<p>I was recently accepted to the Class of 2015 (woohoooo!), and I have a few questions as a prospective math major. Naturally, I know that UChicago has a superb math department in general, consistently ranked with the top departments in the nation, etc., and I apologize if any of my questions are easily answered or overly vague, but here goes. If any current math majors at chicago, or basically any current or former students who took a math class there (which should be all of them, as I believe it's a core requirement), could chime in that would be great. </p>
<p>[ul]
[<em>]I know math is (deservedly) one of the most popular majors at U of C. Given the program's size and popularity, how would you characterize the individual attention received in or generally the aesthetic of the major? Obviously I don't expect the level of attention or intimate interaction one would receive at a liberal arts college -- there are positive characteristics to both educational systems (urban university vs. small LAC) and I wouldn't choose one for the same reasons that I'd choose the other -- but I certainly would like to be able to interact w/ my professors to some extent...if that doesn't make sense, I basically wonder if the program feels large.....not sure if that makes sense either.
[</em>]Could anyone generally describe the academic focus of the math major (abstract, applied, proof-based, etc.)? Any particularly idiosyncratic aspects of it, or particularly well-taught or emphasized fields/classes?
[<em>]I know this is pretty generalized, but what was your experience with the quality and clarity of the lectures? This may seem obvious considering the program's reputation, but if you've ever watched some of the MIT OCW video lectures for Linear Algebra you'll know that brilliant mathematicians (or even mathematicians with important contributions to written mathematics education) don't always lecture brilliantly or clearly.
[</em>]Independent undergraduate mathematics research. Available, reserved for the most brilliant, difficult to approve?
[li]UChicago has a reputation for intense academics w/o intense competitiveness. Does this largely hold for the math department, despite the major's popularity?</p>[/li]
<p>[/ul]</p>
<p>Thanks for any help or info you can offer. UChicago is definitely one of my top choices at this point, but I always prefer to make the most informed decision possible. I'll probably end up posting this on the accepted students discussion boards as well.</p>
<p>I’m not a math major, but I think our VIGRE (REU - Research Experience for Undergraduates) program could say a lot about our school’s approach to mathematics education.</p>
<ol>
<li>First and second years typically don’t receive that much individual attention. You’ll be completing the introductory calculus and analysis sequences, and these are very large, standardized courses. The department is moderately-sized—about 100 people in each graduating class major in math; your experience is largely determined by your willingness to attend office hours, talk to professors, and seek out your own opportunities.</li>
<li>The math major is very abstract, with a strong emphasis on proofs. The 150s and 160s calculus sequences both rely heavily on proofs, and virtually all of the upper-level classes are proof-based.</li>
<li>Teaching ability widely varies, but I’ve had excellent experiences with both of my instructors. The postdocs and L.E. Dickson instructors (who teach most of the lower-level classes) are typically quite good. Full professors, however, may be prone to illegible handwriting and rambling lectures.</li>
<li>I can’t speak to independent research; as you know, research in mathematics is more difficult to conduct than that in the sciences. The REU is an excellent program (I’m attending this summer), but most first and second years don’t get the opportunity to do research independently (as far as I know).</li>
<li>The math department is competitive in the sense that every student wants to challenge him/herself to do his/her very best. There is very little direct competition between classmates, however; your fellow students are your greatest resource for help with studying, homework assignments, etc.</li>
</ol>
<p>I’m only a first year, but I hope I answered some of your questions.</p>
<p>My girlfriend enrolled in an intro calc course last quarter. She told me it was a large class and entirely proof-based. The lectures tended to be off-topic and unhelpful; there was a pretty large group of students from whom she sought clarification on the more poorly-explained concepts.</p>
<p>What if a first or second year learned the requisite concepts independently, then contacted a professor for research? Would that likely result in early research opportunities.</p>
<ol>
<li><p>I mean, all of my professors/TAs know me by name and some of them have given me their phone numbers (home & cell not office). I’ve been offered to come over for a beer, watch football, etc. Office hours can be in both groups as well as individual. Class sizes vary between 15 and 30 for the introduction sequences. I’ve had professors tell me “My office is open to any of you whenever I am there, so don’t hesitate to come on in.” Is this what you mean by intimate? The program is ‘large,’ I guess, but the average class only has 70-80 majors (I think) and many of them are double majoring with math being less of a focus than their other major. Thus, the real ‘serious’ majors probably are 30-40 each.</p></li>
