Honors Calculus at high level math programs focus almost entirely on proofs vs solving integrals. Frankly solving integrals is trivial to me vs having someone being able to understand the basis of calculus. You don’t have to have a fundamental understanding of calculus to solve integrals, frankly it’s like coding, the more you do it the more patterns you recognize the easier it becomes to code (or in this case solve integrals).
Usually tests have theory, proofs and applications, it doesn’t have to be just one. The quarter system probably puts some of the harder calc 2 stuff in the third course.
“Maybe you have some idea of proofs that are better or show a more fundamental understanding”
Proofs with trigonometric integrals are tougher, a calcI or II test without trigonometry is a little odd. Anyway so what if people think it’s not a rigorous test, it’s an opinion right. If people think that Riemann or Euler or L’Hopital, Gauss, Maclaurin, Ramanujan, Von Neumann, Hilbert (see that name dropping!) would fail this, fine. You’re entitled to that opinion as well.
These U of C calculus tests are produced as evidence of lack of rigor: @1NJParent pulls no punches - he calls the problems set in them “trivial”; proclaims himself “shocked” by their triviality; and sarcastically asks a commenter who says they look just fine whether “your expectation is a lot lower for a ‘rigorous’ course.”
In the same vein @theloniusmonk says it’s fine with him if we think Riemann et. al. would fail the Chicago exams, that’s just our opinion. No skills in close reading are necessary there either.
Now I’m no mathematician or scientist, but if these exams are offered as a metric of rigor, then we need some rigor in the analysis. We need to see exams from comparable courses offered by other institutions. If the Inspector Javerts of this board can come up with all these tests for Chicago, surely they can find equivalent tests for their preferred schools. Impressionistic evaluations offered by judges already disposed to hang the accused aren’t very persuasive.
I do, however, take from this discussion something that hardly needs to be proved: Chicago’s varying levels of calculus offerings (150s, 160s, 180s, 207, the IBL series) reflect the composition of a student body that is less STEM-oriented than these other schools but in which everyone is expected to learn some calculus in courses offered at varying levels of difficulty. That’s consistent with Chicago educational philosophy and with the constitution of its student body. It is not really a matter of “rigor” in the abstract. If these 160-level courses are in fact composed of students at a higher if not the very highest level of mathiness, and if it is being argued that they are not as rigorous as equivalent courses of that level at other schools, then let’s see the comparables.
You seem to suffer from a bunker mentality, treating everything that isn’t complimentry as an attack on UChicago. I happened to come across the final exams from that particular class (Math 162) and I can’t even find exams from other UChicago math courses (e.g. Math 161). If you have exams for comparable courses from other colleges (or even from UChicago), I’d be happy to do the comparisons.
Back to the topics.
IMO, UChicago’s Math 160-series (I haven’t looked at the 150s or the 130s) in the core curriculum is a rather poor choice for its more capable students who don’t take more math courses beyond the core (i.e. beyond 162) and who would need calculus in their other fields of study. They may have learned basic concepts, but not enough to be useful. Either the 180-series (for students more interested in applications of math) or the IBL-series (for students interested in more rigorous math), or the 207 (very few seem to get the invitation to take this course) would be better, but they aren’t in the core. If students are invited to take these courses, they’re taking them in lieu of the requirement in the core, correct?
Taking courses by invitation only may be consistent with UChicago’s more rigid structure, but it can’t be the best solution for all capable students. Any school (or its math department) can’t know what’s best for all students, even with the help of a placement test. Since Stanford is also the subject of this thread, I took a (cursory) look at Stanford’s math offerings. Its courses seem to be more sensibly structured and integrated to target different segments of its student body.
This makes no sense. As those students would need calculus in their other fields of study, they would of course take enough calculus to satisfy the pre-reqs for those fields as well as any math required directly for the major.
Yes - if you were invited to take higher math, then passing those courses with the requisite quality grade will satisfy the Math core.
Actually, UChicago’s math department seems pretty good at figuring this out. Scores on the placement test and higher math test, as well as high school performance and AP scores seem to be good indicators for them. And of course you can always work with them directly to appeal to get into higher courses if you feel you’ve been placed too low.
How so? Please provide those details for the benefit of those reading this thread.
Boy. This is deep in the weeds.
For math majors, I’m sure there’re other math requirements, but for other majors, do they have additional math requirements from their major beyond the math requirement in the core?
