Hey, all! I’m dual-enrolled at Indiana University taking honors multivariable (s311/312).
Next year I will have the opportunity to dual-enroll again. My professor told the class we’d be ready for the next level of honors 400 level classes (modern algebra and real analysis). Each of those classes is split up into two semesters (s403/404 and s413/414 respectively). I’d also be prepared for the whole gamut of 300 level classes (logic, honors diffy Qs, etc). My question is: what’s good for an aspiring math major to take? Should I worry about transfer credits or prerequisites when I go off to college for real (assuming I don’t end up at IU, of course)? I thought the math-brains of CC might have some insight on the neatest/handiest courses to take!
My personal fav. would be modern algebra, because wow that stuff is cool, but I have a couple of friends taking number theory (also in the 400s) and I could definitely use some better foundations there. Not to mention the calculus of complex variables is looking neat… oh man this is really hard!
And before anyone says it: The obvious choice /would/ be linear algebra, but s311 spends a lot of time on linear algebra (we’re using “Calculus Two: Linear and Nonlinear Functions” by Flanigan and Kazdan) and I’ve already done a fair amount of self-study in that area.
I mean, I have nothing against linear algebra, but I’ve put enough work into it this semester that taking the class proper would feel like getting held back. XD
Edit: To clarify: while our textbook may be titled “Calculus Two,” this definitely isn’t second semester calculus; it’s second year calculus!
Also, s311 (unlike the non-honors section) is very proof-based. It’s basically there to get students ready for s413’s rigorous take on analysis.
Here is the department course list: https://math.indiana.edu/undergraduate/CourseDescriptions.html
Looks like 303 (linear algebra) is listed as the prerequisite for 403, and there is an honors version S303. Also, have you had differential equations? This is commonly taken by second year math majors, so you may want to consider S343.
@ucbalumnus Linear Algebra is a likely suspect, although I’ve heard tell that s311/312 covers much of its content more indepth than even the honors session. I might even get departmental permission for 403!
I also wouldn’t mind diffy Qs (they’re very applicable to my research!) but consensus among those I’ve asked is that the S343/344 sequence isn’t very good.
Either way, I’ve arranged to meet with my undergrad advisor tomorrow! I’ll make sure to ask her about 403 prerequisites and S343/344.
@ucbalumnus Alright, done and done!
That is, I asked my advisor and she was very helpful.
TL;DR:
Spring: s303
Next Fall: s403, some other 400-level class (s463, m453, s415, etc.)
Next Spring: s404, s312
Here’s the full story: s312 won’t work with my high school schedule, so I’ll have to put it off until senior year. However, honors linear algebra is occupying s311’s super convenient timeslot! I was worried it wouldn’t have extra content (and a bit sad to be leaving my professor) but my advisor assured me the professor was nice and would probably give students with more background extra stuff to chew on. So, that’s that! Not to mention doing so ets me take s403 without any red tape.
I can even finish up vector calculus with my friends currently in Calc BC! Definitely a net gain.
s463 (honors probability theory I) is supposed to be one of the easier 400 levels, but it’s also a meaty class and good background for grad courses.
s403/404 are actually somewhat notorious, but they’re supposed to follow pretty naturally from s303. Same for 413/14 and 312 respectively, but I was more excited about algebra anyway haha.
I do plan to ask the linear algebra guy and my current prof. on the differences between s303 and s311! I’ll even show the former our new textbook (the math advisor was pretty surprised by all the linear algebra in there)!
Looks like it makes sense, but you may have to be flexible in future semesters (next fall and following spring), depending on what time of day each course of interest is offered.
Since you’ll need to be flexible, it helps to have some extra options in case you have schedule conflicts.
My son was in a similar situation where he had two years after running out of high school math. In addition to multivariable and linear algebra, he took a Discrete Math class that his HS counted as math (even though it was in the CS department) and then a course called “Automata and Formal Languages” and a digital logic class (that also taught assembly). He really enjoyed those classes, and the formal languages class went pretty deep into proofs.
It looks like you could take MATH 353 along those lines.
@Ynotgo Oooh, good stuff! Discrete math is a crazy cool field of study, and it would certainly complement s403. If one of my mathy friends ends up there I would not mind taking it (I’m a fan of math period, so friendly peers or a well-proven prof./TA is a huge plus in my book haha).
After multi there isn’t necessarily one clear path, but lots of options. My son took multi/linear algebra (at his HS) in 11th. Then in 12th he did a number of independent study classes - one was real analysis, one was algebraic geometry. He spent 2 summers at a number theory camp so didn’t need another class. He had taken a 1 term diff eq class, but will retake it in college since it wasn’t a full semester class. Some classes may not transfer, but that will be school specific. In the spring have to work on this with kid 2 - he will finish multi in the spring and have the math department at the university open to him. Probably he’ll start with linear algebra, but not sure what else he’ll take.
