11 core topics
+ 22 prerequisite topics taught
as needed · approximately 8 hours of instruction
including spaced review
An adaptive diagnostic (up to
40 questions) places the student on the course's knowledge
graph — topics already known are credited, and instruction begins exactly
at the learning frontier. Every topic is taught with a worked-example
lesson and auto-graded practice; a topic is mastered at
75%+ and then maintained through spaced reviews on an
expanding schedule. A cumulative quiz follows every 6
lessons. Prerequisite gaps below the course are detected and taught rather
than skipped, so completion certifies the whole tower, not just the top.
| Mean, Median & Range
[E] |
Center and spread in one pass. |
| Variance & Standard Deviation
[M] |
Average squared distance from the mean — then unsquare. |
| Probability Basics
[E] |
Favorable over total, when outcomes are equally likely. |
| Addition Rule & Complements
[M] |
P(A or B) adds, then removes the double-counted overlap. |
| Conditional Probability
[M] |
Probability after narrowing to a sub-population. |
| Independence & the Multiplication Rule
[M] |
Independent events multiply. |
| Bayes' Theorem
[H] |
Reverse a conditional: update a prior with evidence. |
| Expected Value
[M] |
The probability-weighted average outcome. |
| The Binomial Distribution
[H] |
Count the arrangements, multiply the per-path probability. |
| Normal Distributions & z-Scores
[M] |
Standardize, then use the 68–95–99.7 rule. |
| Correlation & Regression Lines
[M] |
The best-fit line predicts; its slope is the per-unit effect. |