<p>I've been admitted for Class of 2014, and was interested in doing some sort of Math - perhaps Applied. However, I'm wondering if I may be too far behind to do this. I hear about a lot of kids who are taking Linear Algebra as HS Sophomores, etc. etc. and am wondering if my current standing would mean I'd be forever below-average at Chicago.</p>
<p>I'm doing fine in BC Calculus, and I enjoy sitting down with a few difficult problems (right now I'm annoyed at myself that I left my Calc textbook at school; I want to finish the damn thing, although we're more than out of AP test range), but is this enough?</p>
<p>I am currently a 3rd-year math major at Chicago.</p>
<p>The Princeton Guide to Mathematics isn’t a great text for beginners. It has a lot of obscure content you have no business getting into as someone having just taken Calc BC.</p>
<p>Right now, more than anything, you need to boost your theoretical background. That basically means, forget about multivariable calculus, linear algebra, differential equations. You’ll learn those from your analysis classes once you get here. With your background, you’d probably start in the Honors Calculus sequence, which is something of a baby Analysis sequence. You could theoretically start at the non-Honors Real Analysis sequence, but if you want to take Honors Analysis (which many people want to take), this isn’t recommended.</p>
<p>The best and standard text for real analysis, which you should start studying now, is Principles of Mathematical Analysis by Walter Rudin. It is a great text, save for the last few chapters on Lebesgue Measure Theory and Integration, which you should ignore for the moment. If you have enough money (it’s $75 on Amazon), get this, understand the proofs, do the exercises. Go through the first 5 or so chapters. This is what I did the summer before matriculation, and as a result, I got into Honors Analysis. Not that that should be your aim necessarily.</p>
<p>If you don’t have enough money to dish out on Rudin, get Kolmogorov/Fomin’s Introductory Real Analysis. It’s $11 on Amazon, and it’s a pretty great text for beginners.</p>
<p>S1 has friends who entered Chicago at the 160s Honors Calc level (where you will get lots of the theory you’ll need for Analysis) and they are now in math PhD programs. No worries.</p>
<p>@OP: I know that if you go to a good school / live in a place with highly educated parents and motivated children, it may seem like you’re behind, but once you enter the real world, you’ll realize just how ahead of the curve you are. And yes, I’m in BC as a senior, AND struggling.</p>
<p>It sounds like the basic classes at Chicago are important for math majors because of the emphasis on theory?? My son is currently in Multivariable, but should he take the Honors Calc sequence? I’m just asking this hypothetically as I know he would have advising at the college.</p>
<p>Thanks for the responses! It seems that all hope is not lost. One further question…</p>
<p>@phuriku: Thanks for the new recommendation. That book seems pretty tough, though; one reviewer recommends against it if one hasn’t had much experience with delta-epsilon proofs. We only touched on this in my current course, and I never really understood it. I’m wondering if “Elementary Analysis: The Theory of Calculus” may be a better choice for me? Also, if you don’t mind, what was your math background before attending UC? What about other people who placed into Honors Analysis?</p>
<p>At least as far as the contents of the book go, it seems pretty good. It starts from the most elementary concepts, unlike Rudin (which I believe starts with Dedekind cuts), so it is probably more appropriate.</p>
<p>As for my own math background… before I came to Chicago, I had taken Calc BC, AP Stat, Multivariable Calculus, Linear Algebra, Differential Equations, and Discrete Math. I then picked up Rudin during the summer and learned the first few chapters, after having studied Spivak’s Calculus first. However, MVC, LA, and ODE are not prerequisites for getting into Honors Analysis. The best preparation is a solid background in theoretical mathematics, i.e., a firm grip on the concepts of analysis.</p>
<p>Alright. I’m guessing then that Honors Analysis is probably out of the question for me. Still, I think I’ll pick up the Elementary Analysis book, whether or not I matriculate at UChicago and whether or not I ended up as a math major. </p>