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Choosing math courses is one of the most important aspects of being a math major, though these choices are often quite difficult. Upon entering Princeton, many math majors do not know which areas of math to explore. Even for those who have decided this question, it is often not apparent which courses to take and in what order. Moreover, there are always questions of which courses it is feasible to take simultaneously, which courses overlap in material covered, what knowledge does one need before taking a course, and many others.
The goal of this course guide is to provide information to help math majors make these decisions. Before this course guide was compiled, the available sources of information were the registrar's Course Offerings and the math department's undergraduate courses page. These two are important information sources, and every math major should consult them. This course guide supplements these sources by bringing in the student's perspective. All of the information presented here is taken from the experiences math majors have had taking these courses.
Princeton's Math Department is often lauded as one of the very best in the world. Now you can see how they approach the study of the subject there.
(Score: 2) by fubari on Sunday December 04 2016, @04:30AM
Seeking suggestions for online math classes like described in the fine article: linear algebra, multivariable calc, differential equations. I haven't found anything online yet that looks good; for example, I'm surprised Coursera [coursera.org] is sparse on more serious math.
I'm a long time programmer and am looking to step up my analytics game. Eventually I want to get to work in machine learning or computational linguistics; I know I need to make some math progress before I get there.
I am close to finishing working through all the math on Khan Academy [khanacademy.org] and am astonished at how much I've forgotten. :-) Some comes back quickly, some slower, some I realize I never really learned the first time around at all.
Anyway, getting ready for next my steps and would welcome any suggestions.
(Score: 2) by Snotnose on Sunday December 04 2016, @05:17AM
Linear algebra is dirt simple. Can you add 3 lines of 3 numbers in your head? Can you add 5 lines of 5 numbers in your head? If yes, Linera algebra is a sinch.
Diffy Q's were a bitch, but when I got to the math classes after them they were pretty easy.
I majored in math because by the 3rd semester we were rotating things in the 3rd dimension, and I could visualize it. 3rd semester calculus was easily the easiest math class I ever took.
/ your mileage may vary,
// but really, linear algebra is more how anal you are than how good you are at math
/// wanna add 27 numbers? Linear algebra is for you
//// Graduated in '90, things may have changed since then.
When the dust settled America realized it was saved by a porn star.
(Score: 2) by fubari on Sunday December 04 2016, @06:31AM
thanks :-) I'm at the awkward stage of not knowing what I don't know.
(Score: 1) by Ethanol-fueled on Sunday December 04 2016, @10:32AM
If you are mentioning Khan Academy and Coursera in the same sentence as advanced math, then you are in for a world of hurt. Both of those services are shit.
Let me give you a tip - Advanced math is all algebra. Symbolic manipulation, isolating variables. If you are comfortable with intermediate algebra, then you can do advanced math. Don't do what I did and spend your intermediate algebra class pinching your girlfriend's braless nipples and playing Led Zeppelin on your guitar unless you want to do what I did and work your way up to discrete math from high-school level plane geometry in college.
(Score: 2) by fubari on Sunday December 04 2016, @08:35PM
Oh yes, I expect it to hurt so good.
Good to know on algebra, fwiw I do feel on solid ground there.
r.e. advanced: hmmm, maybe for me change my description: s/advanced/next step/ for single-var calculus.
r.e. Khan: I've been pretty impressed w/Khan Academy. They do an impressive job with drills and feedback, for computerized instruction I don't know how they could do better. I often find myself wishing Khan Academy was around when I was first learning about math.
r.e. coursera: I don't have enough data points to say good / bad, just seems kind of sparse, like there isn't much demand for online "math trajectories."
At any rate, I will keep your advice in mind - thank you. :-)
(Score: 2, Informative) by khallow on Sunday December 04 2016, @05:13PM
Linear algebra is dirt simple. Can you add 3 lines of 3 numbers in your head? Can you add 5 lines of 5 numbers in your head? If yes, Linera algebra is a sinch.
Linear algebra goes way beyond that. For example, the Legendre transform [wikipedia.org] which is a rather simple bit of linear algebra applied to real analysis leads to powerful characterizations of integration (such as Holder's inequality [wikipedia.org]), and an explanation of how to transform a classic dynamical system from position, velocity, acceleration, to position, momentum, force (in other words, transforming a Lagrangian system [wikipedia.org] into a Hamiltonian system [wikipedia.org]).
Linear algebra is also instrumental to calculation of various topological invariants (such as a complete categorization of knots)
(Score: 3, Interesting) by Snotnose on Sunday December 04 2016, @05:33PM
Wasn't implying linear algebra was useless. Far from it, it's very useful. My point was that it's pretty simple to learn, usually involving nothing more than adding and/or multiplying numbers. Often lots and lots of numbers, but it's still just addition and multiplication.
When the dust settled America realized it was saved by a porn star.
(Score: 0) by Anonymous Coward on Monday December 05 2016, @12:45AM
Yes, but mental arithmetic has nothing to do with it. Linear algebra is the language of geometry. It is also the study of vector spaces in general (abstract and concrete). In first year linear algebra, learning the mechanics of vector and matrix operations should be incidental to learning the general theory of Euclidean spaces and the maps between them (represented by matrices of reals), and learning how to apply the theory to solve problems, both in mathematics and other fields.
(Score: 1, Informative) by Anonymous Coward on Monday December 05 2016, @04:55AM
I would avoid online courses for math. Google for recommendations from mathies on specific subjects (e.g. linear algebra), then cross-reference the book reviews on amazon, and go back an edition or two to buy used at a good price (usually well under $20). Read reviews carefully for what level of mathematical maturity is expected. As with finding partners for tennis or golf, the idea is finding a match for your level - neither above nor below.
One thing I've learned is that it often takes 2 or 3 editions for a professor to get the textbook right, but after that, they're basically following fads and fashion in the textbook biz. Oh, you want more big color photos to help connect students with exciting work done by professionals? And how about support for Matlab, TI-89, and graphics packages. etc
(Score: 0) by Anonymous Coward on Tuesday December 06 2016, @09:40AM
Don't do it online.
If you understand code, I recommend picking up a copy of an early-undergrad course book on analysis + proof (eg. the one by that name). Literally do it cover to cover, including exercises, especially - if you can bear it - the ones marked challenging. You should expect this to take about one half to one work-month, 80-160 hours; just do evens or odds if there's solutions only for those but don't skip to solutions without spending meaningful time trying first. The book isn't thick and the learning is fast.
This will give you The View . The one where you can mentally 'hold' the pieces of a problem, and see what the missing bits are. The one where you by default consider 0 and infinity, not unlike good coders. Ask your mathematician friends, watch their eyes glaze over as they try to describe it.
Once you have this, you can choose to investigate branches of theoretical math as dalliances, spending more time in what you like. Discrete stuff and number theory? Real and complex analysis? Topology and graph theory? Etc.? All of it will be legible to you, and you'll be able to read and understand some 50-90% of the material about 2-3x as fast as without the initial setup (of the rest, it'll be partly grokkable as fast without, and maybe partly ungrokkable period).
But the learning curve for math is weird. One really must get the foundation for each topic, and most of the foundation for starter-advanced maths is within analysis+proof.