Assume someone has very limited knowledge of math. (low level high school, 5-6 years ago) How would they learn from the basics of algebra, geometry and trigonometry to a solid foundation for calculus and beyond? I would like to relearn math and eventually go to university for computer science but my math currently lacks significantly.
I am looking for book recommendations, math learning strategies (how to comprehend math text’s mainly), and a brief explanation as to how one knows when they are ready to learn calculus.
However as my math lacks, I have found some books language quite overwhelming, how can I better understand the language?
How essential is geometry for calculus? What about for further math such as linear algebra, discrete math or differential equations? Is it a must learn?
How can I make sure that what I am reading / learning will stick? How can I maximize comprehension of a textbook and rules / definitions? Is note taking out of a textbook effective?
Is it essential to master high-school math before attempting calculus or can holes be patched in the process of learning calculus?
I am not simply looking for youtube videos, though they are useful I want more substance than simply being spoon-fed.
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.
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!
Currently relearning HS Math myself. My current reading list is:
Serge Lang – Basic Mathematics
I.M. Gelfand – Algebra
I.M. Gelfand – Trigonometry
George F. Simmons – Precalculus in a Nutshell