<p>As somebody who took the Calculus Accreditation Exam recently, here’s what the free response questions covered:</p>
<p>Question 1: Define limit, continuity, and there’s a simple quadratic delta epsilon proof.</p>
<p>Question 2: Define derivative, prove that the derivative of f(x) = something with square roots is f’(x) from definition of derivative (multiply out by conjugate, etc.).</p>
<p>Question 3: Define Riemann integral, asks whether a function defined as a definite integral attains minima/maxima (application of first fundamental theorem of calc, take 1st and 2nd derivatives).</p>
<p>Question 4: Sketch a function with certain properties (some sort of weird trigonometric function, just be familiar with properties of cos/sin).</p>
<p>Question 5: Define Taylor series, find 5th order Taylor polynomial about point of a certain function, find radius of convergence for a certain power series (ratio test).</p>
<p>Question 6: Prove that a_n = (-1)^n diverges. Define Cauchy sequence and prove something basic involving Cauchy sequences.</p>
<p>Question 7: Define upper bound/least upper bound. Prove something basic involving least upper bounds (forgot what it was). Prove the Archimedean property of the real numbers.</p>
<p>Question 8: State the field axioms and prove that the product of two negative numbers is positive. Prove that there exists no integer between 0 and 1.</p>
<p>^If you can do all of the above, huzzah, you’ve made Honors Analysis.</p>
<p>I placed into MATH 195/199/200. For reference, I only did problems 1,2, first part of 3, 5, and the first part of 6. I attempted problem 4 but may have done it incorrectly. Looking at the questions, you’ll see I did mostly the mundane stuff you should’ve learned in your BC class, and not much more. Problems 7 and 8 are real analysis types of questions - I just drew a big sad face on those pages.</p>
<p>I know plenty of people who placed into MATH 160s (Honors Calc) just by doing the first three or four free response questions. They also missed a good number of the multiple choice (maybe 10 questions out of 75). Considering that the first 50 questions were essentially precalc (trig and absolute value inequality type of stuff), if you took BC in high school and take the placement test, you should have a very, very good shot of placing into Honors Calc.</p>
<p>I know PhD students in stat and econ and so on that would be hard pressed to give you back 6, 7, 8 with the kind of rigor the graders likely expect. Why anyone would know that stuff prior to taking analysis in really odd (since they are canonical, first semester topics that do not figure into any plausibly antecedent courses).</p>
<ol>
<li><p>Nothing says that you have to get everything on the placement test right to place into Honors Analysis. What fun is a placement test if it doesn’t really differentiate among the students at the top? People who do really well in 163 are usually offered a place in Honors Analysis (or at least that used to be true), and they wouldn’t necessarily be able to complete those questions.</p></li>
<li><p>Based on my son’s experience, I think you will be offered the opportunity to take Honors Calculus (160s) if you can answer any of the questions on this test. You may not even have to be right, just have half a clue so you don’t completely freak out the first week.</p></li>
<li><p>I suspect any number of people in Honors Analysis have spent time studying analysis in real numbers, with or without a class to take. I also think that Honors Analysis covers more than the standard real analysis course.</p></li>
</ol>
<p>The University has a policy of either placing students into either the Honors Calc 160’s sequence, a hodgepodge of one or two quarter courses (MATH 195/199/200 which are meant to prep students for econ, chemistry, and/or formal proofwriting), or Honors Analysis MATH 207. No one gets placed into MATH 203 “regular analysis” - at the advanced math info meeting J. Sally said that the difference between 203 and 207 is too fine to be judged by the placement test. </p>
<p>So essentially you need to be one of the 13 or so people each year who have taken analysis in high school to have a chance of taking any type of analysis in your first year.</p>
<p>Uh, what? No. The University mathematics curriculum already draws a distinction between the material of “Honors Calculus”, which is the beginnings of proof mechanics and elementary real analysis as tied to the properties of functions with both range and domain in the real numbers, and the material of “Analysis” which, is similar, but deals with the generalizations: metric spaces in general, various types of nice normed linear spaces, measure spaces, and multivariate calculus.</p>
<p>To get into Honors Analysis, a solid reading of the first couple of chapters of Spivak would probably suffice, given a sufficiently strong familiarity with the basic calculus that makes up the previous sections. To stay in is of course another matter. However, to characterize this as in any way analogous to the Analysis that the university teaches in 203, and especially in 207, is patently absurd. </p>
<p>P.S. Of course there are many PhD students in Statistics, Computer Science, Physics who couldn’t do this. Why do they need to? Again, the math taught in the math major at Uchicago is not just “extra special more number crunching”, it is a highly theoretical discipline that often can seem very divorced from the applications.</p>
<p>I agree with parts of what both ramboacid and davorin said.</p>
<p>Students do not place into 203. If they are like my son and do not want to kill themselves as first years taking 207 but believe that the 160s will be too repetitious of high school, then they can take 199 and then go into 203 the next quarter.</p>
<p>Firstly, while this discussion would be informative, I really don’t think that the exam problems should have been posted. If you only get into 207 because you looked at those problems and figured out answers to these specific things, you’re doing it wrong. The best preparation would be to work through the first few chapters of Spivak over the summer - then you’d have the foundation they want and the questions would be easy.</p>
<p>And a few comments on the discussion (I’m a current first-year):
Firstly, about 2/3 of the students in 207 are second-years. There are several such students in my house; they both took the IBL (Inquiry Based Learning) format of Honors Calculus (see <a href=“http://talk.collegeconfidential.com/university-chicago/1543530-ibl-vs-non-ibl-math.html[/url]”>http://talk.collegeconfidential.com/university-chicago/1543530-ibl-vs-non-ibl-math.html</a> or something). If you aren’t prepared for 207 but want to be, IBL 160s will make you prepared.
It’s possible to get into 207 with placement into 199. You just have to impress Paul Sally by working on a sheet of math problems he gives out at a meeting.
It’s also possible to go directly into 203 first quarter. It’s unusual, but it’s what I’m doing. I had placement for 199, but talked to a department counselor and was placed into 203 (almost against my will as I started panicking). I had a lot of experience proving things in high school - just not proving calculus. I know of other students, though, who tried to talk their way into 203 and were unsuccessful. I think that the math department knows what they’re doing regarding placements, though, so you’ll end up where you belong.</p>
<p>There used to be another outcome from the placement test: Placing out of all math with satisfaction of the requirement without placement in honors analysis.</p>
<p>Do not know how often this happens, but it was the result for my D 9 years ago. </p>
<p>Other than that, sounds like nothing has changed. Sally still in charge. Still a desire to understand the process.</p>
<p>Anyone who places into Honors Calc or higher can decide to accept credit for 3 quarters of Calc 150s instead of taking courses at their intended placement level. I placed into 199 but but am not interested in higher math; consequently, I’m “skipping” the math requirement (by accepting the credit) and plan to take a pertinent Mathematical Methods course for my major in the future, which has calculus as a prerequisite.</p>