<p>Hi! I'm an incoming freshman for the fall, and I've been trying to plan my schedule a little bit, and I'm curious if any math majors would be able to offer advice on coursework.</p>
<p>Already taken equivalents to 53, 54, 104, and very competent at formulating rigorous proofs, probably going to do upper div. differential equations and algebra (maybe finish linear algebra instead?) at UCLA over the summer. I'm planning on taking 202A in the fall, but I'm curious to how students in the past have felt about 204 and 214 (I'm leaning towards the former simply because it seems like 214 has 202A as a prereq). I haven't really been able to get a whole lot of information on 204, other than arguments aren't really as formal as in 202A, so any help would be appreciated.</p>
<p>Besides that I'll probably be going into one or two breadth courses and Math 98. Does anybody know good history/arts and literature/international breadth/biology breadth courses which aren't too many credits?</p>
<p>Side note: I've been looking at second semester, and other than 202B I might take 185 or 113 depending on which route I take over the summer. If anyone has any other suggestions for classes, I would very much appreciate it! Thanks!</p>
<p>In general, most people do not take more than 3 math graduate classes unless they really really are gifted at math.</p>
<p>202a is the fundamental class that almost every math and physics grad student must go through. Some like it and some hate it. Depending on how comfortable you are with analysis, 202a could take up a lot of time too. One of the graduate students, Peyam, constantly states that 202a is “2 times harder and more time consuming than 104” and he also states that “104 is a really hard class.” </p>
<p>214 does not require 202a as a prereq. You will do fine if you have the mathematical maturity to go through 104, although rudimentary knowledge of differential forms, Lie Algebras, the fundamental group, exterior algebra, etc does help.</p>
<p>204 is just time consuming. A couple of my friends took it and they just complained about the difficulty of the problem sets. Though, that was with a different professor in Fall 2011.</p>
<p>If you plan on taking all 3 grad classes, I’d highly recommend that these are the ONLY classes you take. Even then, it’ll be a very heavy semester.</p>
<p>Thanks! I’m only planning on taking one of either 204 or 214 along with 202A, so hopefully it will be a little less intense, but from what it sounds like they are very time consuming classes. I am currently mostly self-studying analysis from Rudin (although I’m officially taking it through Stanford OHS) and I have a pretty solid handle on all of the material. My only concern about 214 is that it seems like a lot of topology would come into play there, and my only experience there has really been the limited point-set stuff in Rudin.</p>
<p>Would you happen to know how the curves are in 204/214? I’ve heard that it varies a lot with 202A, depending on the teacher, but I haven’t been able to get much information about those two. Do you have any experience with whether most of these classes have finals or are solely classwork?</p>
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<p>Math 160 (history of math) counts as a history course for L&S 7 course breadth. History 30 and 180-183 may be of interest if you are interested in the history of science and engineering.</p>
<p>For biology, there are a number of courses that may be of interest to breadth seekers: MCB 31, 32, 41, 50, 55, 61, 62, 64; IB 31, 35AC, 41, C82. There is also ESPM C12 / English C77, which can fulfill either biology or arts/literature for the L&S 7 course breadth.</p>
<p>But really, the course catalog is huge. What kind of things are you interested in (besides math)?</p>
<p>For breadth I’m already thinking down the road, of math 135 for philosophy breadth, random econ for social science breadth, and random physics for physical science breadth. For biology I’ve been considering nutrisci 10 for second semester (does anyone know whether it is usually impacted?) simply because I’ll have pretty difficult other coursework, but in general I’m just looking for easy and engaging classes. I’d prefer classes with less reading and fewer lecturing hours, so I’m hoping to try to get mostly 2-3 credits for breadths.</p>
<p>Just a note, I’m probably going to use all of my breadths as P/NP if I feel confident enough that I can do well in the math courses and need more time to focus on them. Would that be a bad idea, as it gives little room for error in terms of GPA?</p>
<p>The topology you will encounter in 214 won’t require any background. It might take a bit of time to understand the material but most other people will only come in with a background of one geometry course. </p>
<p>If you really want, check Munkres’ “Topology” for more information. His book teaches you pretty much all the topology you need to have a strong foundation that you build upon in 214.</p>
<p>At Berkeley, there are the “graduate-level” courses and the “undergraduate graduate-level” courses. You will quickly see that 202a falls into the latter and 214/204 falls into the former. In the “undergraduate graduate-level” courses, you pretty much have a standard math class with weekly (or biweekly) homework, in-class midterms, and a final exam. More importantly, most of the class is comprised of undergraduate students. In Fall 2012, there were 3 graduate students and over 57 undergraduates taking 202a at the beginning of the course (this number decreased to around 40 later). Since almost everyone who takes a graduate level math class is probably somewhat good at math, there is reason to suspect that almost no one gets under a B. The lowest I heard of was a B+ for Fall 2012. </p>