Stanford offers the 50-series, the 60cm-series and the 60dm-series, each targeting a different segment of its student body. The two 60-series are the more rigorous proof-based versions, but they’re very different. 60dm-series doesn’t even teach calculus (it assumes a score of 5 from AP BC exam is sufficient). Instead, it covers linear algebra, discrete math (including graph theory), some number theory and group theory (62dm), probability and random processes with some information theory and game theory (63dm). It clearly targets CS and math majors who are more interested in “purer” math (than analyses for which calculus is the foundation). The 60cm-series is the more typical proof-based sequence of calculus, linear algebra and differential equations (the first two are taught in a unified way as it should). It also requires a AP BC score of 5. The 50-series is for everyone else.
I am not understanding the purpose of the thread, but I really do not understand the 100 posts about calculus sequence. In the absence of a valid explanation, move on or risk having the thread closed
Of course. The Core is minimums for everyone, not maximums. For my son, an Econ major, he has an additional 3 math courses and 1 Stat (Calc used) at a minimum on top of the Core requirement.
There seems to be a radical misunderstanding of the purpose and goals of the UChicago Core by some folks in this group.
The Core requirements are not the ceiling of complexity or depth in a subject area. They are instead the floor for all students in a subject area irrespective of major
Thus you can be a physics major, but you must have a minimum exposure to a core Humanities/Civilizational sequence (as against disjointed or standalone random Gen-ed Humanities related course). Similarly you can be a Political science major, but you must have a sequence of Physical sciences courses
In addition, if you don’t have a foreign language credit from your AP classes in school, then you must take a year
worth of foreign language in a sequence
You don’t get to waive these, but you can take stronger classes if you desire.
It is fundamentally a different philosophy than a loosely structured/flexible gen-ed curriculum and is very much part of the UChicago ethos and whether you like it or hate it, that is very different from many schools.
This ethos of a structured core at UChicago attracts a somewhat different student profile also. That makes a difference in RSO participation and dinner/lunch/lounge conversations.
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Everyone understands the core or gen ed requirement sets the minimum bar. The question is whether there’re additional requirement in math from a student’s (non-math) major beyond the core. I also understand that if a student wants to take courses which require additional math courses, s/he would do so. However, that depends on the courses s/he would take and doesn’t raise the minimum bar for everyone in that major.
“Similarly you can be a Political science major, but you must have a sequence of Physical sciences courses”
This is the point others are trying to make, Chicago is not unique is that requirement. Poly Sci majors at UC Berkeley have to fulfill a seven course breadth which includes bio, physical, humanities, s/s etc in addition to English comp, Math and a foreign language. Now you can satisfy some of those with APs tests or may be just honors/APs classes. However while Berkeley students do complain about it being tough and stressful, they don’t go around saying look at us, look at us, we’re the only campus with rigor and stress, like UC students apparently do, at least on this thread.
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A non-math major such as you find in the humanities or some of the social sciences divisions will not require additional math beyond the Core. The requirement is that you must take at least two each of Physical and Bio and at least one of Math with a total of at least six. A very typical combination would be Calc I and II, PHSC I and II, and Bio I and II. (We haven’t touched on the bio core but there are options there as well for non-science majors). My D, a history major, is entering the K-12 education industry and the number of core math and science courses on her transcript qualify her to teach middle school STEM, so she’s preparing for the teaching certification in that area. Now, recall that this is a liberal education degree program; obviously MIT and Cal Tech require more math and science. Any non-STEM kid looking into UChicago or other peer schools with a liberal education should consider that they will need to take this much Math and Science, that the choices are limited relative to many other places, and that it’ll have to happen within the first couple years of their degree program. In contrast, If they were interested in Stanford, they would notice that the requirements are about 2/3 of UChicago’s: two courses in Scientific Method and Analysis, and one course each in Formal Reasoning and Applied Quantitative Reasoning. For sure, both schools overlap on some course content within these categories, but the required number differs as does the degree of choice and flexibility. At UChicago, the content is cumulative; at Stanford, there’s more of a “stand-alone” approach for the general ed courses.
This pattern is repeated with Hum/Civ/Arts - at least two each of Hum and Civ, at least one of Arts; total must be 6, sequences must be paired, etc. Arts tends to be writing-based more than being a studio program. For the Sosc Core, you must take three courses beginning in the autumn and continuing each quarter. No exceptions and no opportunity to begin the sequence at any other time.
