As a junior in PSEO right now I’m currently finishing up taking Calc 3 and 4 this semester and in the fall I’m planning to take three math classes:
Sequences and Series (Mainly Proof Writing) -Sophomore/Junior Level
Differential Equations with Applications -Junior/Senior Level
Fourier Analysis -Junior/Senior Level
I know that the applicants for MIT all excel in math and science, but I was wondering what the math levels were like of accepted freshmen, and if my math background would give me a competitive edge or would be viewed as more normal considering the level of applicants for MIT. I’m also asking because I’m not too great at high school math competitions since none of them involve calculus and that’s what I’ve been studying the past few years.
Math levels of accepted freshmen I know vary widely, from having just taken pre-calculus or calculus, to studying graduate-level courses in Lie theory.
While it’s not necessary (as MITer94 noted above – levels of math for entering freshman vary widely), it certainly doesn’t hurt, assuming you are doing well in those classes. (The levels that you are taking I would say are not the norm for entering students, though there would be some whom have attained that and beyond). You are right – the math competitions you speak about are a whole different animal. You may find math and science research more suited to your interests, and involves an entirely different skill set.
I was in a similar situation some years ago (I graduated from hs in 2012). I think MIT undervalues difficult college math classes although this may because they have a hard time distinguishing which classes are legitimately hard or easy. I’m pretty sure some 4xxx/5xxx level math classes at UMN are quite easy even though some are quite difficult. Even some hard math classes are graded extremely generously (e.g. differential geometry with the notorious Jack Conn) so I understand MIT’s hesitance in putting lots of weights on these classes even though it meant my A-s in 5615/6H (honors real analysis) probably hurt my application a lot (I was initially deferred and then accepted at MIT but was rejected from Caltech and Harvard). FWIW, of the handful of people I know who took similarly or more advanced math classes PSEO almost all got into MIT although there is massive selection (many also did RSI/USAMO). This group fared much worse in admissions at Harvard though so perhaps MIT values these classes more than Harvard (possibly just noise/Harvard being generally more selective).
On the bright side I found the PSEO math classes I took 5615/6H, 5285/6H (honors algebra), 5378 (differential geometry) to be excellent preparation for MIT and MIT is also much more generous with transfer credit for advanced classes than almost any other elite school (I got credit for 18.100B, 18.700, and 18.703).
@“UMTYMP student” Do you know if 5xxx math is viewed as more difficult than 4xxx math outside the U? This somewhat gets into the dilemma of what is legitimately hard/easy since I know at least one 5xxx course that I’ve refrained from taking because I wouldn’t learn anything new. From what I understand about the U, the difficultly levels are comparable so I chose my 4xxx level courses because I had the professors recommended to me by a TA. Do you think this could be disadvantageous for admissions? (I’m only asking since you’ve been through this before, it’s totally good if you don’t know)
I doubt MIT or other schools care or notice about 4xxx or 5xxx. I think MIT unlike other schools doesn’t even require college transcripts when applying if the grades are also on high school transcripts. In terms of admissions, the only thing I would recommend is to ensure you get a good grade. Even if the average MIT student would get like a C in the class getting a B+ in a math class will hurt your application. Subject to ensuring you get an A or possibly an A- I think you should choose by learning/convenience.
If you are taking the class because you have an interest in it, it may help. If you are taking the class because you think it will look good on your application, it probably won’t. Very few things done solely so an application looks good help.
That would be understating things. 
@MITPhysicsAlum Don’t worry. Pretty much all math is interesting to me except for maybe geometry or combinatorics. If the class number did make a difference I would have still stuck with Sequences and Series and Fourier Analysis, but my interest in Differential Equations with Applications is very comparable to other classes offered so it wouldn’t have made that much of a difference to me to switch. Now if I was told to switch to a math that only involved the intersection of geometry and combinatorics, then I wouldn’t care how it looked, I still wouldn’t get within ten feet of it.
Especially for a technical school like MIT, being well-lopsided is looked upon favorably. And if your stats are just as strong as your math background, you have a good chance of being accepted. A friend of mine completed the entire standard math major sequence in high school (took Math 55 her junior year), and then some, had high stats, and was accepted into MIT.
