Road to understanding mathematics

This is my journey to learn and understand mathematics from the basics to the advanced level. This is to help me become better as a biologist who want to be a theoretical biologist and study evolution and stuff.

Aims to complete

1. Learn 10th class mathematics. -- Mainly Pre-calculus stuff This includes basic algebra, trigonometry, geometry, statistics and probability.

2. Learn 11th-12th class mathematics -- Basics done, working on harder parts. This includes better and deep learning of pre-calculus and calculus. Along with other important topics.

3. Undergraduate mathematics -- casually reading Napkin by Evan Chen, and complete udemy and courseara courses After undergraduate mathematics, the learning of advanced topics will be the emphasis.

4. Mathematical modelling for Biology(especially Evolution and Ecology)

Method of learning

• Solving problems and reading examples will be most important.

• Cannot move to the next step unless the understanding of the basics seems weak. Unlike a classroom method of studying for a year and moving to next year's syllabus.
  Self-paced learning of this type should emphasize understanding each example and topic properly and then moving on.

• After completion of each level of mathematics/bid topic, give myself a final self-exam, including all methods and examples in detail in each answer(godspeed, I am making things harder for me). *Self-checking along with taking help to check my exam if possible.

Notes will be written using LaTex/notes written on tablet(I prefer hand written than typed), there will be programming questions from Project Euler (To help in learning programming: Doing this using Julia, C and Rust[preference based on mood]) solved so I learn how to make cool graphs and show proofs using programming.

Topics studied till now

1. Linear algebra: Basics, including matricies, determinants, matrix algebra,etc
2. Calculus(Basics)
3. Sequence and series:Fundamental concepts, convergence tests, alternating series, series of a function and Taylor expansion.
4. Statistics: Hypothesis testing and error analysis, including all important statistical tests for parametric and non parametric tests.
5. Mathematics behind ML: on going; learnt about Linear Regression, Multiple Linear Regression, Non-Linear Regression, Logistic Regression, Classification, clustering, Principal component analysis, Reinforcement learning, transformers and neural networks. More depth is required.
6. Evolutionary game theory and Game Theory in general

Online resources related to maths(and a little extra)

1. https://proofindex.com/resources-for-undergrads
2. https://tutorial.math.lamar.edu/
3. https://web.evanchen.cc/napkin.html - Evan Chan : Napkin
4. Youtube: Michael Penn, 3blue1brown, Professor Leonard
5. Online courses: Coursera and Udemy(Hania Uscka-Wehlou)
6. Khan Academy
7. https://projecteuler.chat/index.php
8. https://www.feynmanlectures.caltech.edu/ : Some Physiscs is nice
9. https://github.com/ossu/math
10. https://aimath.org/textbooks/
11. https://www.mathsisfun.com/

Books used

1. Mathematical Techniques: D.W. Jordan and P. Smith
2. Mathematics for Machine Learning - Marc Peter D.
3. Mathematical modelling in Biology: Henson and Hayward
4. Evolutionary game theory by J McKenzie Alexander
5. Game-Theoretical Models in Biology: Broom and Raychtar
6. Other books I have pdf of, for what I could catch hold any resource of, are here. I plan to sort them into appropriate folders.