How Do College Math Placement Tests Work for Advanced Students?

[Battousii]

How exactly do placement tests work for most colleges? Do you say "I want to take so-and-so upper math class", and they'll give you a specific test for that class to make sure you have knowledge of the prerequisites? Ex. If you want to place into a graduate-level analysis class, will they test your analysis skills? Or is there a general test for everyone? Let's say you're homeschooled and you've taken some of the classes from your local university, and some of them by yourself (using online notes, books, problem sets, exams, video lectures, etc.,)?

What happens if you have studied mathematics at the rigorous undergraduate level before you leave high school? Let's also say that you're aware that what you study by yourself often is not as rigorous as what you would find in a university, and so you have consequently been very diligent in your studying, following online curricula strictly and using several books and sources to expand your knowledge so that you minimize your misconceptions about mathematics and don't learn it wrong? If you have already studied all of the degree requirements for a B.S. in math? Do you place into graduate classes, assuming you do well on the test? Do these graduate classes count towards your B.S. or a graduate degree? What happens when you get to grad school, then?

Just a hypothetical situation.

 

[bravernix]

Placement tests are generally only for the basic classes. For example, you might be able to place into the first Calculus class..something like that. Of course this various at each school, but you can't just "place" yourself out of an undergraduate degree.

 

[Battousii]

Okay, how about this:

The Academic Enrichment Opportunities (AEO) program at NC State University provides high school students the opportunity to take college level courses (subject to the conditions outlined below). If you plan to pursue a Bachelor’s degree at NC State, the courses you take can apply toward your degree requirements. If you attend college elsewhere, credits earned with a grade of “C” or better are generally transferable.

If the person wants to attend NC State and s/he takes many of the required classes for the B.S. math degree through this program, what happens? What if you start out at NC State at grad level? Do these graduate classes count towards your B.S. or a graduate degree? Should the person contact the school?

 

[bravernix]

Okay, how about this:



If the person wants to attend NC State and s/he takes many of the required classes for the B.S. math degree through this program, what happens? What if you start out at NC State at grad level? Do these graduate classes count towards your B.S. or a graduate degree? Should the person contact the school?

So all throughout high school you are going to attend college full time as well? Think about it. Also, I am sure contacting the school will answer many of your questions.

 

[Battousii]

Oh, right. There are other classes you have to take besides math to get the degree. I think they are a few classes in the natural sciences, and your normal core.

So all throughout high school you are going to attend college full time as well?

Well, he's homeschooled, so it is possible to take many college classes in a day. I think I'm talking about just the math portion of the degree -- if you finish all of the math required for the degree before you enter college (I am assuming these are all of the undergraduate classes), then I suppose you'll be taking graduate classes that count towards the same degree (because you also have to finish your other requirements)?

 

[jtbell]

This is such an unusual situation that you really need to talk to the math department and the admissions office at the university (or universities) that you're considering. All we can do here is speculate. I've never seen a situation like this myself, but then again, my school isn't very big and we probably don't attract that level of student.

 

[Battousii]

Thank you for your advice. He'll contact the university, but if you have any more advice, please post.

 

[mr_coffee]

When I was going to transfer to NC State I wanted to test out of 3 of their programming courses, the dean of the engineering wouldn't let me. She wouldn't give me a reason, she just said, that's not going to happen.

She was like, the best way to show you know the knowledge is to take the course and get a grade. I was quite pissed that she wouldn't allow me to test out of all of them.

 

[Battousii]

Fish. Limitation is the worst thing you can do to a man.

What if you take them through AEO? The classes he is studying are officially the classes he is taking through the homeschool.

 

[mr_coffee]

lol did you just call me a fish?

Anywho,

I didn't want to put up with that, and they gave me issues with other credits transferring so I said screw them so I'm not transferring to NC State.

It worked out better in the end, now I can graduate sooner and pay less money for tuition (becuase I would have been considered out of state which is like 8k, instate is only 2k a semester.

 

[Battousii]

"Fish" is an expression of surprise. Glad to see that it worked out well for you. If NC State gives him similar issues, then I suppose he'll have to look at other schools. Hopefully the AEO credits will be transferable to most other colleges.