Stanford matches UChicago more closely in terms of the number of required non-STEM generals; nine for UChicago and seven for Stanford. However, again all of the latter can be stand-alone courses with no sequential content and there are no rules about when those courses must be taken. This is why the non-STEM portion is considered to be “hefty;” there’s a ton of reading and writing; many struggle with just how arduous the demands are on their time in these courses. Furthermore, as you are expected to complete the Core within the first couple years of study, many feel that they have very little “true” flexibility of curricular choice till third year. And they would be correct on that; the only way to get around that is to take an extra course every quarter. That’s why many enter their third year of study with nearly 60% of their degree requirements completed. They take four courses every quarter for two years (some used to take five but I think that’s since been disallowed except in fourth year if you are behind).
For foreign language both schools have a similar requirement - one year of study - except that Stanford allows you to fulfill on a C/NC basis. At UChicago any course applied to this requirement must be taken for a quality grade.
I believe you will find that if you compare UChicago’s requirements for any particular major to that in another liberal arts program, they will be similar. UChicago allows for various tracks on several majors so it can get complicated, but I’m sure that’s true elsewhere too.
You’re rolling two distinct kvetches into one here, Thelonius.
Several schools have remnants of what was once pretty universal at all schools - a gen ed Core. However, Chicago (along with Columbia) has retained the genuine article. Being required to choose random courses from fields other than your major is fine and the courses may be great, but this does not make a Core, as OP has reminded us. There’s a reason why some on this board have called the Chicago approach “rigid.” We hear often on this board that many kids do not like it and avoid the school for that very reason. Even many kids at Chicago grumble about it - the appreciation typically starts later. Love it or hate it, Chicago is known for it. If Berkeley really has something like the Chicago Core, I have never heard mention of it but would applaud it.
As for the moaning and groaning, as many have said, take that with a grain of salt. It’s an old student trope and largely a performative one. History matters, and culture is sticky. The miseries of the scholar’s life go back to the “Anatomy of Melancholy”, and serious studiousness has always been what this campus was about. There’s a reason that the library is where the social action has always been. Add to this the legacy of the recent past - grade deflation, the departure of athletics, the decay of student facilities, the Chicago winter - well, it all adds up. You Californians live a sunnier life.
Not sure that UChicago has the monopoly on rigor and stress 
Like many of the top privates, UChicago doesn’t tend to grant more than elective credit or perhaps perhaps higher placement with a top score on AP. AP Bio will help with the Bio core, however. As for Berkeley, their breadth requirements do differ from UChicago’s gen ed because they are stand-alone subjects that can be taken anytime during the four years. All universities have some sort of general education program. The difference between UChicago and other places is that UChicago is actually known for theirs. No one really discusses or posts questions about Berkeley’s or Stanford’s general ed. They are just not considered to be that big a deal. That’s mostly how it is at other institutions. In contrast, UChicago’s Core has had a controversial history since generals were first strung together back in 1930.
MIT and Caltech seem to have stronger core humanities/social sociences requirements (each requires 12 quarter-equivalent courses) for any student. Most of their students are in STEM and I don’t hear them crying for these requirements. Few of them in humanities/social sciences face even greater challenges with their much more significant STEM requirements (than they would be at UChicago).
As we all agree, these core requirements are just the bare minima. If you have to be concerned about these minimum requirements, you don’t belong there. When my S and I were deciding on colleges a few years ago, we compared all the courses he would take, or likely to take, over his four years in college. Their general requirements never crossed our minds.
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Our S had a similar experience as @1NJParent (and S). The core requirements were not the prime driver his college selection. He mapped out 4 years of study and it was the entirety of the classes that he considered as he made his college selection. I was, however, happy to see that he would take (required actually) several classes outside his CS major.
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Actually, the UCB L&S 7-course breadth does not allow AP or other exam credit to fulfill them (the English composition, quantitative reasoning, and foreign language do). However, the science part of the 7-course breadth does allow for “physics for poets” type of courses.
St. John’s College is probably the maximal example of a core curriculum, which is the entire curriculum there.
Other colleges with their own varieties of core curricula include the well-mentioned MIT, Caltech, and Harvey Mudd (obviously science and math heavy, but with substantial humanities, social sciences, and arts) and the US service academies (with obvious emphasis on subjects useful for military officers).
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