Note: This is not an exhaustive list of the basic subjects in mathematics and physics. Rather, this is just a collection of the posts on this blog that have tackled some of these basic subjects, and were written as more of introductions geared toward beginners. See also Book List.
Mathematics
Calculus
An Intuitive Introduction to Calculus
Linear Algebra
Vector Spaces, Modules, and Linear Algebra
General Topology
Basics of Topology and Continuous Functions
Abstract Algebra
Modular Arithmetic and Quotient Sets
Real Analysis
Metric, Norm, and Inner Product
Complex Analysis
Physics
Classical Mechanics
My Favorite Equation in Physics
Relativity
Quantum Mechanics
Some Basics of Quantum Mechanics
More Quantum Mechanics: Wavefunctions and Operators
Theories and Theorems 