http://www.mindingthecampus.com/originals/2014/04/a_sorry_at...
Further, a citation to Caltech's admission policy would be handy; I found sources directly disputing your claim (also in the context of Common Core), citing Caltech Math1a to rebut it.
This is the classic proofs based text, in other schools what's commonly used for "honors calculus", including MIT but not with such a name. I suppose in theory a really mathematically adept student could start with it, but that's not what I remember any school I've looked into, including CalTech, requiring before you start it.
The link you cited is just an attack on a particular contention; it's entirely unrelated to my examination of it, except second hand reports of it (some of the phases quoted are familiar) probably in part prompted mine.
Try Harvard's Math 55b.They hit you with Rudin freshman year.
4 years of math (including calculus)
1 year of physics
1 year of chemistry
3 years of English (4 years recommended)
1 year of U.S. history/government (waived for international students)
What if my high school does not offer Advanced
Placement (AP) or International Baccalaureate (IB)
courses?
Many schools don't offer the AP or IB curricula.
Regardless of the curriculum your school offers, we
expect that you will have challenged yourself with
demanding courses. The Caltech curriculum will require
that you have completed rigorous courses in calculus and
in physics. If these courses are not available in your
high school, we strongly encourage you to take them at a
local college or online.
--------- BEGIN QUOTE -----------
Ma 1 abc. Calculus of One and Several Variables and Linear Algebra. 9 units (4-0-5); first, second, third terms. Prerequisites: high-school algebra, trigonometry, and calculus. Special section of Ma 1 a, 12 units (5-0-7). Review of calculus. Complex numbers, Taylor polynomials, infinite series. Comprehensive presentation of linear algebra. Derivatives of vector functions, multiple integrals, line and path integrals, theorems of Green and Stokes. Ma 1 b, c is divided into two tracks: analytic and practical. Students will be given information helping them to choose a track at the end of the fall term. There will be a special section or sections of Ma 1 a for those students who, because of their background, require more calculus than is provided in the regular Ma 1 a sequence. These students will not learn series in Ma 1 a and will be required to take Ma 1 d. Instructors: Marx, Katz, Mantovan, Aschbacher, Ni, Kechris.
Ma 1 d. Series. 5 units (2-0-3); second term only. Prerequisite: special section of Ma 1 a. This is a course intended for those students in the special calculus-intensive sections of Ma 1 a who did not have complex numbers, Taylor polynomials, and infinite series during Ma 1 a. It may not be taken by students who have passed the regular Ma 1 a. Instructor: Staff.
---------- END QUOTE ----------
Note: don't freak out over the unit numbers. Caltech's unit scale is different from that of most other schools. 1 unit corresponds to 1 hour of work per week, so a 9 unit course is one that should take 9 hours a week. The numbers in parentheses, such as (4-0-5) break it down by number of hours of lecture, number of hours of lab, and number of hours of outside preparation and homework.
Ma1 does start with a "review of calculus", so you could probably do it without having had calculus in high school if you were really good, but it would be rough.
[1] http://www.admissions.caltech.edu/applying/freshman
[2] http://catalog.caltech.edu/courses/listing/ma.html
[3] http://admissions.caltech.edu/uploads/File/general/FAQapplyi...
(Most, but not all, MIT students enter with their first semester under their belts and part of the second, so the second semester calc class offered to first semester freshman is traditionally a wild monkey cage of chaos and freshmen held inside a giant lecture hall. This may have changed in recent years with on-line courses -- this would definitely be the perfect class to kill the lecture. But the first-semester calc is still offered in various difficulty levels for the first semester.)
(Oh, and MIT uses the same freaky unit numbering.)
And as I can attest, there's this nice bit about how they have many fewer spaces than qualified applicants, not going into the minor detail of if you were one of the latter (I wasn't).
CalTech is very special, even more so than MIT I gather (I'm Class of '83 of the latter). Much smaller, 1/4 the class size (~250 vs. 1100), much more intense, much more science focused. Someone, commenting on how they'll clean up your room every week (a service MIT is sadly lacking in :-), said it was like a Hogwarts for science, and very simply, if you can't do magic at its level, they don't accept you.
For some historical perspective, as I understand it, at the post-Civil War beginning of MIT, most students were mastering the calculus by the end of their undergraduate program.
(And our "freaky" unit numbering is great, totally transparent, and at least at MIT there's a committee dedicated to the task of keeping professors and departments in line with the Institute's limits on work demanded, and has been known to take classes away from abusive professors. That's also done at the departmental level, as I witnessed one semester while on the EECS department's staff (took over and finished the sysadmin part of the job of moving it from Multics to UNIX(TM), with the help of one on and off student like me who was an old friend).)