<p>Harvard, Princeton, MIT, UChicago, and Caltech (Harvard Math 25 and 55, Princeton Math 214-215-217-218, etc.) are the only schools that seem to offer advanced courses or placement options for students with significant exposure to rigorous proof-based courses while in high school. With so many students nearly learning all the material usually covered in the core curriculum for undergraduate mathematics majors through advanced coursework, research and independent study, why do so few schools allow students offer courses for these students when admission top schools as a math or physics focused student demands mastery of material far beyond what is taught in honors versions of introductory mathematics courses?</p>
<p>Michigan-Ann Arbor has a pretty intense intro to Theoretical Mathematics (sequence 295-296).</p>
<p>Oh! I forgot about Michigan. The sort of course I was thinking of is more like 395-396, which open to both first-year students and sophomores. </p>
<p>UMich – Ann Arbor and the other schools are schools known for attracting strong math students, but there are capable students everywhere. Why not cater to them?</p>
<p>How many students have significant exposure to proof based math courses in high school?</p>
<p>Almost all of them going to Top 25 schools to study mathematics, no?</p>
<p>I think you seriously overestimate the number of students who’ve taken such courses even if they intend to study math. Also, if they’re that advanced, they typically move onto grad work at a larger university.</p>
<p>Some magnet schools offer courses in real and complex analysis right on site.</p>
<p>The work is requisite for admission as a math student at a top school, anyway.</p>
<p>As whenwhen said, I think you’re seriously overestimating the level of math people are coming into college with. Most high schools don’t even offer such courses. My high school only went up to Calculus, and didn’t really go beyond the rough equivalent of Calc II. Bear in mind also that high school calculus is frequently a dumbed down version of Calculus that doesn’t even really prepare students for college level math.</p>
<p>Rigorous proof based courses? Not at the high school I went to. I never even took Calculus in high school, and I’m now a physics/math double major.</p>
<p>I’m a high school senior and right now I want to be a math major (and I know this will probably change because I don’t, y’know, know any math).
My high school doesn’t even have AP Calculus AB, and I’ve had to go out of my way just to take linear algebra, differential equations, etc. (which aren’t proof-based as far as I can tell) in high school. Even doing this is pretty rare unless you go to a really fancy high school, which most people don’t.
I won’t be going to a top school (my ECs suck and I have no money), but the level of math I’ve reached is decidedly not the bad part of my resume.</p>
<p>I’m not sure I understand your question. If students have mastered the lower division material because of advanced coursework when they were in high school, could they not move onto the more advanced subjects in college? Are you asking why don’t more schools offer honors versions of introductory math courses for math majors who are well prepared for them or are you suggesting that the “honors” courses at these particular colleges are more rigorous than another school’s “honors” course (in which case, how would you even know that, unless you’ve taken these courses)?</p>
<p>I’d say Duke is another heavy-weight in math. It’s graduates have been well-represented in the William Lowell Putnam mathematics competition in the past.</p>
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<p>This assertion is baseless and false.</p>
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<p>Honors math courses are available at many schools which are more selective than the average school (i.e. where there is likely a “market” for honors math courses):</p>
<p>Berkeley: H prefix in course number: [Honors</a> Courses | Department of Mathematics at University of California Berkeley](<a href=“http://math.berkeley.edu/courses/choosing/honors-courses]Honors”>http://math.berkeley.edu/courses/choosing/honors-courses) and [Course</a> Catalog Descriptions | Department of Mathematics at University of California Berkeley](<a href=“http://math.berkeley.edu/courses/choosing/course-descriptions]Course”>http://math.berkeley.edu/courses/choosing/course-descriptions)
Harvey Mudd: “frosh calculus” (30B/30G) would be an honors course at other schools: [Program:</a> Placement for Core Mathematics Classes](<a href=“http://www.math.hmc.edu/program/placement/]Program:”>http://www.math.hmc.edu/program/placement/)
Ohio State: H suffix in course number: [Courses</a> | Department of Mathematics](<a href=“http://www.math.osu.edu/courses]Courses”>http://www.math.osu.edu/courses)
Rutgers: Math 192, 291, 292: [Mathematics</a> Department - Mathematics Undergraduate Courses](<a href=“http://www.math.rutgers.edu/courses/ug_courses.html]Mathematics”>http://www.math.rutgers.edu/courses/ug_courses.html)
Stanford: H suffix in course number: [Stanford</a> University Explore Courses](<a href=“Stanford University Explore Courses”>Stanford University Explore Courses),
Texas: H suffix in course number: [Course</a> Descriptions](<a href=“http://www.ma.utexas.edu/academics/courses/descriptions/]Course”>http://www.ma.utexas.edu/academics/courses/descriptions/)</p>
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<p>Not necessarily. It is likely that many have just completed normal versions of calculus (usually a high school AP course) and possibly sophomore math (at a local college, not necessarily an honors or proof-heavy version of the course, particularly if the local college is a community college or a less selective four year school). The super-prodigies who have taken courses like real analysis while still in high school are rare even among math majors.</p>
<p>baktrax, the OP i not asking why there aren’t rigorous Mathematics courses, he is asking why aren’t there rigorous introductory sequences. Those sequences help undergrads establish a foundation in Mathematics in a cohesive and comprehensive way.</p>
<p>I’m in a community college, and I’m currently taking an honors section of calculus. We’re writing a lot of proofs, and the course so far has been very rigorous. There are plenty of schools that have honors sections of introductory calculus.</p>
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<p>Don’t many schools offer honors introductory sequences (for courses like linear algebra, vector calculus, etc) besides the schools that the OP listed? Or does the OP not consider these courses “rigorous” enough?</p>
<p>Many schools offer honors sections of these courses. As I posted above, my community college even offers honors sections of them.</p>
<p>Are they going to be as rigorous as some of the infamous honors sections at the highly selective schools like Harvard, Stanford, or UChicago? No, but these schools are highly selective for a reason, and the majority of students wouldn’t even be able to handle these classes anyway.</p>
<p>There is no real need for a rigorous introductory sequence because most math departments administer their own placement exams, and students skip straight ahead into higher level coursework.</p>
<p>Northwestern has a 2-yr sequence for freshmen/sophomores with a passion for math.
[MENU</a> Program: Math Department, WCAS, Northwestern University](<a href=“http://www.math.northwestern.edu/undergraduate/menu/index.html]MENU”>Mathematical Experience for Northwestern Undergraduates (MENU): Department of Mathematics - Northwestern University)</p>