Curriculum

Eight modules

Each one is built around a single recognition moment and takes two to three focused hours, with optional depth. Go in any order.

MODULE 1Suggested week 1~2.5 hNo prerequisites
Learning to Read Equations
Mathematics is a language for describing relationships.
$\sum_{n=0}^{4} 3n \;=\; \texttt{for}(n=0;\,n\le 4;\,n{+}{+})\ \texttt{sum += 3*n}$
Σ is an addition loop. Π is a multiplication loop. Most of what looks like a wall is a loop, a function call or a ratio.
MODULE 2Suggested week 2~2.5 hBuilds on 1
The Physics of Systems
The universe operates through relationships, constraints, and change.
$F = ma \;\Longleftrightarrow\; \texttt{velocity += (force / mass) * dt}$
Newton’s second law is an update rule. Every physics simulation, and every training loop, is a loop that nudges state by a rate times a timestep.
MODULE 3Suggested week 3~2.5 hBuilds on 1
Biology as an Information System
Life is a collection of interacting, evolving systems.
$\text{DNA} \xrightarrow{\ \text{transcribe}\ } \text{RNA} \xrightarrow{\ \text{translate}\ } \text{protein}$
The genetic code is a lookup table: three letters in, one amino acid out. But the cell that runs it is not a computer. It is chemistry that happens to process information.
MODULE 4Suggested week 4~3 hBuilds on 1
Probability, Entropy, and Information
How science measures uncertainty.
$H = -\sum_i p_i \log_2 p_i \;=\; \texttt{for (p of probs) H -= p * log2(p)}$
Entropy is a loop over outcomes: for each one, weight its surprise by how often it happens. The same loop is your language model’s training loss.
MODULE 5Suggested week 5~2.5 hBuilds on 1, 4
Complexity and Systems Thinking
Simple rules can produce surprising collective behaviour.
$p(k) \propto k^{-\gamma}$
A straight line on a log-log plot is a fingerprint, not a confession. Very different machines leave the same print.
MODULE 6Suggested week 6~3 hBuilds on 1, 4
The Mathematics Inside Modern AI
Decode the equations behind the models.
$\theta_{t+1} = \theta_t - \eta\,\nabla_\theta \mathcal{L}(\theta_t)$
Training a model is one line in a loop: look downhill, take a small step, repeat a few trillion times.
MODULE 7Suggested week 7~3 hBuilds on 2, 3, 4, 5, 6
The Physics–Biology–AI Connection Lab
Recognise common structures without manufacturing false equivalences.
$\text{same notation} \;\not\Rightarrow\; \text{same mechanism}$
The skill is not finding connections, which is easy. It is grading them.
MODULE 8Suggested week 8~2.5 hBuilds on 4
The Scientific Skeptic’s Toolkit
Distinguish genuine connections from beautiful nonsense.
$P(\text{true} \mid \text{published}) \neq P(\text{published} \mid \text{true})$
Most bad arguments are made of true sentences. The skill is finding the exact sentence where evidence stops and story begins.