I’m considering majoring in math, because I like it. I am interested in statistics or economics as well, but NOT computer programming as I don’t like that so much.
I’m in BC Calc now, all A or A- in advanced math through high school. I haven’t taken the SAT since I was a junior but I only got a 760 on math (740 on english) and I feel like my math grades are mostly the result of hard work, not genius. I always do well but I don’t “get” everything right away so I’m worried that I’ll be outclassed by a lot of super geeks from countries with kick-ass math programs, or by people who took AP Calc as junior or sophomores.
What’s the major really like? How worried should I be?
I’m not sure how to guide you exactly but I will say that being a math major takes more than just grinding out an A in hard high school math classes. S is a freshman at Bowdoin and considering a math major. Got a 5 in BC calc as a junior and got an A in multivariable calc as a senior. They placed him in linear algebra and it is HARD. Like no math he’s ever seen. He’s doing ok in there but it has taken a lot of work and a lot of office hours to keep up. He’s not 100% sure he’s understanding it as well as he’s understood calc and he’s not sure if that’s “normal” or a bad sign.
His prof has been very supportive and talked to him a bunch about the next class in the math major’s series. It’s called Math Reasoning. It’s all proofs and supposed to be one of the hardest classes. Math minors don’t have to take it but majors do. S is worried about the class but has heard the prof is amazing and his current prof feels like S can do it.
I don’t think being a math major is for the faint of heart. Lol. Calc is applied math many times. Linear algebra and this math reasoning class is anything but applied. All theoretical. That’s not to keep you from trying but I would be looking at colleges that have small math classes and a supportive environment. I don’t know if S would still even be considering being a math major if he were at a bigger school with less direct support.
That same thing happened to a family member who was also placed in linear as a freshman and was miserable.
His advice is simple: “Ignore the BC placement, and retake either the full year of college calc, or at least half of it. You’ll be better off in the long run because there is much more to college calc than you’ll ever learn in an AP class; the school doesn’t care; and it will give you a year to completely nail down those fundamentals before you start higher level work.”
I bet the intensity of the math major varies quite a bit across colleges. There is also an applied math major, although certainly you would need the same calc and linear algebra courses as discussed above.
A 760 is a great score on math in the SAT! There are always going to be folks that are ahead of you no matter which major (and many of them may be better at math and not a super geek) but there are so many opportunities. If you like math then you should do that and I am sure there are many just like you that like math but not programming.
I think you should keep pursuing math and keep your eyes open for the careers you find the most interesting. Good luck!
Math is unlike most other subjects in that hard work usually loses out very dramatically compared to innate talent (though of course how much of that talent is present will depend on which college you go to). In other words, for the best mathematicians, it is possible to be at the top of the class with less work than in almost any other subject, whereas less talented students grind it out and are often still way behind. That’s why I did math, because I was quite lazy, and didn’t want to work as hard as the engineers, chemists and physicists (I also did a PhD because I didn’t want to get a job, and it was the most relaxing and enjoyable three years of my life, most of my key solutions were worked out in the bath). I think most math majors would also find math enjoyable and appreciate its beauty - 30 years later and I can still enjoy doing a Putnam problem for fun.
The long tail of talent is seen at all levels, you can read Hardy’s “A Mathematician’s Apology” (https://www.math.ualberta.ca/mss/misc/A%20Mathematician%27s%20Apology.pdf) to see how he felt inferior to Ramanujan. I was tolerably good, but studied with many much more talented mathematicians, quite a few of whom are now famous professors, and I always felt I had to work harder than they did. But the students who weren’t so able had a miserable time, because they worked much harder with very little to show for it. Of course, that may not be so true at a program with fewer really talented students and teaching that is therefore not as oriented towards those with grad school ambitions - it really depends on your choice of college (and talent is not particularly correlated with how much math each student has covered in HS).
On the subject itself, pure math is often the hardest conceptually (but as Hardy writes, to many mathematicians also the most rewarding), it usually doesn’t require more than a paper and pencil (with a few exceptions such as the four color theorem). Some (though not all) applied areas of math are more likely to require a computer. And stats and economics really are quite computationally oriented nowadays (big data!) - intro stats classes are often basically a programming lesson in R.
Linear algebra is rather different from calculus or multivariable calculus, which can be harder for some students. If the college introduces more logic and proofs there, it can be harder for many students that way. Many upper level math courses like abstract algebra and real analysis will be mainly proofs.
Most students with 5 on BC would be wasting time repeating single variable calculus. You may want to try the college’s old calculus 1 and 2 final exams to check your knowledge by the college’s standards. Multivariable calculus may be a better first math course than linear algebra for a student with advanced placement out of single variable calculus, since it is just building on the more familiar subject of calculus.
If proofs and pure math are not your thing, statistics and economics can be worth a look as math heavy subjects. Operations research and industrial engineering also.
But you should expect to use and program computers as tools in the work.
@ucbalumnus , I don’t want to sound like an idiot, but what are some easier, high paying majors out there? I know hard - $$$$$$$$ and easy - $, but I would just like to get a general idea.
PS, don’t get mad and say stuff like “if u want an easy major go to Podunk State U and major in janitorial studies.” thanks.
Accounting requires solid arithmetic and computational skills. It is not theoretical at all- learn the rules, do the calculations, figure it out. A strong math student like yourself would likely find it reasonably easy especially if you are quick on memorization. You’ll need grad school now to have enough credits to sit for the CPA exam, but it’s a solid career path which can go in a number of different directions.
Finance is likely to be a little harder but it does not attract the super brilliant students if you are at a college with a strong program in econometrics, statistics, CS or big data where some of the stronger applied math brains are likely to be. The really lucrative jobs right out of undergrad- places like DE Shaw or Bridgewater- prefer non-finance degrees though- they hire lots of math and physics majors and teach them the finance stuff.
Urban Planning is a solid major for someone good in math and it has a lot of cool directions to take these days (sustainability and climate change have created problems AND opportunities; self driving cars, increased urbanization around the world, etc).
Demography and Epidemiology have fewer career paths in private industry- many more careers in government or think tanks, but solid careers without a lot of risk if you are good at what you do.
Take a look at actuarial science- it is not necessary to major in it, and if you are really good you can get an actuarial adjacent job while you are preparing for the various exams in the field. But a caution- it does attract some very strong and smart students. It’s a great field for someone who wants to work hard but not kill themselves (I know a lot of actuaries and that’s exactly how they describe themselves. Thorough, hard-working, analytical but no killer instincts.)
There are likely a lot of other majors would you enjoy, but you asked about math. HTH.
https://www.aicpa.org/becomeacpa/licensure/requirements.html says that there is a 150 hour (= 5 academic years of full time college work) requirement, but (emphasis added) “To obtain 150 semester hours of education, students do not necessarily have to get a master’s degree. They can meet the requirement at the undergraduate level or get a bachelor’s degree and take some courses at the graduate level.”
Agree 1000%. When I was an undergraduate, I was in a class and interacted with someone who went on to be a 3 time Putnam Fellow, and only 3 times because he graduated in 3 years. My feeling is only people who have done at least a little serious mathematics can understand just how long the tail of talent is, and just how great the gap is between the best and the merely good.
Math potential is probably 99% innate. Preparation counts for almost nothing, as Hardy no doubt found with Ramanujan.