How should I schedule abstract algebra and real analysis?

College Majors Math/Computer Science Majors
1

<p>I screwed myself by not taking college credit in high school I had to take calculus courses my freshmen year. I am a math major and I'm a bit worried I'm going to be a bit off track but here goes my plan.</p>

<p>Sophomore year fall semester </p>

<p>Statistics and probability</p>

<p>Linear algebra</p>

<p>Differential equations </p>

<p>And a basic physics class 103M (I think its modern mechanics or something)</p>

<p>The last will probably be a fill class. Maybe history or something</p>

<p>This is very concrete and I am sure that I have to take this schedule this semester.</p>

<p>After that I am lost</p>

<p>I know I need real analysis I & II and algebraic structures I & II</p>

<p>But I also want to throw in Topology I & II and number theory for sure.</p>

<p>I have all the prerequisites for all of these classes except for topology which requires real analysis I.</p>

<p>Sophomore spring semester</p>

<p>Number theory </p>

<p>Algebraic structures I</p>

<p>Junior fall semester </p>

<p>Real analysis I </p>

<p>Algebraic structures II</p>

<p>Junior spring semester</p>

<p>Topology I</p>

<p>Real analysis II</p>

<p>Senor fall semester</p>

<p>Topology II</p>

<p>Im still not sure what other math classes I'll take senor year but I was wondering if this sounds like a doable order for algebraic structures, topology, real analysis and number theory?</p>

2

<p>Seems doable. I took algebra 1 without real analysis and did fine (I might actually be taking real analysis this semester), so you can probably do them in either order. Apparently MIT lists real analysis as a pre-req only because they want you to know how to write a solid proof. Since I had olympiad background, I decided to skip real analysis for now and take algebra 1.</p>

<p>However, even for me, algebra 1 was a fairly difficult class, and if you have little proof-writing background, it may be a good idea to take real analysis first.</p>

3

<p>Are you a sophomore?</p>

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4

<p>Real analysis is often considered one of the more difficult proof-oriented math courses, so some math departments recommend taking it after some other proof-oriented math course. You may want to ask your school’s math department what order they suggest taking proof-oriented math courses in. Some math departments offer a sophomore level course in proof techniques, or include that in another sophomore level course like discrete math, or offer honors or proof-oriented versions of the usual sophomore level courses like multivariable calculus, linear algebra, and differential equations.</p>

5

<p>I took Real Analysis I in the fall. I’m taking Real Analysis II, Abstract Algebra I, Complex Analysis, and Applied Probability right now. I had a Set Theory/Logic class that was the gateway course that taught us how to write proofs, but it wasn’t essential to me since writing proofs in Real Analysis was a whole other ballgame. My professor was about to fail 75% of the class, but he ended up passing around 50%, I think. It’s difficult, but it’s not terrible. Abstract Algebra is interesting so far, but I’m only one week in. Complex Analysis is pretty interesting. We had to learn some topology for my Real Analysis I class and it’s popping up in my next lecture in Complex Analysis. I had Linear Algebra with proofs, so jumping into a proofs course wasn’t that bad. It was around 90% theory. </p>

<p>Are you a pure math major? I’m an applied math & statistics major, but I got stuck taking all of my theory classes my senior year (on the quarter system). I took classes in mathematical physics, upper-level Differential Equations, Partial Differential Equations, Operations Research I/II, Sampling Theory, Graph Theory, Numerical Analysis…</p>

<p>Outside of our core, we can pretty much tailor our courses to our liking from mixing and matching statistics and applied math classes. If you have some idea of a direction you want to move in, I’d tailor my plan towards that if I could.</p>

6

<p>I tip my hat off to ANYONE to takes Real Analysis II voluntarily. I was also an applied math major. Hell, I was applied-applied math. I only needed Advanced Calculus I…and after I passed that course I made sure I was done with ANYTHING requiring a proof.</p>

7

<p>I am a pure math major. I think I am interested in algebra as one if my professors in my one of my entry level courses explained abstract algebra to me at a basic level and it interested me greatly. I would ,however, enjoy tethering in more applied courses like partial differential equations or a more advance statistic or probability class if I have the extra room.</p>

<p>I was advised to take the number theory class before real analysis because it is supposedly a good course to get acquainted with proofs. </p>

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8

<p>I am debating on whether I should try to get an internship my sophomore summer. I’ll definitely try for my junior summer but I am still debating, what do you guys think?</p>

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9

<p>Internships certainly don’t hurt they only help. Just make sure you’re able to perform the duties that are outlined in their job description though. I’ve seen a few students who think they could fake through internships only to realize that they certainly can’t. As much “job experience” as you can possibly get prior to graduating will only help your chances post degree on delivering a career quickly.</p>

10

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<p>Internship would obviously be better than nothing, so you might as well try to get one.</p>

<p>If the choice is between an internship and undergraduate research, then it may be a more complicated choice, based on the things you would work on, and your goals of industry work (favors internship) or PhD study (favors research).</p>