 

[mr_coffee]

Oh hah, I never heard of that.

The math department might not be as strict, I remember the majority of my maths transferred fine, even discrete math/Diff EQ.

Goodluck.

 

[PowerIso]

Odds are even if you feel your student has worked hard and is at the ability to be at the graduate level, it'll take time to prove it. Even so, the odds are high that he may have some very big gaps and will need to take some undergraduate courses to fill in the gaps. However, I know at my university, they do allow you a chance to place out of a class, but you'll have to face a committee and answer their questions with only a white board behind you. It gets pretty tough, but it's possible.

 

[Battousii]

Odds are even if you feel your student has worked hard and is at the ability to be at the graduate level, it'll take time to prove it. Even so, the odds are high that he may have some very big gaps and will need to take some undergraduate courses to fill in the gaps.

Indeed. However, he has 3 years time before he enters university to fill in most of those gaps. Hopefully that will be enough time, given the pace he at which he is currently working.

However, I know at my university, they do allow you a chance to place out of a class, but you'll have to face a committee and answer their questions with only a white board behind you. It gets pretty tough, but it's possible.

Committees are scary. Hell, white boards are scary.

 

[JoeTrumpet]

Every school definitely does this differently. As I'm applying to colleges right now I've read a decent amount, and I've looked mainly at math placement due to my independent study of calculus beyond AB. One lenient example is from the Brown Math Department's site:

"If you didn't take an AP exam, or if you don't think that your score on the AP exam is a good indication of your calculus knowledge, take the Brown Calculus Placement Exam. Your grade on this exam will allow us to provide you with a nonbinding recommendation of the best math course. Second, if you have any questions, come to the Brown Math Department Open House during Orientation. There will faculty members available to talk to you and to answer your questions."

"# I have already taken a linear algebra course. What course should I take next?
If you took a full semester college-level linear algebra course...[and] if you also took a multivariable calculus course, then you may be prepared to begin with our 100-level math courses. Good 100-level math courses with which to begin include Math 101 (analysis), Math 106 (differential geometry) Math 126 (complex analysis), Math 153 (algebra), and Math 161 (probability)."

Other schools, like the aforementioned NC State, are much less happy with skipping. Every school I've seen offers a math placement exam, and from what I can tell the top-tier schools make this test useful for placement till about linear algebra. I'm not sure if they go further than that or if other schools don't tend to be as nice and extensive about it. Sometimes these tests can be very unforgiving; for example, at my girlfriend's university if you miss one question out of 20 for trig material they force you to take college trig.

I'm sure if you talk to the head of the department, especially at more intimate schools, a solution wouldn't be too difficult to work out. Some schools, such as University of Chicago, allow placement into graduate courses for undergrads, and it's often encouraged.

 

[Battousii]

Thank you very much for your advice, Joe!

He loves the University of Chicago -- in fact, it is one of his top choices, if not #1. His dream is Honors Analysis there, which I believe is for freshmen. Also, I think NC State requires a GED, so it may not be an option for him at all (Chicago does not).

 

[JoeTrumpet]

I'm pleased to be of help! University of Chicago is actually my #1 school as well, and I'm pretty sure they depend pretty strongly on the placement exam. The highest course I've seen them offer through the placement exam is actually honors analysis:

http://math.uchicago.edu/undergrad/

"Math 20700-20800-20900. This is a highly theoretical sequence in analysis, which is reserved for the most able students. Admission is by invitation only. Students who wish to enter this sequence must earn high grades (A's and A-'s) in Mathematics 16100-16200-16300, and receive a strong recommendation from the instructor in these courses. Admission may also be gained by exceptional performance on the Calculus Placement Test. This sequence covers the real number system, metric spaces, basic functional analysis, the Lebesgue integral, and other topics."

(16100-16200-16300 is the honors calculus sequence.)

