want to eventually understand general relativity, or understand Wiles' proof of Fermat's last theorem, or attend graduate school in mathematics, or obtain some background in certain areas in mathematics for your job, or . . . ? It's kind of hard to give the kind of advice you're asking for when we have no idea what your intentions are. Also, this is probably better suited for Mathematics Stack Exchange. $\endgroup$ Feb 7 '18 at 18:52
  • $\begingroup$ Thanks @DaveLRenfro My apologies for not making my question more specific and yes i wish to attend graduate school. $\endgroup$ Feb 7 '18 at 19:01
  • $\begingroup$ My advice would be to do one at a time just to lower the confusion factor and since the approach you are taking to the material is rather intense (proof based) so it may be better to concentrate. $\endgroup$
    – guest
    Feb 7 '18 at 19:29

If you are also quite new in Mathematics, I would recommend the book :

"The Art and Craft of Problem Solving"

by Paul Zeitz

Although it does not talk about specific math topic, it teaches you how to "behave" effectively and strategically when encounter math problems and ideas. This is useful for strengthen the basic, and therefore it can be applied when you learn other specific math topics.

In addition, you may want to learn Linear Algebra or Number theory first, before learning Abstract Algebra. The former is more concrete than the latter, and Abstract Algebra contains both of them.

A final addition : Do not study in a hurry. I may refer to a quote "A pupil in such hurry, learns slowly."


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