High-school bridge: High school and college bridge
Build the mathematical tools that causal and quantum models use. Work with numbers, vectors, functions, and uncertainty. Each calculation has a stated meaning. A correct calculation does not by itself prove that a model describes a physical system.
Lessons in this level¶
| Lesson | Objective | Lab |
|---|---|---|
| L3-01 · Complex numbers and phase | Calculate a complex magnitude and explain the difference between magnitude and phase. | Interference |
| L3-02 · Vectors and inner products | Normalize a vector and calculate its overlap with a basis vector. | Qubits and the Bloch sphere |
| L3-03 · Matrices as transformations | Apply a matrix to a vector and test whether a simple transformation preserves norm. | Qubits and the Bloch sphere |
| L3-04 · Tensor products and joint systems | Construct a joint vector and distinguish a product state from a correlated state. | Entanglement and Bell tests |
| L3-05 · Eigenvectors and observables | Find an eigenvalue and connect it to a possible measurement result. | Qubits and the Bloch sphere |
| L3-06 · Derivatives and gradients | Calculate a derivative and interpret a gradient as local change. | Variational circuits and gradients |
| L3-07 · Expectation and variance | Calculate a distribution’s mean and variance without treating the mean as a certain outcome. | Chance and repeated trials |
| L3-08 · Entropy and uncertainty | Calculate binary entropy and distinguish it from the value of one outcome. | Noise and quantum channels |
| L3-09 · Optimization and learning | Perform a gradient descent step and explain why a lower training loss is an incomplete success test. | Variational circuits and gradients |
| L3-10 · Estimation, intervals, and repeated tests | Estimate a probability and describe the sampling meaning of a confidence interval. | Chance and repeated trials |
Watch & listen¶
Complex number fundamentals | Ep. 3 Lockdown live math. 3Blue1Brown · 1h 22m · 2020. 3Blue1Brown live lecture on complex number fundamentals.
Vectors | Chapter 1, Essence of linear algebra: 3Blue1Brown- Linear transformations and matrices | Chapter 3, Essence of linear algebra: 3Blue1Brown
- What’s a Tensor?: Dan Fleisch
- The essence of calculus: 3Blue1Brown
- Solving Wordle using information theory: 3Blue1Brown
More for every level on the Watch and listen page.