You first need to define your boundaries and limits. Don't get me wrong, but mathematics is grinding, and if you think you have an idea where you're getting you

You first need to define your boundaries and limits. Don't get me wrong, but mathematics is grinding, and if you think you have an idea where you're getting yourself into because you've studied calculus and algebra as an undergrad CS, you will fail miserably. Don't make the same mistake I did :) Undergrad math is tooling; I like to use the analogy that it's like entering a workshop where you have all the tools available, but you're blindfolded, and you have no idea what each stuff is used for. So you'll have to touch everything. Look down for the tooling advice. When venturing in Mathematics, for your own sanity, please have an objective in mind. I'm down serious! Understand what you want to research and go in that direction. One last piece, Find a mentor, share, talk to people. You won't advance from yourself. As a piece of tooling advice, I have the following I've stolen from Reddit a few years ago (sorry I haven't found the source to it) __ TOOLING __ First of all, most important, GO LEARN ALGEBRA. Seriously, I know you think its bullshit but its the most basic skill in some ways that any mathematician should know. Second learn Calculus: Single and Multivariable. If you are still interested here are some things to go onto next: Discrete mathematics: This includes equivalence relations (probably one of the most important things for you understand ever), propositional calculus (logic) proof techniques (induction) and some basic combinatorics (Pigeonhole principle). You can literally find any textbook and start reading. The theory is kinda a hodgepodge, but those are the major themes. Linear Algebra: Again, one of the most important subjects you will ever study. Once you understand this, you are really on your way, and this stuff comes up everywhere. Many mathematicians have said many of the biggest proofs in the world come down to "just some linear algebra". The major point here is to understand that there is only one vector space for each dimension over a field and understand how a linear transformation becomes a matrix only after a choice of basis. Here equivalence relations come up again! Differential equations: Unless you're focused on engineering math or serious applied stuff, don't worry too much about this. Seriously, it's not that integral (haha get it!). Complex Analysis: Yes, mathematicians and Engr. Actually, do study "imaginary" numbers, but there is nothing imaginary here. This is serious stuff, do it. Okay, so now you're about as a sophomore/junior level place in mathematics. How to finish it off? It's not that unclear: Abstract Algebra -- Grab any book read about groups, rings, fields, vector spaces, and modules. Proofs will be difficult here but work through it. There are so many books here, avoid Lang (good book but not for starting out), Dummit/Foote is okay. As a undergrad I had a good time with Rotman's An introduction to abstract algebra. Analysis -- Grab Baby Rudin. No seriously, Grab this book, sit in a room for a semester and just fuckn' read it. You will basically be "redoing" calculus. This is a trial by fire, go! Topology -- Grab Introduction to Topology by J. Munkries. Its so well written it might as well be a coffee table book. There now, you have done everything a math major would. Yes, there are lots of things that are missing, arguably the most important things depending on what your goals are. Typically one studies Number Theory along with Abstract Algebra, or studies Analysis and Differential Equations together or Analysis and Topology. Seeing the links across different topics is essential, but I'm just giving the overview here. Not every mathematician studies logic, and there are LOT of fringe topics that I'm omitting (including some of my favs: Projective Geometry, Varieties, Lattice/Order theory, Combinatorics, Elliptic Curves, Coding theory, Harmonic Analysis, etc.). However, none of these are required courses at more than a 1% of programs