Calculus Is Just Linear Algebra
An introduction to functional analysis
Higher Math
Itô's lemma and the Itô Differential Mapping
Deriving Itô’s Lemma and analyzing the Itô ’d’ operation as a formal linear mapping.
Conditional Expectation as a Least Squares Approximation
Conditional Expectation defined as an optimal predictor for a random variable through orthogonal projection
Proof of Equal Number of Odd and Even Permutations using Determinants
A proof of the equinumerosity of the number of odd and even permutations via determinants.
Overview of Modern Mathematics
A survey of some important modern mathematical fields and their applications.
Key Concepts in Abstract Algebra
A list of key concepts in abstract algebra with concise natural language definitions.
Function Bases
A Linear Algebra Perspective on Infinite-Dimensional (Function) Spaces
Basic Concepts in Information Theory
A brief overview of some important concepts in information theory.
Understanding KL-Divergence
An interpretation and explanation of the KL-divergence (Kullback-Leibler divergence) via probability theory.