/sci/ - Science & Math

Does it even make sense to major in math nowadays? It seems like all the mathematicians end up having to move to America to get a job. But based on what I read on Reddit, America is a terrible evil right-wing country where you will end up shot or dying of strange diseases without a doctor. CS majors in my country say they won't move to America for even treble their salary.

> be math instructor
> Change variable name from x to y
> Students cannot solve problem any more

When did you realize that "Harvard University" is a meme

Algebra is one of the major fields of pure mathematics, so is also considered one of the major courses in the undergraduate math degree. It should NOT be in the top three along with linear algebra, advanced calculus, and ODE. These are the most important topics in the undergraduate math major to do well with old applications in other fields or for more advanced work in mathematics.

What is just CRUCIAL from algebra is the real number system, and it is FAR better to see this system in action in linear algebra, advanced calculus (completeness, compactness, continuity), and ODE before going for Dedekind cuts, Cauchy sequences, or whatever to 'construct' the reals from the rationals. Besides, for the reals themselves, the really astounding properties are best treated as side topics in measure theory, e.g., from Oxtoby's Measure and Category and Gelbaum and Olmsted, Counterexamples in Analysis. The really good stuff, even the philosophical stuff of the continuum hypothesis, even the simple stuff such as the Cantor diagonal argument that the reals are uncountable, just is NOT a main part of 'abstract algebra'.

CS is basically math++, and a CS graduate is considered élite, capable of mastering in 1 year what math graduates do in 2 years. Deal with it!
World's élite universities (e.g. MIT, Princeton) will tell you right away that as their CS student you are considered the best group they have and that math students go slower than you are, and increase your load to crazy levels As a CS student, you are expected to master (continuous) calculus, discrete calculus (discrete math proofs, hypercubes for parallel algorithms), optimization (machine/deep learning, compilers), category theory (functional programming), logic (up to automated proofs, i.e. including set theory), differential equations, topology (computational geometry, distributed algorithms), probability and statistics (reinforcement learning, queueing), number theory (cryptography), graph theory (almost everywhere)... There is no functional analysis needed yet, but it's heavily used for PhD degrees anyway. You need to know all this down to the level of proving theorems if you want to achieve anything in CS.