Calculus Placement Exam

Colleges and Universities A-Z University of Chicago ✅
1

<p>Hi, long time lurker here --</p>

<p>I've just sent in my application to the University - EA, of course. I won't bother you with any chances questions. My query is a bit more specific...</p>

<p>I have a strong interest in mathematics. I haven't had the opportunity to take very advanced classes in maths (ie, college-level), but I'm a final-year IB student with some mathematical ability, maths contest experience and a lot of enthusiasm. (Assuming I am accepted) I would really love to get into the 160s sequence. To this end, I am curious about the calculus placement exam, and have a few things to ask of current students (particularly phuriku - if you took the exam at all):</p>

<p>1) How many questions were there on your exam?
2) What questions seemed to be intended to target those who would place into Honours Calculus (eg, epsilon-delta, LUB and GLB)? Any for students better suited to jump right into the Analysis course?
3) Were there any proof-based questions?
4) Did you feel you were placed into the correct sequence?</p>

<p>Also, if any current maths majors/hobbyists at the University would humour me:</p>

<p>1) Has anyone here done an independent reading in maths? What topic did you choose? Did you enjoy it?
2) How is the teaching, overall? (I know of some of the excellent teachers, like Paul Sally or Diane Herrman - what are their strengths?)
3) What are the REUs like? (They look wonderful)
4) Did you take any of the inquiry-based sections of any class? What did you think?
5) What courses have you particularly enjoyed? Have any disappointed you?</p>

<p>My main area of interest (as far as I can say right now) is in set theory, mathematical logic and the philosophy of maths - but the real reason I'm applying is that I'm an academic at heart, and want a full and thorough humanist and mathematical education. </p>

<p>I know many of these questions are far too specific, but any relevant information would be greatly appreciated.</p>

<p>Thanks for your time - most of this is a product of idleness and anxiety, but I'd really like to get some 'insider' information. My visit, interview and tour were all fantastic, but there weren't any maths majors on hand. :(</p>

<p>Thank you again, and good luck to all who are applying.</p>

2

<p>Basically, people who took and did well in a BC Calculus-type course will get the option to take 160s, so I don't think you have to worry about not getting into 160s. Even if you don't, you'll almost certainly be allowed to take it anyway, at least on a trial basis. The test is mostly multiple choice, and then there's a short answer section (with 6 questions?) aimed at determining 160s vs. 195/199 vs. Analysis vs. Honors Analysis. If you try any of them, even if you get nothing right, you'll probably be put in the 160s, assuming you did well on the calc portion of the exam. Honors Calc does not assume knowledge of proofs, and you don't need to know proofs to get into 160s. The lines between 199 and Analysis are sort of blurry since not many students are placed into those courses--most students who place out of the 160s are put initially into Honors Analysis, it seems. </p>

<p>People are basically placed into the correct level, and if not, the math department is very loose with letting students try out a higher class or drop down to a lower one if necessary. </p>

<p>Teaching tends to improve with math level. The 150s and similar sequences don't have great teaching, but a lot of people love their 160s professors. I have a friend who took 160 experimental and loved it. I have a friend who took Honors Analysis and loved it. I know a lot of people who took 130s and 150s and were pretty apathetic about their experiences, which is probably to be expected.</p>

3

<p>corranged, I know one student who placed out of all calc but not into honors analysis. </p>

<p>FWIW, less than 10% of the students place out of all calc.</p>

<p>I agree that the line between the 150 series and 160 series is to a great degree a personal preference thing, although I'm sure advisors would advise a student who blew all the proof related questions to think twice about the 160s.</p>

<p>The OP should keep in mind that the goal of the placement test is NOT to reward students, and not to identify the "stars". It's goal is to match the student to the class, based largely on the preparation the student had. Since many first years find the math classes something like drinking from a firehose, the math department wisely decided that having a kid stretch in calc placement does no one any favors. One's UofC career will be better served with a good grade in the 150s than a mediocre grade in the 160s, just for example.</p>

<p>So I suggest that the OP should focus on doing well this year, and just do a short review of the material covered in calc before the placement exam, then let the chips fall where they may.</p>

