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The idea that Common Core prevents students from taking calculus is disputed:

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.

Their Math1a uses Apostol as its textbook (http://www.math.caltech.edu/~2013-14/1term/ma001a/#text).

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.

>Their Math1a uses Apostol as its textbook.

Try Harvard's Math 55b.They hit you with Rudin freshman year.

Academic preparation Caltech says you should have [1]:

   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)

They really want you to have calculus. From the admissions FAQ [3]:

   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.

Here is Caltech's required first year math course [2]:

--------- 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...

It is also apparently helpful if you bring donuts.

What does CalTech do for students who didn't get first semester calculus? Are they basically not admitted, or is there some summer crunch course for bringing them up to speed?

(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.)

It sends them a very nice rejection letter, as Heinlein notes in his 1958 Have Space Suit---Will Travel (his juveniles were intended to teach readers what they needed to know to go out into space, from attitudes to what they needed to learn. The latter was touched upon in the first, the 1947 Rocket Ship Galileo, this book gave it a very thorough treatment in the beginning when the (genius, scientist, etc.) father of the protagonist realized how awful was the public school education he was getting).

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).)

AP Calculus has never been a standard part of the requirements for a high school diploma in any state in the union. Common Core did not change that. In fact Common Core has added to the requirements in math as it brought many states upwards to Trigonometry as a requirement.

Remember, this curriculum is not for Advanced Placement, it's for common placement. No school is prevented from offering AP courses and they have quite a few incentives to do so.

I was never particularly good at math. I also never took precalculus in high school. It was Algebra 2, Geometry, Discrete Math, and Statistics for me. I struggled a little with Calculus when I got to university, but managed to pass the class and got pretty good at it by the time I was in Multivariable Calculus. I know many people who were in the same situation. I don't think "precalculus" is requisite for learning calculus (I also never took any "prealgebra" and managed algebra just fine). I can't even imagine what a pre{calculus,algebra} course would possibly teach.

They introduce some of the fundamental concepts of the later courses (and try to tie them into previous knowledge).

In the U.S. system, they also serve as a review, I guess with the hope of shoring up knowledge that students were missing (but I think such an approach for math education is pretty optimistic; figuring out what they don't know and fixing that must be more valuable than just showing them things again).

Precalculus as I'm using it is a level of math, not a particular course (although there are of course courses with that title). In addition to what you learned in high school, assuming your Algebra II was like mine, plenty of analytic geometry, it would also include trigonometry.

To do as well as you did, you obviously picked that up on your own, as did I.

(While in theory I took a trig and further analytic geometry course in high school, followed by a semester of the calculus, the teacher flatly refused to teach anything, and trig at that level in that textbook was absolutely boring and unmotivated (e.g. didn't mention you needed it to do calculus on rotation including AC electricity); I only stayed in these automatic A courses so I'd have them on my transcript (I'd already taken my first go at the calculus in a summer course taught at a university before this, but focused most of my attention on a PDP-11/70 running UNIX(TM) Version 6, which ended up being infinitely more valuable (as it turned out, perhaps lifesaving; the introductory programming class that was my excuse for using it was easy, so I focused on UNIX(TM), Adventure and other games, wandering around the filesystem (very much like Adventure :-), software engineering, helping others debug their final class project, and using nroff for my class project which had more exposition on software engineering than code; included that in my college applications)).

Expanding on maxerickson's comment, I gather formal precalculus courses also start teaching you about limits and stuff like that; since basic differentiation, especially speed and acceleration, is relatively simple, I'd hope it would teach an intro to that, which goes along nicely with the limits. It could also be a fancy name for a (further) analytic geometry course, and/or include trig motivated by the calculus vs., oh, surveying.

Thanks for the clarification. I changed schools a few times growing up and "missed out" on some actual courses called "prealgebra" and "precalculus", which lead to my assumption.

I think what really helped me pick up different branches of math was actually getting the motivation from somewhere. My learning of Discrete Math was fueled by my interest in programming; for Calculus it was the neat applications in Physics. Calculating for calculation's sake was always pretty boring, and I'd tune out without some other kind of applicable motivation.

By the sounds of it, I'm much younger than you (having attended high school in the mid-2000s), but it's interesting that I did pretty similar stuff when I was bored in school. I wrote more than a couple of essays using groff just for the hell of it. Good times :)

You're very welcome, and indeed, back in my days, late '70s for high school, not only did we have to walk uphill both ways in snow to get there, but the computer programming course was taught in conjunction with the local college, probably the same course they used. It was punched card FORTRAN "IV" on an IBM 1130 (scare quotes because IBM's definition of FORTRAN IV was so permissive this compiler only have numeric ifs; that is, an if statement evaluated an expression and it had three lines it would goto if negative, 0 or positive).

It wasn't as bad as it might sound; sure, punched cards were a bit of a pain, and we all knew they were obsolescent (1978-9), but then again it was a chance to learn how they did things when dinosaurs roamed the earth. But the neatest thing was no computer priesthood for this class: the main computer for the school was an 370/115 (360 series: revolutionary '60s architecture using discrete silicon transistors and core memory, the 370 series used ICs including for main memory (!), the -115 model was the lowest end/slowest, but it ran BASIC fine :-), and they leased the obsolescent 1130 and just put it in a corner.

We'd put our cards in the card reader, hit go, hit the right buttons or whatever to break it out of an infinite loop if necessary, feed in a boot card if it got really confused, all under essentially no supervision, but good help, of the priesthood in the other corner of the room tending the mainframe. It also had a console, and an interactive program was one of the projects.

Lots of people older than me also cut their teeth on the 1130, Wikipedia has a partial list: https://en.wikipedia.org/wiki/IBM_1130#Influence_of_the_1130 I wonder, if only the university library had a book on LISP; instead it had lots of good books on software engineering, which along with the programming taught me the basics. Like don't mix up '0' and 'O' in your variable names, especially if the first cut of the card deck is being produced by students learning how to do date entry from a coding form you filled out (http://www.atkielski.com/PDF/data/fortran.pdf).

Whereas the DEC PDP-11/70 running UNIX(TM) I used was at a big university's summer school following that. And fortunately not at all loaded down then, and it was a very fast system, even had a fixed head disk for swapping. So in my case I was semi-bored with the introductory programming course (at the end the professor privately but nicely called me out for being a ringer), and wrote up the final project using nroff and a XEROX Daisywheel to counter that. Just because even primitive word processing that was extremely neat, and a lot better than typing out a paper in the previous summer on a Selectric typewriter with auto-erase, the best there was at the time.

Interesting story. I always enjoy reading about the history of our field :)

P.S. I contend that {n,t,g}roff is still a lot better than typing out a paper in MS Word, though I mostly stick to LaTeX for that sort of stuff nowadays.

Article only mentions that learning to teach the common core addition/division/multiplication/subtraction is as difficult as 'learning' calculus.

I'm sure that the current common core level for math ends around Trigonometry.

You might, like I did, check out the online sources on this, from reports on a professor who was one of the drafters admitting it, to the official curriculum. It's enlightening.