<p>Hi guys,</p>
<p>I looked under the academics section of the Chicago website, and they said that you could get a master’s degree in math if you placed into Honors Analysis. For those that don’t place into Honors Analysis as a freshman, is it still possible to graduate w/a masters in 4 years? Through like summer work or doubling up on course etc? </p>
<p>Thanks!</p>
<p>First of all, what are your reasons for wanting a master’s degree? According to Paul Sally, only about 1 person a year gets a joint-degree in mathematics, because it’s pretty useless if you plan on going to grad school for your PhD, which most math majors do. And if you’re good enough to place into Honors Analysis (only 10 people a year do), you probably would want to go on to get your PhD.</p>
<p>If you don’t place into Honors Analysis as a freshman, it is NOT possible to graduate with a masters in 4 years. The reason for this is that hard math courses (160s and up) are unavailable during the summer, so you have to take all hard courses during autumn, winter, and spring. And you’re already going to be doubling up on your courses if you want the master’s degree.</p>
<p>If you want your master’s degree, here are the courses you’re going to have to take:</p>
<p>Honors Analysis (3 quarters)
Honors Algebra (3 quarters)
Complex Variables (1 quarter)
Topology (1 quarter)
Algebraic Topology (1 quarter)
Functional Analysis (1 quarter)
Differentiation/Integration on Manifolds (1 quarter)
Differential Equations (1 quarter)
Graduate Algebra (3 quarters)
Graduate Analysis (3 quarters)
Graduate Topology/Geometry (3 quarters)
<p>…and that’s the bare minimum. Plus you have to worry about Core.</p>
<p>Wow, that’s rough–even for kids that do place into Honors Analysis. It’s looking pretty bleak for the kids placed into Honors Calc. Hmm…</p>
<p>I figured it would look good when applying to the top PhD programs, or it would be great prep for some of the nutso quant firms, if I didn’t feel like continuing with academic math.</p>
<p>I don’t think top PhD programs care if you have a Masters or not. PhD programs care about research potential, whereas a Masters degree merely shows that you know a lot about math. We have something called REU that even a lot of freshman participate in over the summer, where you can do research one-to-one with an advisor; you even get a nice $1.5k-3k stipend. That’s a much better way of getting into a PhD program than having a master’s.</p>
<p>And I’d say that to get through the masters program at Chicago, you’d really have to be dedicated to academic math (so chances are, you wouldn’t want to enter into any sort of firm afterwards). The grad courses here are seriously crazy hard.</p>
<p>What do you need to have learned in order to do well enough on the calc placement test to place into Honors Analysis?</p>
<p>You need to have a very tight grasp on the BASIC concepts of analysis and topology, i.e. the fundamentals of our honors calculus course. You’ll especially be expected to know proper definitions of fundamental concepts of calculus (convergence, limits, derivatives, integrals, continuity). You’ll be expected to be able to manipulate the tenets of theoretical calculus, by which I primarily mean delta-epsilon and supremum/infimum stuff. Field axioms are also a must.</p>
<p>Remember, though, that there’s no shame in taking Honors Calculus beforehand. Honors Calculus is a very advanced, theoretical course, and few are displeased with it. Most of the people I know who are happy in Honors Calculus are people who were originally very disappointed and a bit depressed that they didn’t make it into Honors Analysis.</p>
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<p>Quite true. If honors calc is a love bite of math for students who really want to do it, honors analysis is a soul-sucking demon. (Sorry for taking the words out of your mouth, phuriku). </p>
<p>Students who place into honors calc (I placed into honors calc, it more or less entails showing that you know work that’s a little above the AP BC Calc curriculum), take the class, and stay with the class have to maintain an A throughout the year to make it on to honors analysis. Honors analysis, to give you an idea, requires a 30 hour minimum of work a week-- my friends in honors calc/ not-honors-but-higher-than-regular analysis easily spend 15-20 hours a week on it. Just to give you the idea that there’s the deep end, and then there’s the the shark tank.</p>
<p>… and, of course, there’s the inquiry-based sections of Honours Calculus. Depending on your maths background when come to Chicago, it might be a wonderfully challenging class. Since you’re at Andover, I couldn’t say if it might be appropriate. You can judge from these lecture notes and problem sets: [Math[/url</a>]. Furthermore, if you can do very well (A/A-) in the 160s, you’ll probably be invited into Honours Analysis and possibly be better prepared to succeed in it.</p>
<p>Also, CesareBorgia is a 4th-year (?) at Chicago who has taken an undergraduate analysis sequence and is taking the graduate analysis sequence (IIRC). If you’re interested in finance and whatnot, then you should talk to him.</p>
<p>I posted a thread a while back about maths, and there is a lot of detailed information there on calculus and analysis at Chicago, the maths department, etc: <a href=“http://talk.collegeconfidential.com/university-chicago/409363-calculus-placement-exam.html[/url]”>http://talk.collegeconfidential.com/university-chicago/409363-calculus-placement-exam.html](<a href=“http://www.math.uchicago.edu/~abert/moore/moore.html]Math[/url”>http://www.math.uchicago.edu/~abert/moore/moore.html)</a></p>