From what I've learned of Chicago through my discussion with alumni, it sounds like if you can show them that you truly already know that and have the professor's consent, you can begin in whatever level you'd like. My interviewer (who studied economics) put it this way: "pretty much the main restriction I know of is undergrads can't take surgery classes, but other than that it's mostly fair game." Of course, perhaps things have changed, but at least honors analysis is definitely a strong possibility.

Edit: By the way, mathematics placement at UC counts for both placement and credit.

http://collegeadmissions.uchicago.edu/level3.asp?id=349

 

[Battousii]

Edit: By the way, mathematics placement at UC counts for both placement and credit.

http://collegeadmissions.uchicago.edu/level3.asp?id=349]

Excellent! I suppose that if you passed out of many of the other math classes, you could theoretically start off near grad level?

 

[Feldoh]

I think that honestly if you're taking highly advanced math and a younger age then odds are that somewhere along the line there are holes in your education. For instance, at my high school they offer PSEO for those who took Calculus BC their sophomore/junior year when you can go and take Calc III at a near-by university if you passed with a 5 on the AP test. I'm currently doing this along with some others and I can say that there are some holes in my knowledge because I paced it too fast then I could handle, now I'm doing fine but I mean something are harder to gain a deep understanding in since I didn't take these classes at the normal high school pace. Basically what I'm saying is that you might be the same -- it might be wise to start in some classes you've all ready taken, that why you will fully understand everything. Does that make sense?

 

[JoeTrumpet]

Unfortunately, I've seen no mention on the website about beginning in math courses beyond honors analysis. This is definitely a step closer to grad courses, though. From what I've seen of the mathematics catalog, UC seems to offer no shortage of undergraduate courses to take:

( From Opportunities in Mathematics http://collegeadmissions.uchicago.edu/pdfs/math.pdf )

"The department offers an honors curriculum for the most advanced students that often includes one or more graduate sequences."

Also it talks about how it's one of the largest mathematical departments (and if you check the course catalog http://collegecatalog.uchicago.edu/pdf_08/MATH.pdf there really is a bunch to take, even some your friend might not have covered), rated 5 nationally in terms of faculty and quality of teaching, etc etc etc.

 

[Battousii]

I think that honestly if you're taking highly advanced math and a younger age then odds are that somewhere along the line there are holes in your education. For instance, at my high school they offer PSEO for those who took Calculus BC their sophomore/junior year when you can go and take Calc III at a near-by university if you passed with a 5 on the AP test. I'm currently doing this along with some others and I can say that there are some holes in my knowledge because I paced it too fast then I could handle, now I'm doing fine but I mean something are harder to gain a deep understanding in since I didn't take these classes at the normal high school pace. Basically what I'm saying is that you might be the same -- it might be wise to start in some classes you've all ready taken, that why you will fully understand everything. Does that make sense?

Yes, that does make sense, and your words are very true. Thank you very much for your advice.

Joe - Indeed, Chicago is among the best for mathematics. The B.S./M.S. Joint Degree program looks very interesting.

 

[Gib Z]

I think that honestly if you're taking highly advanced math and a younger age then odds are that somewhere along the line there are holes in your education. For instance, at my high school they offer PSEO for those who took Calculus BC their sophomore/junior year when you can go and take Calc III at a near-by university if you passed with a 5 on the AP test. I'm currently doing this along with some others and I can say that there are some holes in my knowledge because I paced it too fast then I could handle, now I'm doing fine but I mean something are harder to gain a deep understanding in since I didn't take these classes at the normal high school pace. Basically what I'm saying is that you might be the same -- it might be wise to start in some classes you've all ready taken, that why you will fully understand everything. Does that make sense?

Seconded, very much the same case here. I admit it does get somewhat boring learning the same things over and over again at regular school classes (it seems you are home schooled so never mind about that), however I still find I learn something new every time I relearn it. It's exactly why I'm going through Courant again, even though it takes a huge amount of time. Every time I do it again I learn a bit less, but I still do learn, and more often then not, It's the harder stuff I pick up. My advice is don't go too fast, take your time. Maths isn't a race, and it isn't for money or for acclaim, Do maths for the pure love of the subject and you'll still think Euclid's Elements is one of the best things ever written.