4

<p>I know several students who placed out of calc but not into Honors Analysis, but it seems as if there are fewer first years initially placed into 195, 199, or Analysis than other courses. They are sort of like in between courses, which is why fewer students place there (though some drop to one of those). </p>

<p>Almost any student who has taken and done well in a BC Calc level caluclus and didn't completely blow the placement gets the placement of: "153, Strongly suggested to take Honors Calculus" or something to that effect. I've met one student who placed into 153 without the suggestion of 160s. The 160s isn't very exclusive in terms of getting in; the hard part is staying in and doing well.</p>

<p>I also disagree that someone's U of C career would be better with a high grade in 150s versus an OK grade in the 160s for many, many reasons. First of all, I believe it goes against the University of Chicago's tradition of true academic and intellectual thirst and challenge to take a less challenging course for a better grade. Second, the 160s has an entirely different atmosphere than the 150s. The 160s are for students who love math; the 150s are largely filled with students who need to fulfill their calculus requirement. One's experience will be very different in each course. For someone who loves math, loves challenge, and is at the appropriate level, I can't imagine why they would choose the 150s (though I realize pre-meds and such do it). For a potential math major, the 160s will give a much more accurate picture of future work and course-load than the 150s, not to mention the fact that the U of C math department strongly suggests that interested students take the 160s if they have that option. There is more to this than grades. What about the experience? peer group? Major experience? Challenge? A feeling of accomplishment, pride, and satisfaction? Superior teaching? etc.</p>

5

<p>My first year is one of those who placed out of calc but not into hrs analysis. He was offered one of those in between type classes. He didn't like that choice so he's in hnrs calc (#?)...the point here is that he absolutely loves the class. Like corranged said, the experience, peer group, teaching, undrestanding and satisfaction ( pride doesn't play with this boy) make for major happiness.</p>

6

<p>hahaha. Those looking for a fun time should check out the inquiry-based honors calc. It's a class where, from what I've heard, the students teach proofs to each other and the professor sits in the back and corrects them.</p>

<p>I placed into 15300 and was urged into honors with a strong performance on the BC exam and a solid foundation in proofs and delta-epsilon-- corranged estimations are, I think, totally correct. (Since I satisfied core with placement and am not a calc person in the slightest, I opted not to take the class).</p>

<p>There's generally less enthusiasm for 130's and 150's sequences to begin with, anyway-- the classes are not stellar, but they're not hated.</p>

7

<p>Thanks to everyone for your responses! I've a few things to add.</p>

<p>newmassdad -- Don't worry, I'm not studying for the placement test a year in advance. :) I have no illusions as to where I might fit in the UChicago community. I'm no prodigy, but I do have a fairly good feel for the pedagogy and content of the 160s sequence and they look like precisely the classes for me, mathematically and from a personal perspective.</p>

<p>If any other prospies are interested, I've dug up a thread from six months ago on Honours Calc:
<a href="http://talk.collegeconfidential.com/showthread.php?t=331985%5B/url%5D"&gt;http://talk.collegeconfidential.com/showthread.php?t=331985&lt;/a&gt;&lt;/p>

<p>It's slightly less informative than this one.</p>

<p>Also, the websites for this year's 160s are up (and no doubt have been for a while). See
<a href="http://www.math.uchicago.edu/%7Ekevin/161/%5B/url%5D"&gt;http://www.math.uchicago.edu/~kevin/161/&lt;/a> ,
<a href="http://www.math.uchicago.edu/%7Eshulman/162-winter07/%5B/url%5D"&gt;http://www.math.uchicago.edu/~shulman/162-winter07/&lt;/a>
and <a href="http://www.math.uchicago.edu/%7Ekevin/163.html%5B/url%5D"&gt;http://www.math.uchicago.edu/~kevin/163.html&lt;/a>
for one of the inquiry-based sequences.</p>

<p>Thanks all!</p>

8

<p>
[quote]
I have a strong interest in mathematics. I haven't had the opportunity to take very advanced classes in maths (ie, college-level), but I'm a final-year IB student with some mathematical ability, maths contest experience and a lot of enthusiasm. (Assuming I am accepted) I would really love to get into the 160s sequence. To this end, I am curious about the calculus placement exam, and have a few things to ask of current students (particularly phuriku - if you took the exam at all):

[/quote]
</p>

<p>
[quote]
1) How many questions were there on your exam?