<li><p>All math here is proof-based with little hints of applied things every once in a while. (By that I mean there may be one or two application problems on a homework assignment – ugh.) You don’t need to take a traditional multi-variable class or differential equations, etc. The program is very unique in this fact. I would <strong><em>HIGHLY</em></strong> recommend taking honors sequences when possible, even if that means going down a level. Better professors, better TAs, etc. And you will learn more the kind of math you use in higher classes.</p></li>
<li><p>Depends. Some professors are great lecturers (John Boller!) and some are terrible (Paul Sally – though people take his class for the letter of recommendation ;-)). Just talk to others and get as much information as you can. A huge portion of the time, they will have 2+ sections of the same class and your experience in it can largely depend on which section you are in.</p></li>
<li><p>I honestly don’t know many doing actual research. There is the math REU but, honestly, it is really just more classes you get paid to take. You write a paper but this most of the time means re-writing parts of a textbook :-/ There are research opportunities though…just probably not for 1st/2nd years (maybe 3rd/4th). The classes themselves will keep you busy ;-)</p></li>
<li><p>I have found it depends on what class you are in. Honors is very collaborative and everyone just wants to learn as much as they can (no competing to do better than the guy next to you but to learn as much as you possibly can). Many of my friends tend to claim this doesn’t follow down to the lower level classes (i.e. Regular Algebra instead of Honors). People still aren’t wanting to do better than the next guy… but they are less collaborative via group studying, etc. (Could be just that the problem sets are less difficult.)</p></li>
</ol>
<p>wow…thanks for your very informative answers. perhaps someone could help clarify the placement system and the most common sequence for incoming math majors? for instance, this year i’ve taken Calc II and am taking Linear Algebra at a top 20 LAC. Linear Algebra is writing-intensive and extremely proof-based, but Calc was largely computation (and pretty easy). i got a 5 on AP Calc AB, but my school doesn’t offer AP Calc BC. assuming adequate performance on the calc placement test, would i want to begin with the 16000 calc sequence and then progress to Honors Analysis, or intro to analysis and linear algebra (19900)? the conditions for first-quarter placement into 20700 as described in the math department catalog are a bit unclear. is placing out of the Honors Calc sequence not recommended, or simply impossible if you haven’t taken the BC exam?</p>
<p>if it’s not obvious, i’m terrible with interpreting course numbers and prerequisite instructions and qualifying for credit and placement and blah. i have no idea why i find it so confusing. basically, i’m trying to translate the typical sequence from the college where i’m currently taking math (calc II > linear algebra > diff eq > vector calculus > real analysis > beyond) into uchicago terms, which is surprisingly confusing. considering my current track, what would be the standard placement and sequence for freshman year? thanks again for all your help and info and candidness.</p>
<p>If you haven’t seen the material on sequences and series covered in AP Calc BC, you have little chance of testing out of calculus entirely (i.e., placing into 199 or 207). However, if you’re willing to self-study this material and have an aptitude for abstract math, it’s possible; I hadn’t taken any math beyond AP Calc BC, and I still managed to place into 199. I prepared for the test by looking at some basic concepts in analysis (Cauchy sequences, fields/rings, judicious use of the triangle inequality, etc.) and through recreational reading in math. Just do your best; regardless of placement, you’ll be taking high-quality, intensive courses from largely excellent instructors.</p>
<p>In terms of the typical math major sequences, most people take calculus as a first year (presumably honors), analysis as a second year (mostly regular, IBL, or accelerated [Rudin]; very few take honors), and algebra as a third year. Most of the electives are accessible after taking analysis, so people usually take various electives and upper-level courses as third and fourth years.</p>
<p>For my background, I took Calc and a class on adv. calc / differential equations (junior & senior years of HS). I took IBL 160’s Calc my first year and LOVED it. Now taking Honors Analysis and finding it extremely difficult/time consuming but liking it.</p>
<p>If you want to be a math major here and go to grad school for math, I would highly suggest taking non-regular analysis (IBL, accelerated or honors). To get into these sequences, you have to start fall quarter (i.e. place into 203+/207+) which many, but not a ton, do. So for me, I decided to take 160’s instead of start in 199 (I was placed into 199), so I could take a higher level of analysis. For me, this has been the correct decision. You may be borerd in 160’s though if you have been introduced to proo-based math in HS (I didn’t have this).</p>
<p>In general, I would say those intending to be math majors place into 160’s or 199 and a handful (25?) into 203/207. You can argue your way into IBL/Acc./Honors Analysis if you get placed into 199, and I would recommend it if you decide not to take Honors Calc.</p>