<p>I'm more of a pure math guy (though I do enjoy some humanities classes), and I'm trying to find more about Chicago so I can make my decision. I've gotten into other schools (MIT, Stanford, Michigan w/ scholarship, Berkeley) with similarly good math programs, and I'm not looking to see which has the "best" program; I think they're all good. I just want to know what the differences between these schools would be for a guy like me. I've tried reading the Chicago blog, but the only posters are two female humanities majors. I haven't visited any of these schools, and I'll only have the opportunity to visit two. I'm completely lost. Would anyone on this site be able to help?</p>
<p>Oh, and yes, I do know I'll study math. I am always told that people generally change majors when they get exposed to college-level courses in their major. Howver, I've taken an analysis and an algebra course, so i'm somewhat familiar with proof-based maths.</p>
<p>chicago is very strong on math, and very strong on humanities. professors for both are great all around. it allows you to go into grad stuff pretty much as soon as you start.</p>
<p>As a prospective math major with a great interest in UChicago, I’m extremely attracted to this honors analysis course. What kind of caliber students end up taking HA as freshmen? I have heard comparisons to Harvard’s MATH55, and the only freshman I know to have taken that course (and survived) won a silver medal at the IMO. Is taking HA as a freshman reasonable for someone like me?</p>
<p>I’m a junior this year taking multivariable calc/differential equations, and I plan to take linear algebra and an introductory real analysis course through Stanford’s EPGY OHS next year. I scored 8 on last year’s USAMO and I’m quite comfortable with proofs (I qualified again this year with a 10 on AIME and I’m shooting for a 15 on USAMO). I saw a link to one of the HA tests and could only solve one part of one problem though I understood most of the solutions when I read them. So does it look like I could take HA as a freshman assuming I get in and everything?</p>
<p>I have a first year math major who is in Inquiry-Based Analysis – he took MV, DiffEq, Lin Alg, Discrete, and Complex Analysis his junior and senior years of HS, plus spent a summer at a wonderful math program where he did lots of proofs. He has also done a lot of combinatorics/CS theory on the side, which is pretty much all proof stuff. He liked the IBL format better than HA, and has found that the IBL course has covered the same material as HA, and feels it’s been done with just as much depth. Having Lin Alg under your belt makes analysis easier, so you aren’t trying to do proofs and learn the field simultaneously. (Chicago integrates LA with its 160s and Analysis sequences.)</p>
<p>The regular Analysis and Honors Analysis sequences are by invitation only based on calculus placement test scores, which you’ll take as soon as arrive for O-Week. (Seriously — last year move-in was Sat., the test was Sunday.) However, the math department advisors are very good at working with students who feel their results on the calc placement exam don’t reflect their preparation. Their main concern for students going into Analysis is that you are comfortable with proofs. An alternative route is to take Math 19900 (a proofs course) and then enter the regular analysis sequence winter quarter.</p>
<p>In future, please don’t post folks’ IRL names without their permission. The FB poster offers terrific advice, but may not want to be identified here.</p>
<p>Getting into HA as a first-year is difficult, but feasible. You must have a very strong background in pure mathematics. One of the first things you’ll learn when/if you come here is that math contests are, well, completely useless if you actually want to become a successful mathematician. Mathematical ability itself means very little, and very few have the mental capacity to deal with the abstract nature of the topics of Honors Analysis.</p>
<p>I’ve found that the most valuable thing to success at math at the University of Chicago is being able to learn mathematics independently. I had only taken MVC, LA, Diff Eq before coming to Chicago, but I taught myself Analysis over the summer, which meant more to my ability than any course I had taken previously. Subsequently, I was able to test into HA as a first year, primarily by showing the test graders that I was familiar with concepts in metric spaces, topology, and other areas of analysis.</p>
<p>What kind of mathematical ability should you have for HA? The ability (not necessarily knowledge) of a first-year graduate student at a top-50 university in mathematics. Because that will be the level of content.</p>
<p>As to the OP: The distinctions between Chicago and other top universities in mathematics are very clear. Firstly, it seems that Chicago is rather disconnected from “mainstream mathematics” in the sense that we are rather apathetic toward math competitions such as the Putnam. This gives us a much more serious tint - if you want to be a serious researcher in mathematics, Chicago is a good place to come. Second, we are a very test-focused school. If you go to MIT, for instance, most of the classes will be graded 100% according to how well you do on the psets. At Chicago, 70-80% of your grade will be decided on test results. Third, Chicago probably has harder classes than other top universities. HA is the obvious example, but some of our teachers are really rather insane. For instance, in a class I’m taking this quarter called Differentiable Manifolds, the professor is approaching the subject matter via sheaf theory, a rather advanced theory usually not even taught in graduate school. In addition, as far as I’ve seen, our graduate classes are easily the hardest in the nation. I’ve seen graduate course material at Harvard, Stanford, Berkeley, and MIT, and I can say without hesitation that the course content at Chicago is significantly more difficult than at any of those schools. This will be very important to the more serious researchers who will get into graduate classes by their 3rd year or so.</p>
