I should start off with a bit of an introduction. I'm completing my first year at the university and have decided to pursue a degree in mathematics. Pretty funny how I thought I would never touch theoretical math or proofs coming into college. My math professor suggested I get an account on this site, and that is what I did! While many of the questions that I have looked through have been quite advanced, I have definitely enjoyed seeing the beauty of math being played out.

Now, for my question. I'm completing a course in Linear Algebra at the moment. I've already gone through Calc I-III. I'll be taking differential equations next semester along with a course called "Intro to Math Reasoning." It's basically what the math majors here take to get a rigorous introduction into higher mathematical thinking. However, I have been doing some proofs on my own time, and I am enjoying it very much. I would like some of your input into any reading I can give into this summer with an understanding of linear algebra and (differential through multivariable) calculus under my belt. I realize that the level of math I'm at is relatively low compared to a lot of the material on this site. However, any insight into topics I may want to research during the summer would be greatly appreciated! Thanks in advance for your help.


closed as off-topic by zz20s, Shailesh, Ben Sheller, choco_addicted, colormegone Mar 23 '16 at 3:59

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  • "Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – zz20s, Ben Sheller, choco_addicted, colormegone
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  • $\begingroup$ Calculus and linear algebra are the gateway to just about every area of mathematics (at least at the basic level). You can pretty much start on anything at this point. Just figure out what seems interesting to you. $\endgroup$ – user137731 Mar 22 '16 at 23:02
  • $\begingroup$ Thank you very much for the response! I will definitely keep that in mind. I think it is very sound advice - someone I was talking to told me that, as one gets higher in mathematics, many times only a true passion for the work at hand will lead to success in that field. It makes sense, given the difficulty of all areas in the realm of mathematics; natural talent will only take someone so far. $\endgroup$ – cray712 Mar 23 '16 at 0:29

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