[/quote]
</p>

<p>Well, there are two parts of the exam: the first part is multiple choice, the second part is proofs. The multiple choice section had about 80 questions. I think the proof section had about 10 questions, but they were pretty long.</p>

<p>
[quote]
2) What questions seemed to be intended to target those who would place into Honours Calculus (eg, epsilon-delta, LUB and GLB)? Any for students better suited to jump right into the Analysis course?

[/quote]
</p>

<p>I think this has already been answered, so I'll leave this alone for the most part. I think that to an extent, even if you answer every question correctly, you still won't be placed into Honors Analysis. The reason I got in was because I was a show-off and defined the Riemann-Stieltjes integral when they told me to define the Riemann integral, used metric spaces and topological spaces for the other definitions, randomly used Cauchy sequences to prove things that have no relation to Cauchy sequences, etc. If you answer most of the proof questions "correctly", you'd probably be placed into the 199-203-204-205 sequence. Pretty much anyone can get into Honors Calculus, as has been mentioned. Starting this year, no one can be placed into 203.</p>

<p>By the way, if you enter into Honors Calculus, you won't be assumed to know epsilon-delta proofs, LUBs, or GLBs.</p>

<p>
[quote]
4) Did you feel you were placed into the correct sequence?

[/quote]
</p>

<p>Hmm. This year, probably not, but that's probably because Lenya Ryzhik (professor of Honors Analysis this quarter) is a madman and assumes that everyone taking the course already has an extremely good grip on undergraduate analysis and all of the concepts presented in Baby Rudin. From what I have heard, teachers of 207 (Honors Analysis) usually spend the first quarter covering the basic elements of undergraduate analysis at an extremely fast pace instead of declaring everything a prerequisite.</p>

<p>Anyway, there's a serious problem with the analysis sequences at UChicago. 203 is non-honors Analysis, and the advanced section of this course covers all of Rudin. But if you take 203, you can't take 207. So you can either cover undergraduate analysis, or graduate analysis, but not both. This means that most of the people in 207 have studied undergraduate analysis by themselves, unless you consider 161-162-163 "baby" Analysis. Hopefully, 207 will change back to how it used to be next year, though.</p>

<p>Back on topic, though, my girlfriend has a friend who got into 207 but dropped back to 203. She says he's really struggling even with 203, so apparently the placement test isn't very accurate.</p>

<p>
[quote]
2) How is the teaching, overall? (I know of some of the excellent teachers, like Paul Sally or Diane Herrman - what are their strengths?)

[/quote]
</p>

<p>I talked about this at lunch with someone today, actually. Basically everyone on the mathematics faculty here is well-known in the field of mathematics to some extent, and with this, there is a large variation of teaching strength. You will have professors who are good teachers but outside of the classroom leave pretty much everything to their TAs (Fefferman is an example, if I have been told correctly), but you will also have professors who are very dedicated to working one-on-one with undergraduates. Even if you don't have a professor of the latter description, I really don't think it's that significant, because you can work with a TA very closely doing the same things.</p>

<p>
[quote]
My main area of interest (as far as I can say right now) is in set theory, mathematical logic and the philosophy of maths - but the real reason I'm applying is that I'm an academic at heart, and want a full and thorough humanist and mathematical education.

[/quote]
</p>

<p>I don't know how advanced you are in mathematics, but pretty much every course 160s and higher is based upon set theory. I've heard that the professors in 161 are having a difficult time getting certain ideas across because they are based on set theory, and AP Calculus seems to have embedded silly, fallacious concepts into everyone's mind. My girlfriend is taking 161 this semester under Fefferman, and I've seen all of her problem sets and tests. Comparing what I've seen from her class with the problem sets on the websites listed, it really depends on the professor how tough your course is going to be. (Although, grade-wise, the tougher the problems, the easier it is to get an A. Even though the problems in her psets are very closely tied with basic analysis concepts (such as those in Rudin) and the average grade on the psets is 50-60/100, the professor has made is clear that the lowest grade in the class will be a B-, a policy I am very much against.)</p>

<p>My neighbor (who took Honors Analysis last year) is taking a Logic course this semester (and is the only sophomore in that class, according to him). He's really enjoying it.</p>

