Mike, the Mathematician

Rotation Matrices in Two Dimensional Space

Expected Value and Variance of the Gamma Distribution

Function of Bounded Variation are the Difference of Increasing Functions

The Binet Formula for the Fibonacci Numbers

Laplace Transforms

Inverse Laplace Transforms with Partial Fractions: Example 1

The Taylor Series of tanx

Vector Identities with Divergence and Curl

The Sample Variance and its Chi Squared Distribution

Courant Fischer Min-Max Theorem

Householder Transformations

The Polar Decomposition of a Matrix

Lagrange Polynomial Interpolation

Limit Superior and Limit Inferior of a Sequence

Distinct Eigenvalues Have Linearly Independent Eigenvectors

The Sylvester Matrix Equation Theorem

Properties of the Adjugate Matrix: Determinants and Products

The Axioms of a Probability Function

The Countable Union of Countable Sets

Solving an SDE with Itos Formula

Computing a Determinant by Considering a Special Product

Existence of Eigenvalues of a Self Adjoint Operator on a Real Vector Space

The Fourier Transform of a Gaussian Function

Finding the Median from a PDF: An Example

Iterated Limits Existing Does Not Imply the Limit Exists

Stock Prices as Stochastic Processes

The Matrix Exponential

The Sum of Exponential Random Variables with Moment Generating Functions

Chebyshev Polynomials

Finding the Covariance of Two Random Variables from the Joint PDF

The Sylvester Rank Inequality

A Visual Proof of the Arithmetic Geometric Mean Inequality

Law of Total Expectation: Example 1

Law of Total Expectation: An Example

Solving a First Order ODE by Substitution An Example

Law of Total Expectation

The Law of Total Variation

Some Standard Functions from Calculus

The Adjacency Matrix of a Graph and its Powers

Writing a Piecewise Function with the Heaviside Function

Linear Transformations Map Balls onto Ellipses: The Singular Value Proof

Lee Carter Method of Mortality Improvement

Chebyshev Polynomials of the Second Kind

Simultaneously Diagonalizable Matrices Commute and a Partial Converse

The Weierstrass Nowhere Differentiable Function

Schur Triangularization

The Nine Point Circle with Vectors

Unitary Equivalence of Matrices

The Cholesky Factorization

The Adjugate of a Matrix and Invertibility

The Arithmetic Geometric Mean Limit