I want to self study a math major, for my own self respect. But

start by telling us what is your background and, since you don't want to learn everything, what is your interest? (analysis/algebra/geometry/foundations/statistics or whatever)

Some of the MIT Open Courseware classes are pretty decent. If you look up a topic and see that they have several semesters archived, look for one that's labeled "OCW Scholar" if you want the one that's most geared to online study; it will have assignments and exams for you to practice and test yourself, and also have videos from the recitation section.

Start with Calculus I, and then after that see what courses have that as a pre-requisite and go where you like.

A good and useful practical core to start with is:

Calculus I (single-variable)
Calculus II (multivariate)
Linear Algebra
Differential Equations
Introduction to Probability and Statistics

If you get serious about math it eventually starts leading to some high courses where you write a lot of proofs, and then it can get really interesting. A good course from the MIT selection that will get you started on that and have some practical application is their "Mathematics for Computer Science" course. I took some courses on discrete structures, algorithms, and theoretical computer science in college and they were really interesting.

Another route to higher math is "Book of Proof" by Richard Hammack.

>>8847973
I'm a CS major who wishes he was a math major but is happy that I can actually make money unlike you guys, but also wishes he was a math major

The most math I know is Calc 3 but I forgot most of it, I only know Calc 2 for sure

I would want to learn the most important math major topics regardless of whether I like them, but my personal interest would lean towards physics simulations and computational fluid dynamics in the end, also circuit simulations. This requires physics as well after I guess.

>>8848004

Protip:

1. Look at the grad school catalog of your own or a really good university.
2. Look at the math prerequisites.
3. Take those now or for non-degree credit after you graduate.
4. Apply to graduate school.
5. Now you can profit off all that!

I just got into a graduate program and all these people talk about how they didn't have as much math as they'd like to have for some of these really advanced courses - you can have fun and make it pay off. P.S. If you really want to work on the interesting stuff, get a master's.

>>8848004

P.S. If you haven't taken linear algebra, that's the one that will give you the most bang for your buck if you study machine learning, graphics, computer vision, image processing, and the like later.

>>8847953

There is no set math major, it's mostly electives. The core subjects are:

Single Variable Calculus
Multivariable and Vector Calculus
Ordinary Differential Equations
Matrix Algebra
Applied Linear Algebra
Finite Vector Spaces
Complex Variables or Complex Analysis
Fourier Transforms or Fourier Analysis
Partial Differential Equations
Proofs and Mathematical Reasoning
Probability (Multivariable Calculus based)
First Year Algebra (Undergrad)
Real Analysis (Metric Space based)
Analysis on Manifolds
Point-set Topology

Corresponding books here:
http://4chan-science.wikia.com/wiki/Mathematics

>>8847953

Not necessarily textbooks, but a core of content, especially given your request:

A calculus I/II sequence.

A course in elementary linear algebra. Pick up the basic jargon and crunch the numbers and do the theory. This one might be the easiest to do under your own power and really "get".

Some vector/multivariable calc. Glimpse the jewels (Gauss'/Green's/divergence theorems).

Foundations (naive set theory, understanding that naive set theory fails, mathematical logic, cosets, relations, what a function actually is, that type of thing. It turns out that Bertrand Russell was actually quite right and somewhat relevant after all.

Algebra. College level algebra where you take the basic number system ideas of the integers/real numbers etc and check out related number-systems. GROUPS, RINGS, FIELDS.

some exposure to DEs and concepts around them (truncate this at will. There is this thing call the wronskin which might be good to know).

There remain topics like geometry, analysis (as opposed to calculus)...

LoOK up undergrad programs. At the very least you need

Calc 1,2
Diff eq
Multivarable Calc
Foundations
Linear algebra
Discrete and or statistics
Real analysis

You should study in that order too. Taking linear without multivariable and diff eq is doable but you can't really understand the motivation for the theorems.

Then you can study
College algebra
College geometry
Topology
Complex analysis
Numerical analysis

Depending on what you like the most.

>>8849307
>Taking linear without multivariable and diff eq

Linear algebra is about solving systems of linear algebraic equations. That is completely independent of calc.

>>8849307
>Taking linear without multivariable and diff eq

what? it's the other way around. like, how do you wanna understand differentiablity if you don't know what a linear map is?

>>8849307
>Foundations
>Discrete

Wut?

>College algebra

That doesn't mean what you think it means.

>College geometry

The only ones that are required to take that are future high school math teachers.

>>8847953
Core subjects and my personal recommendations:

Linear Algebra (Hoffman & Kunze)
Real Analysis (Tao 1/2)
Topology (Munkres)
Algebra (Rotman "A first course...")
Complex Analysis (Ahlfors)
Differential Geometry (Presley)
ODEs (Hirsh & Smale)

I would say this is a good core

>>8851225
>Rotman

Shit.