It is lucky to be in Minnesota and Ohio where have the good PSEO program structure. My son is in very similar situation but he can only register, as dual enrollment, our state university’s math course 1 week before the course open to make space for the college students.
By the way, do you study the math in classrooms with college junior/ senior or mainly with PSEO students ?
how many college math classes will you be able to take before high school graduation? planning for 3 college math courses is a LOT. Do you plan to take one course during the winter semester ?
I agree that it is better to take these college courses for the fun of learning instead for impressing the AO . The college math courses my son took won’t help or be counted into HS GPA,and his school college counselor tried to keep him at HS(elective) and told him taking college math courses will not help on college admission. However he still decided to go for his first real college math course ( Cal 3 ) at age 14. I saw how much fun/ enjoyment he had in those faster speed more rigor courses, especially when mingle together with his classmates 4-5 year older than him. No matter which colleges will value his love and efforts to math and finally admit him, he had the best use of his time and brain.
@MITPhysicsAlum “my A-s in 5615/6H (honors real analysis) probably hurt my application a lot”
my son is taking the same name course this semester “Introduction to Analysis I / read analysis” however, it is a 3XX course in our state university. why the course numbers are so different ?
It really depends on a lot of factors, likely. I know my MIT son audited several upper division physics classes at the local state univ. when he was a junior and a senior in high school. At the state uni, the first series of classes were 400A and 400B, senior level classes. When he visited Princeton Univ. in his junior year, he sat in on the same class at Princeton, and there it was a junior level class. However, there they also used additional materials besides the standard Griffith’s text used in electrodynamics.
@ sbjdorlo
thanks very much for answering my question. i saw your post before that you are a very dedicated parent who home schooled your highly gifted sons.
Other than the 3 AP courses he took at his own high school in order to stay with his friends and school peers , my son has taken most of his college math courses from our state university in hope to have a higher standard and more challenged contents than our community college. He is ultimately an idealist who chose courses only based on “ what is interested to me or what I really want to learn” and totally ignored the course number system or even suggested sequence. He told me students in every of those classes ranged from freshman to senior , and team-up/ work with them and hanging out in the college campus is so far his best experience in his math acceleration journey. He skipped a grade and in a very selective/challenging private boy school, so math is the only subject he has studied in college classroom.
During your son’s application process, which college(s) do you think were valued the most of applicants’ efforts in pursuing their interests beyond HS /in college classroom ? for some reasons that I could not figure out, he doesn’t like the competitions in math and science. He only took AMC once and qualified AIME but without any preparation and motivation to continue, so he doesn’t have the medals most of the selective colleges are valued.
Gosh, that’s a question I cannot answer. I think lots of colleges value work done beyond the HS curriculum. Certainly MIT values that, but they value many other things, as well. My MIT son did do math and physics competitions, but didn’t do much studying for them! LOL He qualified for AIME three times and Physics Olympiad three times, but never made it beyond. He was also doing other stuff, though, and I think MIT liked that. (Nationally ranked in chess, excellent baseball player and violinist, tutor and teacher, and overall, an extroverted leader-type)
I think Caltech probably likes the extra challenging courses as does Harvey Mudd. My son applied to those three STEM schools and got in. Well, he got into all his schools, and I can’t really say which schools liked what. I think all you can do is apply broadly (my son applied to 10 schools-three STEM, two Ivies, two other selective schools, and three safety) and give the schools lots of reasons to admit you (essays, scores, coursework, grades, activities, LORs, interviews, etc). 
Sorry-wanted to add: I think you need to just do what you love. My son loved all his activities, but MIT doesn’t expect everyone to be so ADHD as my kid. His fiance’ didn’t do competitions, but she did what she loved in high school, did extremely well in school, and they saw her excellence and passion. You can’t be anymore than who you are. You will find a school that will value you, be that MIT or somewhere else. Just keep bein’ you!
It wouldn’t “help” in the sense of being likely to make-or-break your application; very few (if any) things are. However, it will help you learn more math, and people who like to learn more math are often good fits for MIT.
Also – this is one reason why the math competitions aren’t “end all be all.” There are many kinds of math.
MODERATOR’S NOTE:
Since Chris posted the definitive answer, and since the original poster asked this question in May and has not been back since, I’m closing this thread.