<p>Hello,</p>
<p>I am currently a high school senior, and I am looking for an engaging math activity for this summer.
For the previous two summers, I attended a summer math program and worked a bit with a math professor, respectively.</p>
<p>Would anyone like to suggest math programs or activities intended for pre-math major students in transition from high school to college? Most of the programs I searched were either specifically for high school students or undergraduate students. I was considering some high school math programs, such as Ross or PROMYS, which do occasionally accept graduating seniors, but I was concerned that most students would be a few years younger than me (I will be 19 by the summer).</p>
<p>As for my background, I am currently studying differential equations/linear algebra and first-year topics in discrete mathematics. I have not done much math competition. I would like to significantly improve my understanding and writing of proofs and work on open-ended questions.</p>
<p>For current math majors: I would like to prepare myself for the rigor of undergraduate studies, and if you'd like to suggest other ways of preparing at this period of time, please let me know. What do you wish you had done before entering college? What would be a good thing to focus on? Should I focus on preparing for my first year math courses or try to broaden my background?</p>
<p>I would love to hear comments from anyone interested in pursuing math. Thank you.</p>
<p>Hi,</p>
<p>I am actually a current high school senior and prospective math major also. Unfortunately, I have no information about summer programs (I found this post curious about them myself, actually), but I think I can still offer some advice. </p>
<p>I think it would be the best idea to prepare yourself for the rigor of college mathematics (especially if you wish to focus on pure math like me). Has all of your math education thus far focused on computation? If so, I would highly recommend working through certain sections in a book like Calculus by Spivak (or even an introductory text on analysis). It will take you back to the foundations and give you invaluable experience with proof-writing and abstraction (and probably also make you love the subject much more). If you are able to at least master epsilon-delta style proofs, then you will probably be very well prepared for your first analysis course. </p>
<p>Linear algebra is also a great subject to prepare for, so it is good that you have some experience with it already. Just like my advice above, I think that it would be beneficial to supplement any computational course with a more theoretical one, one which will talk about linear maps between vector spaces more than it talks about matrices and determinants (again, especially for pure math).</p>
<p>I’d be happy to revise my recommendations if you tell me a bit more about your background with proofs and goals with math. </p>
<p>Also, I have to ask: what work did you do with a math professor and how did that get started? That sounds very cool.</p>