There are, in fact, effectively eight levels of math open to first year students:
– A remedial pre-calculus class that does not satisfy the math core requirement but that prepares unprepared students for calculus. This is generally a very small class.
– I think that there is a non-calculus statistics class that actually satisfies the math core requirement, but that fact is not advertised much to students because the Math Department thinks everyone should take calculus. I don’t know if the pre-med requirements have changed yet, but if/when they do this will probably become a significant option for non-science-major med students. Unless they have done away with it.
– 130s calculus. This meets the core requirement and pre-med requirement, but not generally the requirements for any hard science or high-math major. It is significantly less proof-oriented than other calculus classes. There is a proof class provided for students who take this sequence and then want to “catch up” with more demanding math classes or take a math-heavy major.
– 150s calculus. This is the normal calculus class, and probably the most popular one. Students can place into the first, second, or third quarter, and all are offered out of sequence every quarter. The third quarter is significantly more proof-oriented and is a prerequisite for many math-heavy majors.
– 160s honors calculus. A more rigorous, proof-oriented version of calculus. This is basically the signature course of the Math Department, and they try to get as many kids as possible to take it, unless they are clearly not ready for it or clearly beyond it. Students who have taken AP Calculus (either version) will generally be offered this class unless they have done a lot of post-calculus math. Those who take it seem to work harder and enjoy it more than students in 150s, and the teachers are generally better and the grading more friendly. You can’t start in the middle, you have to start at the beginning. The first two quarters satisfy the math core requirement; the third satisfies additional requirements for math-heavy majors. Students with high grades in 160s are eligible to take honors analysis as second years.
– IBL 160s honors calculus. A few sections of 160s, open only to students who have 5s on the AP Calculus BC test, are taught as “inquiry-based learning” classes, where essentially the teacher guides the students as a group to develop proofs on their own, rather than giving them any of their information in lecture or reading form. Students who take this tend to find it completely stimulating and engaging but time consuming.
– advanced classes other than honors analysis. Students who test into honors analysis can take other higher level classes rather than honors analysis if they want, most often regular analysis or the IBL version of analysis (which covers less ground than honors analysis).
– honors analysis. This is the Chicago entry into the “most difficult math class in the world” sweepstakes, an equivalent to Harvard’s Math 55, except half of the students are second-years who aced honors calculus. I think this uses IBL method, too. Reputed to take 30-40 hours/week. A lifelong badge of honor, which some students who could take it decline. About 10 first-years per year generally qualify for this.
One of my kids came in having taken AP Calculus BC, but done terribly on the test, and interested at the time in a science major. The math advisors made a strong pitch for him to take 160s calculus. He opted for 150s instead. The first quarter was very easy for him, and he did well without too much effort. The second quarter was harder, and the third quarter ate him up.
I think that is a mischaracterization of 150s calculus. The University of Chicago as an institution, and especially its Math Department, believes strongly in proofs, and all majors that involve a lot of math require a strong grounding in proof-based math. I believe 150s calculus becomes more proof-heavy as it proceeds, and its third quarter is intended to qualify students for upper-level proof-based math courses.