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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, 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.