Let's be honest, a lot of us math students are highly unmotivated from reading dull and terse textbooks as well as learning frustrating abstract mathematical concepts. It gets old and boring. Let's make it more fun shall we.
This is where I plan and post advanced math topics for beginner undergraduates or passionate high schoolers to read.
My whole goal is not only self-learn the topic but also make it more engaging and motivating to learn.
We're in the 2020s now, it's time we update our learning materials into something more purposeful and less "elitism".
Advanced Math Planning List:
Intro to Topology
Intro to Functional Analysis
Intro to Partial Differential Equations
Intro to Complex Analysis
Proof-Based Elementary Linear Algebra
Intro to Discrete Math
Intro to Boolean Algebra
Intro to Graph Theory
Intermediate Topics in Number Theory
Intro to Functional Equations
Intro to Laplace Transforms
Intro to Fourier Transforms
Intro to Z-Transforms
Intro to Non-Euclidean Geometry
Road to Calculus Olympiad (Putnam Level Training)
Intermediate Topics in Real Analysis
Intro to Vector Calculus
Advanced Linear Algebra
Advanced Number Theory
Intro to Differential Geometry
Intro to Galois Theory
Isomorphism Theorems
Intro to Sylow Theory
Intro to Free Groups
Intro to Representation Theory
Intro to Field Theory
Conjugation Group Theory
Solvable-Simple Group Theory
Nilpotent Group Theory
Semidirect Products of Group Theory
Intro to Module Ring Theory
Intro to Bessel Functions
Intro to Integral Equations
Intro to Harmonic Analysis