Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Interest in theoretical math = PhD program in math. Look at the feeder schools into math PhD programs: https://www.collegetransitions.com/dataverse/top-feeders-phd-programs
You really want to look at *per capita* rankings not overall. It means a lot more if you have 5 out of 10 math majors at Swarthmore regularly heading into PhD programs vs 5 out of 500 math majors at Berkeley.

Why would you say that?

That page says.
Berkely has 100 PhD-bound math student to Swarthmore's 22.

Another example, UVA sending 41 students to Math PhDs, and Haverford College sending 12.

Those 100 Berkeley students or 41 UVA students are going to be a more vibrant math community with more opportunities and relationships, even though thousands of non-pure-math majors are also on campus.

Berkeley has 30,000+ students; Swarthmore has 1600. Swarthmore students are almost five times as likely to enter into a PhD program. This is largely due to the fact that a SLACs, students develop really close relationships with their professors. Also, the resources per capita are astonishing. Students are not competing against each other for a few coveted internship or research assistantships. While I don't doubt the benefit of a large cohort of undergraduate colleagues, if you're going for a PhD, it's really your graduate school colleagues that will matter the most professionally.

But you aren't a random student at the school. You are you. And no one is picking a random student at a school when they are picking PhD candidates.
The point is that having a bunch of other students doing something else nearby doesn't affect your courses. (But does have other benefits like extra-curriculars.) Bigger schools with more students have more faculty.

Anonymous wrote:The Pomona link above seems a little wonky or indirect, but it offers two functional analysis courses: https://catalog.pomona.edu/preview_course_nopop.php?catoid=47&coid=158836 & https://catalog.pomona.edu/preview_course_nopop.php?catoid=47&coid=158837

And you'll find that its students are also interested in the topic: https://www.pomona.edu/academics/departments/mathematics-statistics/students (See Chloe, Class of 2026).

Thanks for better link.

Yes, Pomona, being a Claremont consortium college, like Amherst in the Five Colleges, has a broader curriculum than most more-isolated LACs.

Anonymous wrote:

Anonymous wrote:Interest in theoretical math = PhD program in math. Look at the feeder schools into math PhD programs: https://www.collegetransitions.com/dataverse/top-feeders-phd-programs
You really want to look at *per capita* rankings not overall. It means a lot more if you have 5 out of 10 math majors at Swarthmore regularly heading into PhD programs vs 5 out of 500 math majors at Berkeley.

Why would you say that?

That page says.
Berkely has 100 PhD-bound math student to Swarthmore's 22.

Another example, UVA sending 41 students to Math PhDs, and Haverford College sending 12.

Those 100 Berkeley students or 41 UVA students are going to be a more vibrant math community with more opportunities and relationships, even though thousands of non-pure-math majors are also on campus.

Berkeley has 30,000+ students; Swarthmore has 1600. Swarthmore students are almost five times as likely to enter into a PhD program. This is largely due to the fact that a SLACs, students develop really close relationships with their professors. Also, the resources per capita are astonishing. Students are not competing against each other for a few coveted internship or research assistantships. While I don't doubt the benefit of a large cohort of undergraduate colleagues, if you're going for a PhD, it's really your graduate school colleagues that will matter the most professionally.

Anonymous wrote:

Anonymous wrote: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?

My son took those courses in high school and his LAC made him retake them. It was because he took them at a CC that taught them with just computations, and the LAC taught them as proof based.

Yes, they vary a lot. CC courses are a continuation of regular high school classes -- plug and chug formulas given without justification. some high schools classes are like that, and others (like MCPS SMACS) are proof-based like university honors courses.

Measure theory is more important than functional analysis for most PhD bound undergrads. Look to see if they offer that.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote: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?

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.

Most SLACs do not even offer functional analysis

Well, that was partly the point. The OP's son would benefit from choosing an LAC at which functional analysis appears as a regular offering in the course catalog.

That's oddly specific. There are several options for upper-level advanced math courses. Functional Analysis is only one, and Functional Analysis being present doesn't necessarily mean that other options are available, or vice versa.

See the original post, in which seven courses are named (five in mathematics and two that may be offered through a physics department).

The Pomona link above seems a little wonky or indirect, but it offers two functional analysis courses: https://catalog.pomona.edu/preview_course_nopop.php?catoid=47&coid=158836 & https://catalog.pomona.edu/preview_course_nopop.php?catoid=47&coid=158837

And you'll find that its students are also interested in the topic: https://www.pomona.edu/academics/departments/mathematics-statistics/students (See Chloe, Class of 2026).

Anonymous wrote:Interest in theoretical math = PhD program in math. Look at the feeder schools into math PhD programs: https://www.collegetransitions.com/dataverse/top-feeders-phd-programs
You really want to look at *per capita* rankings not overall. It means a lot more if you have 5 out of 10 math majors at Swarthmore regularly heading into PhD programs vs 5 out of 500 math majors at Berkeley.

Why would you say that?

That page says.
Berkely has 100 PhD-bound math student to Swarthmore's 22.

Another example, UVA sending 41 students to Math PhDs, and Haverford College sending 12.

Those 100 Berkeley students or 41 UVA students are going to be a more vibrant math community with more opportunities and relationships, even though thousands of non-pure-math majors are also on campus.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote: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?

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.

What is a "Budapest semester"? Thank you for the helpful course layout

Budapest Semesters in Mathematics refers to a notable study abroad program for undergraduates::

https://budapestsemesters.com/

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote: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?

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.

Most SLACs do not even offer functional analysis

Well, that was partly the point. The OP's son would benefit from choosing an LAC at which functional analysis appears as a regular offering in the course catalog.

That's oddly specific. There are several options for upper-level advanced math courses. Functional Analysis is only one, and Functional Analysis being present doesn't necessarily mean that other options are available, or vice versa.

Why do people say Williams is a good Math program?

Williams math major only recommends 9 courses after Calculus I!

https://math.williams.edu/courses/requirements-for-the-major/

A normal math major would be at least 8 courses after Calc 3 and concrete Linear Algebra.

Their Catalog document https://catalog.williams.edu/pdf/math.pdf
offers this awkward advice:

"Students interested in continuing their study of mathematics in graduate school should consider: [the theoretical math options]"

"Students headed for graduate school generally take more than this relatively small number of courses required for a liberal arts major."

And the department is so small that
"Most other 300-level [ = post-calculus] topics are offered in alternate years.
Each 400-level topic is normally offered every two to four years." !!!

Anonymous wrote:

Anonymous wrote:

Anonymous wrote: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?

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.

Most SLACs do not even offer functional analysis

Well, that was partly the point. The OP's son would benefit from choosing an LAC at which functional analysis appears as a regular offering in the course catalog.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote: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?

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.

Most SLACs do not even offer functional analysis

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.

Anonymous wrote:

Anonymous wrote: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?

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.

What is a "Budapest semester"? Thank you for the helpful course layout

Anonymous wrote:

Anonymous wrote: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?

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.

Most SLACs do not even offer functional analysis