Honors analysis

Colleges and Universities A-Z University of Chicago ✅
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<p>I will be a freshman in the fall, and I really want to take the honors analysis course. I took calc in ninth grade, and finished up multi var in tenth, and I've since then taken linear algebra, combinatorics, and a graduate level topology course. I know the honors calc sequence wouldn't hurt me, and I'm sure it would still be hard even though I've already taken multivar, etc., but I would like to do a double major, and it would just be nice not to have to retake calculus. Anyway, does anyone know what exactly the placement test covers? Does it cover anything past, say, calc BC? Any statistics at all? Differential equations? Also, how many freshman usually get "invited" into the honors analysis course and how well does one have to do on the test to get in? Or should I not even be worrying about, since if I don't get in, the course may have been way too hard for me?</p>

<p>I apologize for all the questions; however, any answers/suggestions would be great!</p>

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<p>Regarding the test, about 8% of freshman test out of all calculus. A small percentage of that 8% are invited to honors analysis. Getting out of calc and getting in to analy depends as much on knowing some theory as knowing the basics. you'd better be able to do some proofs.</p>

<p>Yes, if you don't get in, the course would be way too hard. Maybe even if you get in...</p>

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<p>Brooke,</p>

<p>Your post is scaring me. I am considering math as my major as well (I also am considering two majors), yet I have not taken anything above BC calc equivalent. Needless to say, I am starting to become a little nervous. I talked with fellow classmate of facebook, a prospective math/econ major, and he has already taken loads of math courses above calc, like you have. While I know it definitely is possible to major in math if one starts at Chicago with a calc sequence, I feel like I am the odd one out and will never make it through. I have long enjoyed math, but it has never come naturally for me, and like all courses I have taken, I have had to work hard to do well in it. With brilliant future mathematicians surrounding me, I feel like I have little hope. </p>

<p>Is there anyone out there who is considering majoring in math yet is not brilliant at it, per se? :)</p>

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<p>There was a guy on here who started in 131 and finished a math major with honors. Maybe Dioloctean, but don't quote me.</p>

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<p>My S recently finished 2nd year of Math major. He entered into Honors Analysis his first year after scoring perfect score on entrance exam. He had taken 4 semesters of math at college level before entering Chicago. He also studied some for the exam and studied some graduate math texts on his own. He was undecided about taking Honors Analysis even if he was accepted into the class because he did not want to miss any part of his math education and would have been satisfied with taking Honors Calc. Decided to take Honors Analysis when Chicago told him he could drop down to Honors Calc if Honors Analysis was too much. There were approx 8 - 12 first years in the class. The class was like drinking water from a fire hydrant. My S felt the best preparation for the class was to have taken an Analysis College level class prior to entering Chicago. The class is highly theoretical and proof oriented. To start he felt he was behind others in class but by second quarter he had caught up. He ended up doing very well all three quarters but there were those who received grades of D but remained in class because they believed they were learning so much. One can either take Honors Analysis as a 2nd year and have a highly successful math record at Chicago. One can also graduate with a Math major without taking Honors Analysis and still have a very challenging program. Double Majoring at Chicago is tough but possible.
Good luck. Chicago is a great school but earns it's reputation.</p>

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<p>
[quote]
Anyway, does anyone know what exactly the placement test covers? Does it cover anything past, say, calc BC?

[/quote]
I do know what it covers, but out of fairness I won't say what, exactly. There are a few questions at the end which will determine if you're capable of taking more advanced courses. I know when I took the test they looked like nonsense to me, and most people just skip them. If you've been exposed to upper-level mathematics they should be fairly simple, though.</p>

<p>
[quote]
Also, how many freshman usually get "invited" into the honors analysis course and how well does one have to do on the test to get in?

[/quote]
When I was in the class my second year there were maybe half a dozen first-years in a class of between 25-30. Admittance is basically at the discretion of Diane Herrmann and Paul Sally. They'll see if you have the experience necessary to handle the class.</p>

<p>
[quote]
Or should I not even be worrying about, since if I don't get in, the course may have been way too hard for me?

