advice on calculus sequence

[marite]

<p>Unless I read the below wrong, it looks like MIT is more generous than Harvard in awarding transfer CREDIT. It is not automatic, of course, but a grade of B- should not be hard to achieve.

Credit for a Subject Already Taken
Transfer credit for a specific MIT mathematics subject is awarded for work done at another college if the grade earned is a B- or better and if the subject is substantially equivalent to the corresponding MIT subject.</p>

<p>Transfer credit for incoming freshmen is coordinated by the Office of Undergraduate Advising and Academic Programming.</p>

<p>Instructions to Students Seeking Transfer Credit:
Download the Request for Additional Credit Form or pick up a copy in Rooms 2-108, 5-119, 7-104, or 11-120. Fill it out and deliver it to the appropriate Transfer Credit Examiner along with:</p>

<p>A copy of the syllabus for the course from the term in which it was taken.
The author, title, and edition of the textbook used, and the sections of it covered by the book. (You may be asked for a photocopy of the table of contents as well.)
The Transfer Credit Examiner may ask you to demonstrate your understanding of the subject and will then approve or deny your request.
If approved, you must deliver the completed form to the Registrar’s Office, Room 5-119.
Meanwhile, arrange for an official transcript to be sent directly from the school at which the course was taken to the MIT Office of the Registrar, 5-119.
When the “Request for Additional Credit” form and your transcript meet in the Registrar’s Office, the credit will be processed.</p>

<p>The grade that appears on your MIT transcript will be an “S” (for satisfactory) and is not included in your grade point average. In all other aspects, the subject for which you get transfer credit is treated as it would be if you took it at MIT. For example, transfer credit for 18.06 would confer 12 units of credit and, for non-math majors, be counted toward the REST requirement.</p>

<p>The Mathematics Department does not require a further exam for you to receive credit for a subject for which transfer credit has been approved.</p>

<p>Advance Approval for a Subject
To receive advance approval for a subject not yet taken, submit the above information as far in advance of taking the course as is possible.</p>

<p>Transfer Credit Examiners
For 18.01, 18.02, 18.03, and 18.06: Alejandro Morales</p>

<p>For probability/statistics: Professor Richard Dudley</p>

<p>For all other math subjects: Professor Victor Guillemin

[MIT</a> Mathematics | Advanced Placement](<a href=“http://www-math.mit.edu/academics/undergrad/first/transfer.html]MIT”>http://www-math.mit.edu/academics/undergrad/first/transfer.html)</p>

[siserune]

<p><a href=“marite:”>quote</a></p>

<p>Like POIH, you confuse credit and placement.

[/quote]
</p>

<p>A simple question will clarify what (and who) is being confused here:</p>

<p>What functional difference are you claiming exists between the path to credit and the path to placement (that is, exemption) at institutions where there is an enforced requirement to pass classes in those subjects? </p>

<p>POIH asked you this (post #39), I raised it again (#58), and you have not answered with more than the words “you have totally lost me”.</p>

<p>The source of your confusion is apparently the presumption that either (a) Harvard or (b) your son’s experience, are in any way relevant. They aren’t, as POIH has pointed out. Harvard in general and its math department in particular don’t have meaningful notions of “placement”, because they don’t have firm requirements that would force enrollment in, for example, multivariable calculus or linear algebra, even for students who never took such classes and did not study the material in high school. Your son didn’t escape any requirements because essentially there are no requirements. It’s no crime for you to be somewhat ignorant of how Harvard operates but it is much more obnoxious to take personal lack of understanding and cite it as confusion and reading failure in others who do understand. </p>

<p>

Taking the class at Harvard Extension (which is how nearly all the local high school students would “take it at Harvard”) has no bearing on exemption from MIT’s 18.02 first-year requirement, unless MIT deems such Extension classes worthy of transfer credit. Harvard College itself does not give credit for the Harvard Extension School classes, and MIT’s multivariable calculus class is more rigorous than any of the Harvard equivalents, so transfer is hardly a given. That is also true for differential equations and linear algebra.

</p>

<p>My S did not get any CREDIT for the classes he took at Harvard, starting with MV-Calc and LA. He did get PLACED into more advanced math classes.

