If you are an average maths undergraduate student (like me), you might have ended up in a situation of choosing between “just completing the degree by somehow passing the courses without caring about the grades” and “repeating a course/taking fewer courses so as to pass all courses with nice grades only”. Following is a nice discussion from Reddit:
Recently I completed all of my undergraduate level maths courses, so wanted to sum up my understanding of mathematics in the following dependency diagram:
I imagine this like a wall, where each topic is a brick. You can bake different bricks at different times (i.e. follow your curriculum to learn these topics), but finally, this is how they should be arranged (in my opinion) to get the best possible understanding of mathematics.
As of now, I have an “elementary” knowledge of Set Theory, Algebra, Analysis, Topology, Geometry, Probability Theory, Combinatorics and Arithmetic. Unfortunately, in India, there are no undergraduate level courses in Mathematical Logic and Category Theory.
This post can be seen as a sequel of my “Mathematical Relations” post.