<p>(Are you doing the REU this summer, phuriku? Anyone?)</p>
<p>Yes, SCOMathmo, I’m doing REU this summer. Honors Analysis students are supposed to get the full program, but last year, they had to cut back and some freshmen had to settle with the apprentice program. I’ll be happy to do either of the programs, though. My worries lie in finances, as I’ll have to find somewhere to live for really cheap. Hopefully I can find some desperate sub-letters at the middle to end of spring quarter.</p>
<p>I’m a 3rd year who’s taking analysis currently, and will probably also take math 270 (basic complex variables), 272 (basic functional analysis), and maybe 273 (ode), 275 (pde). I’m not even a math major, so taking graduate analysis would be kind of insane for me.</p>
<p>You might be able to do a BA/MA in math if you place into Math 203/204/205 (regular analysis), though I’m not sure.</p>
<p>If you can do a cauchy construction of the reals, you should have the adequete “machinery” to place into hon. analysis, though I defer to phuriku on this one.</p>
<p>Well, even though you can not take the advanced math during the summer (stated by phuriku), you could take the other core classes during the summer, leaving space for the other math classes during the 3 main quarters, although im not sure if it would all work out with pre-reqs etc. Of course, if you go during summer quarters, it would technically be more than 4 years (academically speaking).</p>
<p>Yes, the prereqs are the main problem. You won’t be able to take Honors Algebra and Honors Analysis in the same year (they make all sections of both classes at 10:30 for the sole purpose of preventing this), and you won’t be able to take Honors Analysis and Honors Calculus in the same year, of course, or Honors Calculus and Honors Algebra. Thus, if you start with Honors Calculus, it will take you at least 3 years just to get past the fundamental sequences of each area. I guess you could take all 3 graduate classes in your senior year simultaneously, but that would be hell. You’d also have to pass a reading exam in German, French, or Russian.</p>
<p>You CANNOT DO a joint program if you don’t place into Honors Analysis.
Also, you need straight A’s in ALL THREE GRADUATE sequences to get the Joint Degree. I know a guy who was an IMO gold medalist who could not accomplish that.</p>
<p>That is not to put your hopes down, but coming in, you should just focus on your undergrad. courses and, if you do well in some grad. courses, then you can go from there. I was in your position once, but I quickly realized how difficult accomplishing such a thing actually is.</p>
<p>“they had to cut back and some freshmen had to settle with the apprentice program.”</p>
<p>Lol. I was in that boat. It was a small boat.</p>
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<p>Yeah, this is hard. REALLY HARD. Honors Analysis is tough, and at about the same level (maybe a bit more advanced) as the corresponding MIT Graduate Measure Theory course, if you want a comparison. </p>
<p>([MIT</a> OpenCourseWare | Mathematics | 18.125 Measure and Integration, Fall 2003 | Calendar](<a href=“http://ocw.mit.edu/OcwWeb/Mathematics/18-125Fall2003/Calendar/index.htm]MIT”>http://ocw.mit.edu/OcwWeb/Mathematics/18-125Fall2003/Calendar/index.htm))</p>
<p>Now, take Honors Analysis and make the content go by three times faster. Welcome to UChicago’s graduate analysis course. </p>
<p>([Math</a> 312 Handout](<a href=“http://www.math.uchicago.edu/~ryzhik/MATH312-04/math312-04.html]Math”>http://www.math.uchicago.edu/~ryzhik/MATH312-04/math312-04.html))</p>
<p>Now tack on two more courses that go at about the same pace, Graduate Algebra and Graduate Topology. You’ll probably take all three of these courses at the same time. Sounding fun yet?</p>
<p>Sounding impossible, actually. Thanks for all the feedback guys I really appreciate it–I figure myself a bit of a math guy, no IMO gold medalist but I did place into BC calc as a freshman so my background is pretty strong. I figured that would put me on pace for some masters work by the end of four years but I’m seriously reconsidering my initial position. I thought a masters would put me on track for a sick PhD program, but also open up doors if I wanted to go hardcore quant firm instead of academia. I’m beginning to think it’s unnecessary for the first goal, and overkill for the second. </p>
<p>And phuriku that’s nuts abt the MIT grad course. I had no idea Honors Analysis was that ridiculous.</p>
<p>Would a basic 1 semester course on analysis be enough to prepare one to place into Honors Analysis? The major topics we’ve covered so far are completeness, sequences and series, basic topology of R, and functional limits and continuity. The major things we have yet to cover (to my knowledge) are differentiation, integration, and Fourier Series. Assuming I know all this, is there anything else I should study to do well on the placement exam? (I’m also in an intro Algebra course so I’m familiar with the axioms of a field).</p>
<p>Thanks a lot.</p>
<p>GleasSpty:</p>
<p>That should be sufficient for placement into Honors Analysis, as long as you know the content well. I would learn the basic theorems and definitions for differentiation and Riemann-Stieltjes integration if I were you. You won’t need Fourier Series. Know your definitions and field axioms well.</p>
<p>alrihgt. Thanks a lot phuriku. I’m almost positive we don’t cover Riemann-Stieltjes integration so I’m glad you said somehting so I can study it before the test.</p>
<p>Out of curiosity, what is the other-than-Calc-BC material one ought to know to place into Honors Calculus as a freshman?</p>