What should I learn after calculus?

I had plenty of time to analyze your mom last night
nothing gets bitches wetter than $300K starting

Your honey will never associate with you again after I form an inner product with my vector and an element of her dual space.

calculus 2

The correct answer.

This and then Galois Theory to top it all off

you forgot functional analysis, topology, differential geometry

Those can all be covered in graduate school. While you can take thirst costs as an undergrad if you wish, all you need is the basics

>ready for grad school
>no topology

Yeah no.

I'm assuming single variable calculus? Do some elementary linear algebra, vector algebra (honestly, you probably already know most of the previous two, but it helps to firm up the concepts), and a class in basic differential geometry. The obvious next step is multivariate calculus and a class on ODEs. You could (after multivariate calculus) do vector calculus, intermediate linear algebra (basically a more rigorous approach to concepts in elementary linear algebra like eigenvalues/eigenvectors, Markov chains, diagonalizable matrices/similar matrices, change of basis, etc.), a class in topology/real analysis (generally looking at open/closed intervals and how they relate to a rigorous approach to continuity, differentiability, and the intermediate value theorem), and an introduction to abstract algebra (groups, rings, modular arithmetic, etc.). After that it's up to you. I focused on number theory/basic cryptography and nonlinear systems and PDEs, but you could do more with real/complex analysis (hated analysis, avoided it like the plague), abstract algebra, linear algebra, mathematical modeling, etc.

> ODEs after real analysis
> systems of DEs after vector calculus

I mean, it would work, but this just seems so foreign to me.

Linear algebra. It's arguably the most important branch of mathematics.

Data structures, algorithms, then you can move onto machine learning, statistical learning, and other statistical methods. Youll get a job this way.

pre-calc

While this thread is up, what exactly does real analysis cover? Is it just Calc with proofs/rigor?

That's a lot of it. It's usually defined as real numbers/functions studied in a proof-heavy/rigorous way, so it's pretty broad and depends on your college/professor.

Completeness
Convergent sequences
Summable sequences
Continuitious functions
Differentiable functions
A couple different ways to define integrals
Some motivations to start studying topology
Proofs for all those theorems, rules, and criterons you learn in calc.

Wait, people do calc without proofs?

Make your own maths user.

I remember some weak proofs from precalc/calc, but I don't think we had the techniques to do most of them.

A few theorems being proved in lecture or in the book isn't really the same.

But, spivack contains proofs even if it's not that rigorous.

Differential Equations
Linear Algebra
Number Theory
Group Theory

These are the ones I use.

Differential geometry after you get the prerequisites learned.

It's just derivatives

>tfw you first isolated h in pre-calculus a long time ago
the reason to like math finally became clear

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