a list of textbooks, workbooks, and some notes on the math you ought to know
I got this idea from Cosma. There seems to be a very wide range of people who have a fundamental misunderstanding of what it is that a mathematician does, and how that does or does not relate to the mathematics they desire to Learn. I always reccomend a goal oriented learning. As an example for something like Competitive Programming, I would reccomend learning Discrete Mathematics, and Algorithms. For something like Data Science, I would reccomend learning Statistics, and Linear Algebra. Your required prerequisites, and the overall depth of knowledge you will need to achieve vary greatly depending on your goals. Once you have however identified your goals. The question becomes, what is it that I ought to know? That is what this page is for. A list of some of the textbooks I believe carry value in each of the categories you could possibly want to Learn.
If you have anything to add please fill out the contact form. Be specific, and mention it is for a book suggestion for this exact list. If you have a good suggestion, chances are it will end up on the list. I don't have enmity towards any book or author. I completely understand that different people have different learning styles and preferences, and what works for one person may not work for another. That being said, I do believe that there are certain books that are universally valuable for anyone looking to deepen their understanding of mathematics.
Please take not that this is not a curriculum meant to be followed in any particular order. Rather it is a list of books grouped by category, that I believe are the best in their respective categories. I have tried to include a wide range of topics, from the most basic to those needng the most prerequisites.
Suggestions from tons of mathoverflow, mathstackexhange, mathematics discord, and reddit users have been a massive help. I will try to link of the relevant threads, and discussion here as I find them.