</p>

<p>He did not get PLACED based on any specific class. That’s your confusion. He could have taken the post-multivariable calculus math classes at will without having taken any previous class or examination. Harvard gives a wide latitude and for the precocious mathematicians there is no such thing as being forced to take a less advanced class due to lack of placement. This is different from the situation at MIT and Caltech where hard requirements exist in a range of subjects.</p>

<p>

A friend of his audited Math 25 as a high school senior. He was not asked to repeat Math 25 or go into Math 55. He did not get credit for any of the courses he had taken at Harvard before, but he certainly got placed into courses based on his record. He began taking graduate classes as a freshman.

</p>

<p>He didn’t get “placed”. That is your confusion. Placement is advisory only. </p>

<p>The friend’s story shows that Harvard will let incoming math studs do whatever they like within wide and informal limits. It does not show any bypassing of requirements, because there were no requirements. At Harvard, for students who will take further classes in those subjects, there is no difference between placement and credit for prior classes because neither concept exists.</p>

[marite]

<h1>23

@marite

Why could he not take this (MV-Calc) earlier?

</h1>

<h1>30

@POIH

I never said he couldn’t take it earlier. What I said it will be advantageous to take it in 12th grade as the college math will start from some calculus and most like either Multivariate or Calculus II/III where ever the child is placed based on their AP scores.

</h1>

<h1>35

@POIH

MIT doesn’t allow any college credit.

</h1>

<p>I have never been interested in college credit and said so.
Now, it looks as if MIT does allow transfer credit. Am I to believe that a student who receives credit for work equivalent to 18.02 and even above cannot place into a more advanced math class at MIT?</p>

[CountingDown]

<p>marite, I don’t recall how it works for math at MIT, but I do know that even IOI (CS Olympiad) medalists have to take the freshman CS course at MIT. The rationale is that it is mostly robotics and not many folks have had exposure to the kind of equipment they use. S did not find the argument compelling, but then again, he’s not an engineering kind of guy.</p>

<p>S1’s experience at UChicago was that the calc placement test offered guidance, he then talked to the departmental advisors about his background, and he sat in on several courses the first week of fall quarter. Ultimately picked IBL Analysis over Honors Analysis (he liked the approach better and they covered pretty much everything HA did) and did beautifully. Ditto comp sci. He did not get credit for Lin Alg, DiffEq, MV, etc., but he did not care. (Lin Alg at Chicago tends to get covered as part of 150s/160s Calc anyway.) He gets to replace the intro required sequences with higher-level math electives, including grad courses.</p>

<p>Same thing happened with CS – talked to the department advisor and a couple of profs and got carte blanche to take what he wanted.</p>

[marite]

<p>CountingDown:
Harvard administers a math placement test to everyone, but, as far as I remember, it only covers through calculus. For anything above the Multivariable Calculus sequence, students are expected to discuss with the DUS and shop. Math 55 invariably starts with several dozens students, most of whom drop down to Math 25 after one week or three; many Math 25 students drop down to Math 23, and so on down to Math 21 which is the standard Multivariable Calculus course.
S did not get credit for the several classes he either audited or took, but he did not care, either. Like your son, mine also placed into higher-level math classes, and was able to take grad courses.
MIT does seem to grant transfer credit for some math courses; I have to assume that this allows students to place into higher-level math classes as well, which is what I was trying to argue with POIH. I had not checked the MIT transfer credit policy before posting; I should have. However, I remember that there were quite a few high school juniors who were taking MV-Calc the same year my S did, and some of them ended up at MIT. I don’t recall their telling my S that they had had to re-take MV-Calc. S had had MIT at the top of his list because of them, until he realized he was not an engineering kind of guy.</p>

<p>On another note, I had been keen on Chicago because of the Core. But S less enthusiastic than I and he was concerned that it might interfere with his taking grad courses, entirely because of scheduling. It sounds like your S managed to find his away around that issue; or perhaps, it was a non-issue. Oh well, I think that one way or another, my S took fairly similar courses to the Chicago Core.</p>

[ParentOfIvyHope]

<p>marite: #61
You forgot to include the headline of the page

Studies completed at a recognized college or university with college/university instructors will be evaluated for credit in the same manner as studies completed by transfer students.

