I had some mathematics education during my high school and Electrical Engineering studies, but I never used any of them during my career as a software professional. Now I am again coming across Linear Algebra, complex numbers and Calculus while learning certain topics in computer science such as Quantum Computing and Machine Learning.
Where I did my studies, maths education was pathetic as we were taught in a way that barely helps to develop intuition and real appreciation for the subject. I had to do rote learning all of the matrix operations and formulas and differentiation rules. Same with Fourier transformation etc which I can vaguely remember. Then we repeatedly solved problems using an outrageous number of sample problems so that you can score in the exam.
That is why my maths knowledge is very poor for the level I was formally educated and I realized that in-order to be able to do good quality work in the future using mathematics as a tool, I need to reeducate myself.
After doing scores of hours of curriculum and text book research and course auditing, I compiled a list of courses and text books suitable for self study at my level.
My curriculum is below:
- Single Variable Calculus - MIT OCW and textbook by James Stewart, 8th ed
- Discrete Mathematics - MIT OCW and corresponding textbook from them
- Linear Algebra - MIT OCW and textbook by Gilbert Strang
- Multi Variable Calculus - MIT OCW and James Stewart, 8th ed
- Differential Equation - edX (textbook not decided yet, probably Stewart is enough)
- Matrix Methods in Data Analysis, Signal Processing, and Machine Learning - MIT OCW and a new textbook from Strang
- Linear/Non linear/Convex Optimization - edX
- Introduction to Complex Analysis - coursera
- Probabilistic Systems Analysis and Applied Probability - MIT OCW and textbook by Bertsekas
- Statistics for Applications - MIT OCW and textbook The elements of statistical learning
I made this "semester" thing based on the idea that all of these single courses are covered in a single semester in a college. There are also some rough estimation from course creators on effort needed to self study the topic - which is usually around 150 hours.
I am 2-3 months into this process and now I am realizing that I won't be able to cover a given course in 150-200 hours which I had allotted. The problem seem to be doing exercises, especially what I consider as difficult ones. As an example, Discrete Mathematics book had an innocent looking problem "Prove that $\sqrt2 ^ \sqrt2$ may be rational using Proof by cases"
This is one of the 50 or so problems given and this alone took me a few hours and a whole lot of new insights such as transcendental numbers, Gilfond't constant etc. That's great, but I would be done in...may be 4 years instead of 2 I had planned.
So my question is - where do I draw lines when it comes to exercises and how do students/professors in good Western universities manage to finish a course in a single semester? Do they just do only part of the textbook? What about problems? Attempting only some of the similar problems sound reasonable, but what if they are very diverse and interesting questions? As I am detached from formalized education for too long, it would be appreciated to get some insights into these issues.