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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]My son is on track to finish Linear Alg and MultiCalc when he graduates high school. Would a SLAC have enough advanced math classes to challenge him as an undergrad?[/quote]
Your son will have yet to have taken essential (or important) college-level mathematics courses such as real analysis, abstract algebra, complex analysis, topology and functional analysis. Beyond courses in “basic” topics such as these, he might foresee taking an additional 4 to 10 math courses tailored more specifically to his interests during his undergraduate education, at least on his home campus. Therefore, as your son looks through department sites, he’ll want to see whether he can find close to 15 math courses of potential interest to him as an indicator of whether a college’s offerings would be ample for his level. Wherever he attends, he would be unlikely to be advised (or permitted) to take more math classes than this. Courses in computer science and mathematically-oriented courses in physics (e.g., mathematical physics, general relativity) also should be considered as potentially integral to the mathematical component of his education. Additional opportunities for variety and depth can arise through a Budapest semester or an REU.[/quote] Most SLACs do not even offer functional analysis [/quote]

Indeed.

Pure Math goes:

100 pre-Math: Calculus
200 pre-Math: Multivariable Calculus and concrete Linear Algebra
300 Core Math: Algebra, Analysis, Topology
300/400 Electives: Number Theory, Statistics

Unless a school has a Masters/PhD program, it won't have graduate-level courses (like Functonal Analysis) that have prereqs that are 300-level classes. There just aren't enough students who are interested and prepared. Some schools have nearby universities where seniors can take graduate-level classes.

However, if the student is interested in Computer Science or Applied Math or Statistics or Physics (or any second-major subject), they'll have enough courses to fill 4 years using "breadth", not "depth".

Looking for Functional Analysis at the mentioned schools:

Williams:
https://catalog.williams.edu/2324/math/detail/?strm=9999&cn=401&crsid=017511&req_year=24 Last Offered Spring 2022

Pomona:
https://catalog.pomona.edu/preview_entity.php?catoid=47&ent_oid=2409

Haverford has something some years: https://catalog.haverford.edu/programs/mathematics-statistics/#coursestext

Macalester: https://www.macalester.edu/mscs/courses/ (but it looks more like a "Topics" tutorial)

Swarthmore, Reed, Occidental only loosely cover Functional Analysis in occasional seminars on custom-chosen advanced topics.

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