<p>I'll make an extra note that might serve as a little jolt of excitement. Even as a freshman, I'll be TAing a course next quarter (13- or 15- sequence). I really don't know if I would be able to do such a thing at any other institution. The stuff the math department will let you do is just amazing. I think there are more opportunities for math majors here than any other institution in the United States, but I'm biased in that opinion because I don't know how other leading institutions treat their undergraduate math majors; it's just common sense that they wouldn't let a freshman be a TA (or do independent research with a graduate student, for that matter). Also, it's widely known that UChicago has a strong relationship between the professors, undergraduates, and graduates, moreso than competing institutions, so you'll certainly have lots of opportunities here if you matriculate.</p>

9

<p>I'll say this much: of all the kids I know who turn down the single-letter schools for Chicago, about 60-70% of them are looking to be math majors. I know, for example, a math prof at Brown who thinks that HYPSM and Chicago are stealing Brown's best math students. I think it's a combination of our program and our general atmosphere (academic, very theory-oriented) that brings in a lot of math kids.</p>

10

<p>From a slightly different angle: My son did NOT do well in his BC course, or on the exam. He still placed into the 160 sequence. He turned it down initially because his advisor told him to take it only if he wanted to major in math, but the instructor in whatever 15X course he's taking kept pressuring him to switch. He really hasn't wanted to, because the people he knows in 160s spend about 3-4 times the amount of time on it that the 150s people do. He likes math, but he's really not that interested in it, just wants to meet the prerequisites.</p>

11

<p>And one more angle. My D took AB, not BC, and placed into 15300 with the 160 urging. And like JHS's S opted to stick with 15300, as she also felt it was for math (and physics) majors. </p>

<p>I guess that's why they have placement tests. One school's AB is not another school's BC, nor another school's IB program.</p>

12

<p>i think phuriku is exaggerating what it takes to get into honors analysis. proving the riemann-stieltjes integral is kinda...absurd. i placed into 199 last year and i didnt even attempt the field axiom proofs (because i, like most high-schoolers, didnt know what a field axiom was, which is why honors analysis was no place for me.) i did a delta-epsilon (though from memory, i didnt really know what it meant) and found some limit that had a "trick" to it, and that was good enough.</p>

<p>im a big advocate of 199, by the way, and if youre placed into it i think its a great opportunity to take it over 161 and start taking real math classes instead of the 'fundamental' ones very early on. for instance this year im taking differential geometry and topology which normally 3rd and 4th years take because i had a headstart on analysis.</p>

13

<p>What if you're taking higher than BC courses? Like Linear ALgebra/Diff EQ? Will they let you test into those courses?If they do, is it even a good idea to skip Calculus at UChicago?</p>

14

<p>I am a first-year student taking Honors Analysis.</p>

<p>


</p>

<p>Lots of people place into Honors Calculus, including people who have never taken AP Calc BC. The free-response questions were almost all about standard calculus material (defining limit, derivative, and integral) except for a couple at the end about field axioms.</p>

<p>


</p>

<p>This is absolutely not true. I have never taken an analysis course before this one, and I am having no problem following the class. To take the class, you do have to be very comfortable with math in general, and there may be a couple things you have to learn quickly: I did not have previous experience with suprema and infima, but I figured it out on the first homework.</p>

<p>


</p>

<p>Please don't presume that you know exactly how it was taught in previous years. Until I see evidence to the contrary, I will assume Mr. Ryzhik actually knows what he is doing.</p>

<p>


</p>

<p>You speak as if "set theory" means "mathematical rigor". I would agree that the courses are based on mathematical rigor. Neither of us has taken "pretty much every course 160s and higher", but they're definitely not all about logic.</p>

<p>


</p>

<p>I should hope not. I certainly wouldn't want to be TA'd by a first-year undergraduate if I were taking calculus. This is supposed to be a good thing?</p>

<p>Conclusion: Honors Analysis is lots of fun if you have a very strong math background! Honors Calculus is probably desirable and feasible if you have less experience and want to learn more about how math is done here.</p>

15

<p>I'm also a first year taking Honors Analysis, and I have points of agreement and disagreement with both of the above opinion on the class. </p>

