I would say that you want to focus on what brings you success in your goals for getting a computer science degree.
If you look at a CS program, there are some commonalities, but also differences in how much math they want you to learn. Do you have a specific program in mind? Did you review their prerequisites and the courses you will be required to take? Are you thinking of going to graduate school too as there may be different considerations?
The typical math classes required for a CS major are (check the university/college you are thinking about and make sure you understand their requirements) as follows.
- Discrete Math: Topics include combinatorics, number theory, and graph theory with an emphasis on creative problem solving and learning to read and write rigorous proofs.
- Computability and Logic: An introduction to some of the mathematical foundations of computer science, particularly logic, automata, and computability theory.
- Algorithms: Algorithm design, computer implementation, and analysis of efficiency. Discrete structures, sorting and searching, time and space complexity, and topics selected from algorithms for arithmetic circuits, sorting networks, parallel algorithms, computational geometry, parsing, and pattern-matching.
- Mathematical Analysis I: Analysis of the real numbers, and an introduction to writing and communicating mathematics well. Topics include properties of the rational and the real number fields, the least upper bound property, induction, countable sets, metric spaces, limit points, compactness, connectedness, careful treatment of sequences and series, functions, differentiation and the mean value theorem, and an introduction to sequences of functions.
- Numerical Analysis: An introduction to the analysis and computer implementation of basic numerical techniques. Solution of linear equations, eigenvalue problems, local and global methods for non-linear equations, interpolation, approximate integration (quadrature), and numerical solutions to ordinary differential equations.
- Scientific Computing: Computational techniques applied to problems in the sciences and engineering. Modeling of physical problems, computer implementation, analysis of results; use of mathematical software; numerical methods chosen from: solutions of linear and nonlinear algebraic equations, solutions of ordinary and partial differential equations, finite elements, linear programming, optimization algorithms and fast-Fourier transforms.
- Abstract Algebra I: Groups, rings, fields and additional topics. Topics in group theory include groups, subgroups, quotient groups, Lagrange's theorem, symmetry groups, and the isomorphism theorems. Topics in Ring theory include Euclidean domains, PIDs, UFDs, fields, polynomial rings, ideal theory, and the isomorphism theorems. In recent years, additional topics have included the Sylow theorems, group actions, modules, representations, and introductory category theory.
Some CS majors are doing dual CS/Math and additional math courses like Probability, Analysis, Complex Variables, Differential Equations, Partial Differential Equations may also be required.
As for books, I would recommend perusing some of the wonderful MSE responses, for example:
You mentioned this, but I think it is important. You may want to go through entire courses using opencourseware. For example, MIT. See the OCW Consortium for many more institutions. The goal of this is to gauge where you are with following lectures and testing your understanding.
So, if you look at the specific program you are interested in, I would recommend looking at the math courses in totality (including if you want graduate), checking their required books and looking to see where you stand with all of it. Recall, these programs are also heavy into programming and that is a lot of work, so make sure you are ready for both!
If you've worked through the majority of Apostol, then I highly recommend Hubbard and Hubbard's Vector Calculus, Linear Algebra, and Differential Forms. (Get it straight from the publisher; much cheaper than elsewhere). It is written very well, with the reader in mind. You'll learn linear algebra and some other requisites to start with. From there, you learn a bit of very basic topology and you end up doing some differential geometry-esque stuff later. There is SO much in this book... you could study it for a couple of years (especially if you dig into the appendix). Moreover, despite its rigor, there are many applications (that are actually very interesting).
As well, there is some courseware from Harvard that uses this book (look for Math 23a,b and Math 25a,b). And there is a (partial) solutions manual floating around.
You might also like to read:
-Set Theory and Metric Spaces by Kaplansky
-anything from the New Math Library (from the MAA)
-Particularly Basic Inequalities, Geometric Transformations, or Mathematics of Choice.
-the linear algebra in Apostol (be sure to get Vol 2 also!)
-the whole second volume of Apostol!
-Discrete Mathematics by Biggs (get the first edition!)
-Finite Dimensional Vector Spaces by Halmos,
-Principles of Mathematical Analysis by Rudin with this and this and these awesome lectures.
-Algebra by Artin is amazing, but hard! Enjoy these lectures. Vinberg's algebra text is supposed to be amazing and in a similar flavor to Artin (but a bit more gentle).
And you might also like these (great) reading lists:
-PROMYS
-Chicago Undergraduate Mathematics Bibliography
Best Answer
It is perfectly normal for humans to forget things after a period of time. However, here are some tips to help you "relearn" the material you have forgotten.
From your question, I understand that most of your learning came from KhanAcademy. While KhanAcademy is a great learning tool, it was never intended to replace a full year-long (or semester-long) course. Instead, it is mostly used as a supplement to reinforce concepts learned in the classroom.
Khan Academy is a great tool; however, it should not comprise the majority of your work on a subject. If you still have your high school textbooks, dust off the cover and reread them. Do the exercises at the end of each chapter - I know most textbooks have answers to odd-numbered questions. If you can't do a question, ask for help (like here!)
If you don't have them anymore and you don't want to buy a $200 textbook, you can get free exercises online. Just search up, say, "trigonometric identities practice" or "polar equations review problems". The more math you do, the better you will become.
In the beginning, it will be tough. You might be frustrated, and it might seem like you aren't making any progress. However, it will get much easier as you progress, and you might even find yourself enjoying the problems that you are doing.
But no matter what, don't procrastinate! The sooner you start, the more you will learn. And the more you do, the better you will get. You shouldn't have to memorize formulas by heart, strive for understanding, not for memory. For example, consider all those complicated trigonometric identities like $\sin(x+y)=\sin x\cdot\cos y+\sin y\cdot\cos x$ Do not memorize these formulas; instead, understand why they are true. Only this way will you be able to remember them.
Good luck, and have fun with the problems! :)