Year 1 Summary
Congratulations! You have completed the first third of the Architect Curriculum. Let's look at the pillars we've built:
- Algebra: You can solve for variables, manipulate exponents, and factor complex equations. You have the tools to handle physical constants.
- Functions: You understand that everything in the universe is a relationship between input and output.
- Trigonometry: You have mastered the circle and the wave—the two shapes that define every subatomic particle.
- Complex Numbers: You have unlocked the hidden dimension of "Phase" using \(i\) and \(e\).
- Limits & Series: You have touched the edge of infinity and learned how to approximate the real world.
The Ultimate Wave Formula
Everything you've learned in the last 120 lessons leads to this one expression for a quantum wave:
\[\psi(x, t) = A e^{i(kx - \omega t)}\]
- \(A\): Amplitude (from Algebra/Geometry).
- \(e, i\): The engine of phase (from Complex Numbers).
- \(k, \omega\): Spatial and Temporal frequencies (from Trigonometry).
What Comes Next?
In Year 2, we leave "Static" math behind. We will learn Calculus—the math of things in motion. We will learn how to calculate the rate of change of these waves and use Differential Equations to predict how a particle will move through a field of force. You have the language; now it's time to write the laws of the universe.