∑ XahLee
xah's edu corner extempore! episode №20180115122340
on math courses, and how to become a mathematician for programers
for young coders out there, the proper order of learning math is: highschool algebra, trig, pre-calc, calculus, linear algebra, then optional intro diff equations. These are basics. Must be in that order. These are basic needed for engineering. But are not math major basics yet.
∑ XahLee
for math major (to become mathematician), you need abstract algebra, real analysis. Order doesn't matter. After you had these, you are acquainted with math “language”, or math maturity. i.e. the way mathematician talks. These are typically 3rd year math major.
∑ XahLee
after that, you may have the following in arbitrary order: complex analysis, different geometry, topology, set theory. After studying these, you can consider yourself mathematician. You know what math is about, or know where to go. All the above, are traditional main math courses.
∑ XahLee
for programers, you might wonder, where is graph theory, type theory, game theory, logic, combinatorics, statistics. These are not typical main courses of MATHEMATICIAN. These are called discrete math, sometimes as comp sci. (while statistics n probability r applied math)
∑ XahLee
the discrete math, they do not have the elaborate pre-requisite sequence as analysis/algebra. Anyone can start to learn graph theory, game theory, combinatorics, number theory, etc. But you don't get deep without the years of analysis/algebra of real mathematician stuff.
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