Learning Roadmap
My plan how to learn math:
Since I had to fill many gaps, I bought some school books to solve basic problems and first get a better math intuition. Since problem-solving is the key
to gain a good understanding and intuition I started with that.
I also used Khan Academy where I revised fundamentals as well.
In parallel, I wanted to start all over with proving, and therefore I started working through How to Prove it.
When I am done with that, I planned to continue with Understanding Analysis and eventually dive into a calculus book that has more exercises and less rigorous proofs. The idea behind that is, to gain more intuition from the exercises and apply it to the rigorous theory of analysis and especially the proofs in ‘Understanding Analysis’.
During the time, when re-learning analysis I will also study discrete math and will eventually learn with Discrete Mathematics with Applications.
After working through analysis and discrete math, I plan to continue with linear algebra. Therefore, I will be using Linear Algebra Done Right. While studying linear algebra I will try to take the same approach as in analysis and will look for a book to solve exercises regarding linear algebra in parallel to the rigorous proofs.
After finishing the core subjects above I will either go for A Geometrical Approach to Differential Equations or I will straight jump into abstract algebra with Contemp Abstract Algebra.
As soon as I finish abstract algebra I will jump into topology and will therefore use Topology through Inquiry and after that I wanted to continue with an introductory course to manifolds. For this reason, I will use An Introduction to Manifolds. As soon as I finish this course I will continue my journey in analysis and will study complex analysis with the book Visual Complex Analysis.
If everything went well I will take a look, if I want to eventually specialize more into one of the topics above or I will continue with differential equations.
This would be the basic outline of my journey. Keep in mind that I will edit this site if my path changes and also the books I actually use could eventually differ. I will update any change regarding books or if I switch the order of subjects I learn!