</p>

<p>Which means that you need to take a regular undergraduate standing course at an equivalent university and not taking a extension class at Harvard or EPGY class at Stanford.</p>

[marite]

<p>POIH:
I did not include the headline because your post #35 was quite categorical on the topic of transfer credit. </p>

<p>My S took classes for credit at HES that also counted for credit for Harvard College–which I assume is considered an equivalent university. There were not many of these, to be sure, but the prof scheduled the classes in such a way that it was possible for HES students to take the class together with College students. With the policy negotiated by the former superintendent, I believe that Cambridge students can now take College (as opposed to evening HES) classes during regular high school hours.<br>
Still, my post had to do with being allowed to take higher level math classes, not with transfer credit. It looks like MIT allows both CREDIT AND HIGHER PLACEMENT.</p>

[siserune]

<p><a href=“marite:”>quote</a></p>

<p>Harvard administers a math placement test to everyone, but, as far as I remember, it only covers through calculus.

[/quote]
</p>

<p>Harvard does not “administer a math placement test to everyone”.</p>

<p>Harvard does not require any placement test for taking courses beyond multivariable calculus.</p>

<p>Harvard does not require its math majors to take multivariable calculus. </p>

<p>Harvard has no such concept as “being placed out of multivariable calculus” by learning the subject in high school. You can “place out of multivariable calculus” without ever having learned any multivariable calculus. Your son did not “place out” of multivariable calculus because no such concept exists at Harvard. Do you understand it now?</p>

<p>

Like your son, mine also placed into higher-level math classes, and was able to take grad courses.

</p>

<p>Your son did not “place” into or out of anything. There is no course he could have been forced to take, and no course he would not have been allowed to take, if in high school he had just studied whatever mathematical subjects he wanted subsequent to AP calculus (or trained for math competitions, done research, etc), without enrolling in a single class. It wouldn’t have mattered one bit whether his high school mathematical activities included multivariable calculus. The Extension School classes, in particular, are completely irrelevant to “placing out”, because there is no such thing.</p>

[siserune]

<p>

My S took classes for credit at HES that also counted for credit for Harvard College–which I assume is considered an equivalent university.

</p>

<p>There is no such thing. Your son took regular Harvard (FAS, daytime) classes that were cross-listed in the Extension School catalog. There is an adjunct instructor in the Harvard math department who makes a point of opening his classes to Extension students, and those classes are generally in subjects outside the main math-major theoretical track. </p>

<p>Classes at the Harvard Extension School proper (such as multivariable calculus, math E-21 rather than Math 21) would not be counted for credit at Harvard even if taken by full time students already matriculated at Harvard College or the FAS.</p>

[marite]

<p>Siserune:</p>

<p>Allow me to know exactly what happened with my son. He, like all Harvard freshmen, had to take the math placement exam, together with Expository Writing. Below is an excerpt from a document dated 3/13/2010:

Harvard College Placement Exams: Frequently Asked Questions </p>

<p>Should I study for the placement exam?
No. Placement exams are diagnostic and do not appear on a student’s transcript. Students are not expected to study for these tests. </p>

<p>Where and when do I receive my placement score(s)?
Freshman scores will be posted on the Advising Network Portal on Thursday August 27th. All other students should contact the relevant department beginning Friday, August 28th. Departmental contact information is listed at: [Advising</a> Programs: Concentrations](<a href=“http://www.fas.harvard.edu/~advising/listofprograms.html]Advising”>http://www.fas.harvard.edu/~advising/listofprograms.html). Students should discuss their placement scores and correct placement with their academic advisers.</p>

<p>Which placement exams are mandatory?
Expository Writing and Mathematics placement exams are mandatory. No advanced sign-up is necessary.</p>

<p>How do I decide which placement exams I should take?
 All incoming students must take the Expository Writing and Mathematics placement exams.
 Students interested in the Sciences should take the Chemistry placement exam.
 If you plan to take an advanced Physics course, you must take the Physics placement exam.
 If you are planning on pursuing a language at any time at Harvard, or hope to place out of the first-year language requirement, take a placement exam in any language with which you have prior experience.
 You should take the Music placement exam if Music is a concentration of interest for you.</p>

<p>Which placement exams require registration?
For exams administered by the Registrar’s Office (Physics, Spanish, French, German, Latin, Italian, Expository Writing, Mathematics), registration is not required.

</p>

<p>He “placed” into a class that was more advanced than Math 21 and which, on the website, is not described as requiring a math placement exam.
From the Math Department website;

You should take this class if one or more of these describes you:
The last math class you took was BC calculus, and you got a 4 or 5 on the AP exam and the** Harvard Math Placement** exam placed you in Math 21.
You liked the way that high school calculus was taught.
You are interested in chemistry, physics, or applied sciences and need to learn math that applies directly to other disciplines.
You like to see how math applies to real life, or else you don’t see a point in learning it.