<p>About the placement test I agree completely with scherzo, I think I managed everything more or less correctly except for the last two problems, but it seems like a high score on the standard calculus problems and a decent effort at the proofs will place one out of Calculus and at least into 199, and depending on the last few questions possibly into 207. </p>

<p>More about Honors Analysis( 207), shall we be honest that this is in no way whatsoever a standard first course in analysis, Rhyzhik has taken for granted a great deal of what is normally taugh in a first analysis course. I am not saying this is a bad thing, but I am saying that the calculus placement test is absolutely meaningless in regards to determining whether or not one belongs in Honors Analysis (at least this year, I do not know about other years so i won't comment on that, however I do know the class typically follows Rudin's book and so is probably more in line with a typical advanced real analysis course). The class is using Royden's real analysis text which is a beginning graduate level text and the class does seem very much like an introductory graduate class on analysis. </p>

<p>In regards to the 160s, I have friends in both the regular 160s, and in the inquiry based version. The regular class seems to be following closely to Spivak, whereas the inquiry based class has done quite a bit with set theory because the ultimate goal for the first quarter of that class is to construct the real numbers.</p>

<p>Set theory is a very foundational subject and I'm sure only very few upper division classes do not at least require a basic knowledge of it. Oviously we are using it in 207, and I can't imagine doing any topology or algebra without it. </p>

<p>As for TAing, I can't imagine there is much differnce in the mathematical knowledge of a second year finishing the analysis sequence and a first year finishing the first quarter of honors analysis.</p>

16

<p>


</p>

<p>I agree. I don't think it would be feasible for them to create a placement test to determine well who should take Honors Analysis. People just have to decide for themselves whether it's the right class. It is, however, the right class for some people (like me!), contrary to what phuriku seems to think.</p>

<p>


</p>

<p>It is true that in math classes we talk about sets and axioms. This does not mean that someone who expresses an interest in set theory would by consequence like all math classes! (That is what phuriku seemed to imply.) Set theory is an area of study more specific than just everything with sets.</p>

<p>


</p>

<p>Sure, okay. But I was surprised that undergraduates would ever TA. Is this a pretty normal thing that I'd just been oblivious to?</p>

17

<p>
[quote]
You speak as if "set theory" means "mathematical rigor". I would agree that the courses are based on mathematical rigor. Neither of us has taken "pretty much every course 160s and higher", but they're definitely not all about logic.

[/quote]
</p>

<p>Of course, my use of the words "set theory" doesn't correspond to real set theory, i.e. graduate set theory, but rather, the essential elements of set theory that typical first-year analysis courses use. Obviously, 161 is not based upon the Zermelo-Fraenkel axioms. </p>

<p>
[quote]
I should hope not. I certainly wouldn't want to be TA'd by a first-year undergraduate if I were taking calculus. This is supposed to be a good thing?

[/quote]
</p>

<p>Why not? Does social position really matter that much? I thought the determination of a good TA was based on teaching ability, not age. And what's so different between a freshman TA and a sophomore TA? If you haven't noticed, there are a fair amount of sophomore TAs.</p>

<p>
[quote]
Please don't presume that you know exactly how it was taught in previous years. Until I see evidence to the contrary, I will assume Mr. Ryzhik actually knows what he is doing.

[/quote]
</p>

<p>I never said he didn't know what he was doing, but it definitely doesn't follow how the course was set up in previous years. Sally taught the course generally every year for the past five years up to this year, and if you'll ask someone who took the course, they'll tell you that he started out with basic real analysis, but at a very fast pace (and very algebraically). </p>

<p>Remember the meeting we had at the beginning of the year for freshmen placed into 199/207? He said that 199 and 207 would start out covering the same content (namely, his purple book), but 207 would simply cover it at a faster pace. Ryzhik basically assigned the entire purple book for homework as a reading assignment the first week, and has ignored it other than that (except for the irrelevant problems we had for homework the second or third week). If you'll also tell anyone who took 207 last year that we started measure theory the 2nd week of autumn quarter, they'll think you're joking.</p>

<p>
[quote]
I placed into Honors Analysis (Math 207), and I'm loving it. I created an account on this forum because I was tired of watching phuriku whine about it unopposed.

