Explore Mathematics Beyond the Formulas

Combining functions through composition and operations - Explore how one function’s output becomes another’s input, how multiplication and division create new functions, and which outputs those functions can produce.

Modeling motion through mathematics - See how gravity and velocity determine an object's motion, while quadratic equations reveal its displacement, flight duration, and the domain of its height function.

Finding the domain and range of a function - See how a square-root condition determines its allowed inputs, while inequalities and a reverse check reveal every output it reaches.

Finding the extrema of a nonlinear function - See how critical points, the second derivative test, and endpoint values reveal its local and absolute maxima and minima.

Finding a basis for the null space using RREF - See how free variables and linear combinations reveal the basis of a matrix's null space.

Using RREF to uncover the structure of a matrix - See how basis, row space, column space, and rank reveal the fundamental structure of a matrix.

A simple breakdown of the product and chain rule - See how these fundamental differentiation techniques work together to find the derivative of a function.

A simple breakdown of damping differential equations - See how the mathematics of mechanical vibrations can be applied to model portfolio movement and mean reversion.

A simple breakdown on the characteristic equation - Learn how a simple derivative property leads to the solutions of a homogeneous differential equation.

A simple breakdown on reduced row echelon form - Learn how row reduction reveals the solutions to a system of equations.

A simple breakdown of portfolio optimization - Learn how the Simplex Method can find the optimal investment allocation.

A simple breakdown on annualized returns - Learn how mathematics can help you understand investment returns.

A simple breakdown on models - Find out what makes Investment Optimization app so powerful.

A simple breakdown on learning how to invest - Learn the game of investing.

A simple breakdown on portfolio statistics - Find out the statistical questions people ask when evaluating their portfolio.

A simple breakdown on ETFs - Find out why people use these powerful tools.

A simple breakdown on compound interest - Find out what compounding can do.

A simple breakdown on framing - Find out what framing actually is.

A simple breakdown on optimizing - Find out what optimizing means today!

A simple breakdown on accounting - Find out why accounting can become very complicated.

A simple breakdown on bookkeeping - Find out why bookkeeping is very important.

A simple breakdown on asset structures - Find out how you may be optimizing your portfolio wrong.

A simple breakdown on why I built IO - Find out the “money“ issue still going on in the world.

A simple breakdown on why analysis is of utmost importance - Find out another hidden secret within your portfolio.

A simple breakdown in tribute to Mother’s Day - Find out the secret to portfolio success.

A simple breakdown of how theories work - Find out why they are often misunderstood and the difference between theories, conjectures, and propositions.

A simple breakdown of how linear regression works - Find out how asset returns, market returns, asset-market impact, baseline behavior, and the concept of “noise“.

A simple breakdown of how portfolios actually work - From returns to risk and diversification.