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.