[/quote]
</p>

<p>I never said I didn't like 207; in fact, I like it other than the fact that our homework assignments take too much time. I simply disagree with the way Ryzhik is teaching it. I'm not complaining that it's too fast-paced for me either, as I read Rudin over the summer. However, a Harvard 55-like course would be the most appropriate for the first quarter, and professors have realized that up to this point.</p>

<p><a href="http://www.math.harvard.edu/%7Eelkies/M55a.02/index.html%5B/url%5D"&gt;http://www.math.harvard.edu/~elkies/M55a.02/index.html&lt;/a&gt;&lt;/p>

<p>I bet you can't do half of the problems in those problem sets, and that is fundamental analysis material, whereas measure theory is not.</p>

<p>
[quote]
It is true that in math classes we talk about sets and axioms. This does not mean that someone who expresses an interest in set theory would by consequence like all math classes! (That is what phuriku seemed to imply.) Set theory is an area of study more specific than just everything with sets.

[/quote]
</p>

<p>You apparently don't know what I am implying and what I am not. Do you really think a high-schooler would be speaking of graduate set theory?</p>

<p>
[quote]
I agree. I don't think it would be feasible for them to create a placement test to determine well who should take Honors Analysis. People just have to decide for themselves whether it's the right class. It is, however, the right class for some people (like me!), contrary to what phuriku seems to think.

[/quote]
</p>

<p>Where are you pulling these things from? I never said anything to that extent. In fact, I also think the entire placement test idea is a little silly, as I tried to convey in some of my earlier posts.</p>

18

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<p>


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<p>You said "Lenya Ryzhik is a madman" and "Anyway, there's a serious problem with the analysis sequences at UChicago," and "Hopefully, 207 will change back to how it used to be next year, though." These statements imply that you think something is wrong with the class. So far I think it's going fine.</p>

<p>


</p>

<p>Maybe you've changed your mind, but in this</a> thread you said, "I have learned this the hard way. AVOID 207 AT ALL COSTS."</p>

<p>I had been under the impression that you were complaining that the class was inappropriately hard. Now I guess we agree that it's not.</p>

19

<p>There seems to be some disagreement as to my level of knowledge; I'll try to provide context.</p>

<p>I'm doing my IB Extended Essay in mathematics, on dispelling the fundamental problems with the intuitive notion of set. This means I build the ZF(and C) axioms almost from the ground up. It's partially expository, and it isn't Gödel's L, Diamondsuit or a paper on large cardinals, but it is what seems to be considered 'real set theory' at the undergraduate level. Having never taken a course in the subject, I might be making a false statement - I certainly know I don't cover all of the topic by any means. My primary reading is M Potter's Set Theory and its Philosophy, Halmos' Naive Set Theory and various sets of lecture notes from U(C) and elsewhere.</p>

<p>I also do a bit of reading in maths to make up for the lack of introductory university courses in my area. I've all but devoured C & R's What is Mathematics? and have finally got my hands on a copy of Spivak, which I am working through slowly, doing problems and taking notes. D Vellemen's How To Prove It and various historical books are also favourites. I know no amount of reading or problem-solving can truly prepare me for Chicago mathematics, but I've spent much of the last two years getting acquainted with 'real' maths. I certainly won't be reading 'baby' Rudin by myself any time soon.</p>

<p>Hope that clarifies things a little bit. It's reassuring that UChicago students can have a decent debate about mathematics courses. Thanks again.</p>

20

<p>about TA-ing as a first year...i think most people agree this is a bad idea. most, except for the math department. undergraduates ta in very few departments here, and i cant name a specific one outside of math, actually. that being said, im a ta and get paid for it so im not complaining, but this is only for lower classes (most upper-level classes are ta-ed by grad students.) </p>

<p>obviously there isnt much difference between a 1st year in honors analysis and a 2nd year in...anything, but it's not really about how much math you know. after all, the stuff you're grading and teaching is basic calculus. the social division is actually a serious issue. i wouldn't really like being ta-ed by someone my age, and 3 of my students (out of 10) are older than me and i do feel a little awkward about it even though they seem to respect me. there is something to be said for having 4 quarters under ones belt and just 1 when it comes to leading a few hours of problem sessions a week.</p>