<p>While I agree that you don’t need much contest math experience to do higher math (although if you are struggling to qualify for the AIME, you might want to review the basics), I would take some of phuriku’s statements with a grain of salt. It may be true that UChicago students put little weight behind the Putnam, but that doesn’t mean that students at other schools take the competition much more seriously. It seems more reasonable that many students who indeed did very well at math competitions in the past did not limit themselves to the basics of elementary mathematics.</p>
<p>Having said that, a math competition background is a decent indicator of your problem solving abilities. Nevertheless, there is no reason to confine yourself to topics in elementary mathematics. You should be able to move on to more advanced mathematics, knowing that your experience in problem-solving will serve you well in many areas. But again, don’t think that the contest mathematics itself is more important than it really is for college mathematics.</p>
<p>This is an interesting thread, but most students and parents should realize it is a ‘best of the best’ discussion. A student would need to be 3+ years ahead of a standard high school curriculum to undertake multi-variable calculus, linear algebra, and differential equations at a local college, much less a real analysis course, which is typically a third year (or fourth year) college course. That’s if you have access to a four-year college. Most high schools generally have restrictions about placing ahead in math. RA can be one of the ‘weed-out’ courses for math majors, unlikely to be mastered with a summer of self-study by many students.</p>
<p>UC attracts very talented students, but I would make an educated guess that there aren’t many high school students nationwide at this level. Of course, there aren’t many students nationwide that qualify for admissions to UC!</p>
<p>Anyone majoring in math at a top-tier school is good at math. There won’t be any weak students in your classes.</p>
<p>If you read CC enough, you would think scoring 800 on the math portion of the SAT, 800 on the SAT II Math 2C, and a 5 on the AP Calculus BC is common. It isn’t.</p>
<p>One last point - check carefully for the numbers of math majors at top-tier schools. The numbers are lower than you might expect.</p>
<p>swarthmoredad,
My S was fortunate that he was able to take those courses at his public HS with his classmates rather than hauling to the local university (where RA was a 400 level class and, as you correctly stated, a weeder for many students) . Granted, not many schools offer those kinds of options. </p>
<p>S was not a fan of math competitions and only did those which were given to all the math students in his classes. Never broke 4 on the AIME and didn’t care. However, he was seriously involved in competition algorithmic programming, which did at least as much for his math skills and creative mathematical thinking as his programming. He has always been good at teaching himself, a skill that has served him very well in some endeavors and been his downfall in others. For math, it’s a good thing.</p>
<p>A number even more interesting to check is the number of folks who declare a math major vs. those who actually graduate with one. Attrition can be high, even at the top programs. An 800 math SAT, Math Level II a 5 on BC Calc may be uncommon, but it is not necessarily an indicator that one would do well as a math major, either. It’s a whole 'nuther ball game when one gets to RA. I haven’t seen a problem set of S’s involving actual numbers in a couple of years!</p>
<p>This is a pretty big claim to make, but I can’t say that I disbelieve it actually, even though I have never seen the course material taught in a Chicago course (but have seen the material taught at all the other schools mentioned). Know why? There’s this one professor at my school who is exceptionally famous, and comes from Chicago graduate school originally – the man’s classes always end up being FANTASTICALLY difficult, and students drop out of it rapidly. Also, interestingly his are one of the few courses at that level which are heavily based on exams still, even if less than 70%. </p>
<p>Now, obviously the other schools all produce top caliber researchers too, and the question to ask yourself is if this kind of high pressure environment will help or hurt you. To give an idea, one of the young stars of my school went to Harvard as an undergraduate and did NOT take Math 55, and the kinds of stuff he works on today is utterly crazy. Hard classes are great, but you shouldn’t take them at the expense of starting to grow discouraged with math, because in the end, research is research, and it’s clear that going through the hardest classes isn’t necessarily the way to become the best researcher. It depends what teaches you the most.</p>
<p>I completely agree. Some may think that my posts claiming that Chicago has the hardest classes are nothing more than bragging, but the fact is, having the hardest classes isn’t necessarily the best thing for many individual students. Great researchers often work best under low-pressure environments, and coming to Chicago can take a lot of their time to do individual research away. Other schools could certainly choose to make their graduate classes harder - I just think that they hold the opinion that it wouldn’t be extraordinarily beneficial to their students to do so. (I must also add as a disclaimer that class difficulty often depends more on the individual professor than the school. I’ve noticed that the classes taught by some of the incoming professors are significantly easier than the professors who have taught here for 10-20 years.)</p>