Advanced Math
Very few people have the ability to work in areas of advanced mathematics and therefore never get to experience the magnificent beauty of its topics, among which the following are typically included:
 Logic
 Methods of Proof
 Set Theory
 Cartesian Products and Functions
 Relations
 Cardinality
 Number Theory
 Rings and Integral Domains
 Limits and the Real Numbers
 Second and HigherOrder Linear Ordinary Differential Equations
 Systems of Ordinary Differential Equations: Phase Plane: Qualitative Methods
 Series Solutions of Ordinary Differential Equations: Special Functions
 Laplace Transforms
 Linear Algebra: Matrix Eigenvalue Problems
 Vector Differential Calculus
 Vector Integral Calculus
 Fourier Series, Integrals, and Transforms
 Complex Integration
 Power, Taylor, and Laurent Series: Residue Integration
 Complex Analysis and Potential Theory
 Numerics for Ordinary and Partial Differential Equations
 Unconstrained Optimization: Linear Programming
 Graphs: Combinatorial Optimization
 Mathematical Statistics
 Vector Analysis
 Multiple Line and Surface Integrals and Integral Theorems
 Complex Variables and Conformal Mapping
 Complex Inversion Formula for Laplace Transforms
To keep up to date with the latest work in advanced math, you must read the Journal of Advanced Mathematics and Applications. There are also a small number of tutorial websites that cover advanced math topics, one of which has advanced calculus tutorials.
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