[/quote]
During O-week you'll have the opportunity to talk to Diane Herrmann about your placement. If you think you should be in Honors Analysis you'll be one among many, and she and Paul Sally will put you through the ringer. But, given your background, especially the topology, I think it's a real possibility.</p>

<p>Also, for the record, I took the 160s my first year. I didn't take AP Calculus in high school; in fact, my senior year was the first year my high school offered any calculus course. Then of course there are the kids who took calculus in eighth grade and spent high school in college-level analysis courses. <em>shrug</em> People come to Chicago with greatly varying backgrounds.</p>

<p>Out of curiousity, what did you cover in your topology course? Did you use Munkres for the textbook?</p>

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<p>Diocletian, how on Earth did you place into 161 without any previous Calc? I took Calc this year and I'm hoping to place into 131.</p>

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<p>I took calculus, it's just that my high school senior class was the first to do so in my whole school system.</p>

<p>As for how I placed into the 160s, who can say? Maybe it was a clerical error. But I did well enough in the class, and now they've made the mistake of conferring upon me a BS in mathematics. Oops! Too late to take it back now, Chicago!</p>

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<p>Diocletian: Yes, I used Munkres in topology. We covered almost the entire first half (point set). Unfortunately, I haven't done any algebraic topology yet.</p>

<p>Thanks for your responses, everyone! They have been very helpful.</p>

<p>Oh, I am also going through an abstract algebra book this summer, so I will have even more practice in writing proofs, and, hopefully, preparation for honors analysis!</p>

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<p>it sounds like a 130-range or 8+ on aime would be honors analysis? i only got a 165.5 combined, and i was by far the best in my high school at math, and i considered a math major but i wouldnt touch honors analysis with a a 10-foot pole. i took a similar class last summer at a program, and i was just clueless after a few weeks. i also gave up, but i doubt if i tried i woulda done well. even though i havent been to chicago, id say to be wary. although brooke certainly does sound more than qualified.</p>

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<p>Diocletian,</p>

<p>You sound close to genius-level to me, so I wouldn't hesitate to give you your BS in math. I bet you deserve it. I hope I can make it through, as well. :)</p>

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<p>brooke: to get into honors analysis you need to be comfortable doing proofs. i remember that the last question of the placement test this year (just passed) was: prove that for every natural number n there exists a natural number greater than n.</p>

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<p>Given what assumptions about N?</p>

<p>Given that 1 is in N and that 1 is in P, for any n in N, suppose n+1<=n.
Then n-n-1 is in P => -1 is in P => 1 is not in P, contradiction.</p>

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<p>Part of the problem would be to state precisely what definitions you are operating from. For example, one could take the standard definition of the real numbers (complete ordered field) and then prove the Archimedean property. There are multiple avenues of proof here. The point is to show that you can carry out a (relatively simple) proof.</p>

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<p>I'm probably spouting nonsense since I've never seen a formal construction of N or R, but is my idea valid assuming the trichotemy for the integers, 1!=0, and the closure of N? Or are there more basic things that one ought to begin from?</p>

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<p>You don't have to construct the naturals or the reals, just state what your assumptions are. These questions are designed to show two things: one, whether or not you've been exposed to higher-level math; two, whether or not you can prove non-trivial statements from first principles.</p>

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<p>Are you supposed to assume definitions here (i.e. assume we know what infinite means, assume we know the definition of a natural number, assume we know what countably infinite means, etc.). It seems like this question was put on the exam to see how students would answer it. There are probably hundreds of correct answers, if not more.</p>

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<p>That's exactly right, fool. They're obviously not expecting students to start with, say, the Peason axioms and from that alone prove this statement.</p>

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<p>hahahahaha, i was thinking whoa, diocletian was harsh with him, but i didnt realize his username was literally 'fool'</p>

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<p>Since the test is roughly the same every year, I think discussing last year's problems gives the readers of this forum an unfair advantage. </p>

<p>My opinion is that if you know real analysis really well and are comfortable with proofs, you should be able to ace the test and end up in honors analysis.</p>

<p>By the way, I don't know what the Peason axioms are. Do you mean the Peano axioms?</p>