<p>214 is sort of a transition course where only a few students are math grad students, quite a few are physics grad students, and a significant portion of the class is comprised of undergraduates. I would classify 214 as a “graduate-level” course because all of the grade is based on homework and take-home midterms/finals. The finals and midterms are pretty much homework assignments in that you usually get 1 week to finish them and a lot of the time they are open-book, so I consider these classes to be graded 100% on homework. The reason you get 1 week to do these exams is that it is impossible to test your knowledge of, in the case of 214, differential geometry in 50 minutes or even 3 hours. You might get 2-3 problems done in 3 hours but most people cannot even finish 1 [nontrivial] problem in 3 hours. I think everyone who stays with the course until the end gets either a B or A, with most students getting A’s since you kinda have to know what you’re doing to stay in the class.</p>
<p>Also, having so much background coming into Cal, you might want to consider the Honors classes at Berkeley. </p>
<p>For example Math H53 (honors multivariable calculus) goes over forms and wedge products and the exterior derivative. See the following problem set.<br>
<a href=“http://math.berkeley.edu/~sean/H53/H53Asst4.pdf[/url]”>http://math.berkeley.edu/~sean/H53/H53Asst4.pdf</a></p>
<p>You might actually gain a lot more from taking every single honors class since you have the non-honors background. Actually, this would probably be my recommendation for you since there’s a good chance that there will be some gaps in your knowledge if you just directly go to graduate classes and get thrown 20 definitions and 20 theorems a day. </p>
<p>H110 might also be a class worth taking. I took a screenshot of part of the table of contents of the book the professor is using.<br>
[Image</a> - ■■■■■■■ - Free Image Hosting, Photo Sharing & Video Hosting](<a href=“http://■■■■■■■.com/r/23uou44/6]Image”>http://■■■■■■■.com/r/23uou44/6)
H110 goes over exterior algebra as well, and many interesting topics. </p>
<p>Basically, the honors classes are an introduction to the graduate counterpart and they are challenging enough so that you shouldn’t be bored. </p>
<p>Ignore all of what I posted if you took anything like Harvard’s Math 55 or Stanford 50H series or U Chicago’s Math 207. If so, go directly into graduate classes =]. If you don’t know how to do everything in that H53 problem set or aren’t extremely comfortable with the stuff in the table of contents I linked, chances are you will be well-suited for the undergrad Honors series.</p>
<p>For example, you could take
H110 H104 (and maybe you could waiver out of H54, as I think that this is least rigorous honors math class) your first semester with the Putnam class (191). This is a common path for people with as much background as you.
The next semester, you could take H113 H185 & H53.
Then fall of the following year, you could begin taking graduate classes.</p>
<p>^ is my recommendation.</p>
<p>Keep in mind that the style (and hence challenge) of an honors class can vary significantly based on professor. </p>
<p>The instructor for H104 next semester, Wodzicki, has a reputation for going far above and beyond what you might cover in 104 (and going far beyond his scheduled lecture time…). The same reportedly applies to H110 next semester (well, except for the lecture time).</p>
<p>On the other hand, I think the current instructor for H113 (which I’m taking right now) doesn’t make it much more advanced than 113; the main difference is the higher level of the students. (He’s a postdoc, so there wasn’t much data on his teaching beforehand.)</p>
<p>Thank you both very much, it sounds like both courses would be manageable (although difficult) from what you say, which is very good news. I will try to talk to the professor of 214 or sit in on his class before committing to it, but I am much more interested in differential geometry as a subject and hopefully it will open up some new opportunities.</p>
<p>As far as my background, I’ve currently covered through differentiation in Rudin (working mostly from M.I.T.'s analysis I problem sets which I’ve heard are fairly difficult). I haven’t really had much formal training with multivariable calculus (I had a course in it but it was pretty easy stuff) and I’m currently studying out of Apostol (with M.I.T.'s 18.024 problem sets). I’m hoping to cover up any gaps in my knowledge in Differential Equations this summer with Math 135 at UCLA, and probably to get a better understanding of Linear Algebra with 115A.</p>
<p>That said, I don’t believe that wedge products or the exterior algebra should be out of reach by summer’s end. I will probably tackle some of the multivariable stuff in Rudin in mid-June, and I have Spivak’s Calculus on Manifolds to supplement. The latter has so far been about my current limit for being able to pick up a math book, read it through, and be able to figure out almost everything, but I know he covers everything you’ve mentioned and more.</p>
<p>I’ll also look into the honors classes as possibly another route, but right now it may be looking like 204, 214, +1 to 2 G.E. classes. Thank you very much for your time and effort in aiding me!</p>
<p>Sorry, that was 202A, 214, +1 to 2 G.E. classes.</p>