I understand that students are not pieces of china that get scrutinized and then put down at the appropriate places on the table. When I said that my S “placed” into a more advanced class than MV-Calc, I do not mean that he was put there. There is an advising session where students can learn more about the differences between the various flavors of freshman math. They are then free to shop whichever class takes their fancy (hence the degringolade from Math 55 on down in the first three weeks). By virtue of all the math classes he had taken or audited, my S was able to take a more advanced freshman math class than Math 21 (Multivariable Calculus and Linear Algebra).

My S took classes for credit at HES that also counted for credit for Harvard College–which I assume is considered an equivalent university.

I phrased this badly. The courses my S took count for credit both toward the degree and toward the major if taken by College students. My S received HES credit for these classes while College students received credit either for the major if they were math majors or as electives if they were not. In other words, he did not audit the courses, as he did regular College classes for which he did exactly the same things as College students, including midterms and finals. As I have said repeatedly, Harvard does not grant credit for courses taken at Harvard while in high school.

There is an adjunct instructor in the Harvard math department who makes a point of opening his classes to Extension students, and those classes are generally in subjects outside the main math-major theoretical track.

One of the classes he took is a standard way for math majors to fulfill the math requirements. Having taken it before matriculating, my S took a different, higher-level one in the same sub-field.<br>

Classes at the Harvard Extension School proper (such as multivariable calculus, math E-21 rather than Math 21) would not be counted for credit at Harvard even if taken by full time students already matriculated at Harvard College or the FAS.

Yes, I know so, and have said so.
As I have said repeatedly, I never cared about credits. I was not the one who introduced the subject, and wished only, then and now, to discuss a student’s ability to take more advanced classes.
To get back to the point of this thread, it seems that MIT, through its transfer credit policy, allows math-capable students to skip the freshman level multivariable calculus sequence; so does Harvard; so does Chicago (see Counting Down). While I know that many students re-take Calculus in college even though they scored a 5 on the BC-Calculus exam, it needs not be the case for every student. The OP’s son is on track to take Multivariable calculus in 12th grade. If he does take it, he may or may not wish to re-take it in college. But it is not mandatory and should not preclude a math-capable student from taking Multivariable Calculus while in high school.
I have posted before that the MV-Calc class at HES attracted more high schoolers than college students the one year for which I asked enrollment statistics. Many of the high schoolers were juniors.</p>

[mimk6]

<p>At our school, you can’t skip Calc A. However, some kids take an accelerated course where they do Algebra 2 in the fall semester, and then they do Math Analysis (or trig or Pre-calc depending on what you call it) the spring semester and the following fall. Then the spring semester of the second year, they do a semester of Calc A and then the following year, they do Calc BC. Students have to test into this track through – they have to demonstrate strong skills, particularly in algebra, I think, since Algebra 2 is where they are going to move very quickly. My son started in the Algebra 2 accelerated in 9th grade and so is now in Calculus A, second semester of 10th. So next year will be Calc BC, and then he can do AP Stats in 12th grade.</p>

[collegeround2]

<p>I noticed this old post and wondered how the colleges viewed the math sequence your child selected. What did he decide for a major and where did he choose to go to school? If you were to do it again, would you have considered an on line option for his further high school math? My son a freshman just completed BC calculus and finished with an A+ in the class and a 5 on the AP exam. We are trying to decide between the Johns Hopkins on line program or the Stanford on line program to continue his math.</p>

[ucbalumnus]

<p>

@collegeround2

My son a freshman just completed BC calculus and finished with an A+ in the class and a 5 on the AP exam.

</p>

<p>You may want to start your own thread.</p>

<p>Looks like your son is four grade levels ahead. If he continues on with math, the usual progression is:</p>

<p>10th grade: college sophomore level math courses like multivariable calculus, linear algebra, differential equations (should be available at community colleges from which students transfer to universities as math, statistics, physics, or engineering majors).
11th-12th grade: college junior and senior level math courses like real analysis, abstract algebra, etc. (need to go to a nearby university with a good math department; math at this level is mainly useful for math, statistics, physics, and some economics majors).
college: if a math major, would probably start in junior and senior level courses, and take graduate level courses and do graduate level research as an undergraduate; obviously would need to attend a university with a strong PhD-granting math department (would probably exhaust the math offerings at undergraduate-only or master’s schools).</p>