My daughter whats to pursue a course of study in math, but doesn’t know what direction to take. Business? Finance? Economics? Actuarial Science? Computer Science? Engineering? So many options. She is getting bogged down in her college search, because admissions counselors seem to want to know “what she wants to study,” and she just doesn’t know yet. DD has a 32 ACT score, 4.25 GPA, made a 5 on the AP Calc AB exam this Spring, and, most importantly, has memorized the first 100 digits of Pi. 
Any guidance would be most appreciated.
For the most part, business and finance really don’t suit someone who is looking to practice high-level math. Economics is slightly better but still is far from satisfying for that goal.
CS certainly draws on math and most importantly uses logical / mathematical thinking in similar ways, but in the average CS job and academics, it’s not that much use really. The exception is that high-level research can use a ton of applied math.
In terms of applying high-level math, Engineering would probably be the best bet, though I don’t know the actuarial world as well as others here. Very well could be a solid option as well.
TL;DR Chose a school that allows you to get accepted into admission regardless of major. In addition, make your daughter look briefly over the weekend at “Discrete Math” in the local library or bookstore. If after 3 to 20 minutes of briefly flipping pages she likes it, she might actually enjoy math and computer science route more than business.
Most colleges do not make you chose your major “officially” until 2nd or 3rd year.
In other words, she has lots of time. Don’t fret too much.
However, from my rather limited experience (as I too know over 100 digits of PI ):
A notable chunk of “math lovers” end up loving the more pure aspect of math (especially the girls compared to the guys in my math department)
In fact, though I have only met a few females in the math department, most of them really enjoyed just pure mathematics and its relationship with linguistics. And surprisingly enough, though they were highly interested in computer science, they weren’t really committed for the degree (more for just a minor).
In other words: most of the female math majors I have met (and a very small sample size of only 12) preferred the liberal arts like linguistics with their math degree instead of majors like computer science, actuarial science, finance, economics, etc.
Having said that, at least overall (excluding genders here), I feel that most “math” lovers really love the more pure aspects of it and unless they truly love physics, many just either major in pure math (with some CS courses as a backup) or math/CS or pure CS as Computer Science is arguably the pure-est of the applied math branch.
In other words, as many topics of Computer Science can be considered just “pure math” by itself like combinatorics, number theory, etc. etc., many math lovers tend to also fall in love with CS since the theoretical CS is basically modern math.
Basically, if I was to categorize math students now:
- Loves physics. Can’t live without it and likes to build build build things by TOUCHING on the object. Go try engineering.
- Likes or is indifferent (or somewhat hate) to physics. Really likes physics concepts but seriously rather avoid it if possible and anything PHYSICAL. Go try pure math
- Likes physics for life but not the “PHYSICAL” part. Go try pure physics.
- Not the best in math but still loves math and at end of day, wants to do business. Try finance.
- Really good at fast mental endless problem practice drill math. Try actuary
- Just loves pure math and also enjoys discrete math. Try computer science.
- Likes economics. Try economics. Most economics phd requires higher level math and math students have a serious advantage in this field. Like serious advantage.
Having said that, it should be normal that she does not know what to major in before college. In fact, I believe most schools expect you not to and I personally would recommend schools for undergrad in which it is rather easy to change majors at will.
It hurts to know that the expected major is not the major she wanted after attending so a place in which she can freely chose might be a better choice.
Having said that, I must say overall, I think most math lovers end up just going math/cs or cs or math. Math by itself is some of the best liberal arts degree so don’t worry too much.
I personally would recommend (if I had to) a non-engineering focused school. That way, she won’t be pressured to stay with a certain major due to the atmosphere of the school itself. Also, I do notice us universities often divide admissions to 2 types:
- Liberal arts
- Engineering
Most math majors I know chose liberal arts. Liberal arts school often contain majors like math, physics, economics, actuarial science, and computer science.
Engineering is just… engineering.
And business I believe is not considered an undergrad degree in most schools. Those schools that do, do note for someone unsure, it might not be the best option.
Oh and some easy way to differentiate between math/CS type students and business/economics/finance type students:
During the weekends, go visit like barnes and nobles or what not and let her flip pages on a textbook called “Discrete Math”. If she enjoys the rather blue coloring in the book and its rather funny theorem titles, then more likely, she might be a math/cs type student.
“Letters to a Young Mathematician” by Ian Stewart was available from our local library. Takes 3-4 hours to read. Might be worth a web search.