AI MATH 102
ai-math-102 · v1.0.0
ivyx✓
Mean, variance and the median that survives a millionaire; probability by counting and by seeded simulation; and gradient descent by hand, the slope-following loop machine learning repeats forever.
What this course is for
By the end of this course you can describe a dataset with mean and variance, estimate a probability by simulating it, and find the low point of a curve by following its slope, the move machine learning repeats forever.
What you will be able to do
- Compute mean, variance and standard deviation by hand, and say what one extreme value does to each
- Pick mean or median for a given dataset and defend the choice in words
- Get exact probabilities by enumerating outcomes, and estimates by seeded simulation
- Work a positive-test problem by counting a population, and dodge the base-rate trap
- Measure a curve's slope numerically and minimize the curve by stepping against it
Who it is for
Learners who finished AI MATH 101 and want the statistics and calculus that machine learning actually uses, taught by counting and stepping rather than by formula sheets
Before you start
- AI MATH 101, or comfort with loops, lists and functions
- No calculus and no statistics assumed
Lesson path
One number for a dataset, and what that number hides
- 1The mean and what breaks it30 min
Compute a mean by hand and predict what one millionaire in the room does to it
- 2Variance and spread30 min
Compute variance and std, and tell two same-mean datasets apart
- 3Choosing a summary30 min
Pick mean or median for a given dataset and defend the choice
Probability as counting, estimating, and not getting fooled
- 4Probability as counting30 min
Get exact probabilities for dice by enumerating outcomes
- 5Simulation30 min
Estimate a probability with random, seed it, and say how many runs it takes to settle
- 6The base-rate trap40 min
Work a positive-test problem and see why the intuitive answer is wrong
The derivative as a compass, and the loop that follows it
- 7The slope of a curve30 min
Compute a numerical derivative with (f(x+h)-f(x))/h and read its sign
- 8Follow the slope downhill45 min
Minimize y=(x-3)^2 by stepping against the slope, which is gradient descent by hand
About this course
AI MATH 102: Chance, averages and slopes
Eight lessons on the other half of machine learning's foundation. The first module compresses data into numbers (mean, variance, median) and teaches you which number is lying to you. The second does probability the honest way: enumerate when you can, simulate (with a seed) when you cannot, and count your way past the base-rate trap that fools intuition by a factor of eleven. The third measures the slope of a curve with nothing but subtraction and division, then puts that slope in a loop and walks downhill: gradient descent, by hand.
Everything runs on the Python standard library. Nothing to install, nowhere for the math to hide.
How this course teaches
Same tutor as PYTHON 101 and AI MATH 101: you predict before you run, and hints climb a ladder that ends in an explanation, never in pasted code. This course leans especially hard on cells that run correctly and report wrongly: a variance labelled with the wrong units, a poster quoting a true mean that misleads, a "99% accurate test" read as a 99% chance of being sick. The skill under training is deciding what a computed number actually claims.
What you will be able to do
- Compute mean, variance and standard deviation by hand, and say what one extreme value does to each
- Pick mean or median for a given dataset and defend the choice in words
- Get exact probabilities by enumerating outcomes, and estimates by seeded simulation
- Work a positive-test problem by counting a population
- Measure a curve's slope numerically and minimize the curve by stepping against it
The lessons
Describing data
- The mean and what breaks it
- Variance and spread
- Choosing a summary
Chance 4. Probability as counting 5. Simulation 6. The base-rate trap
Slopes 7. The slope of a curve 8. Follow the slope downhill
Where this course sits
Second mathematics course of the ivyx AI series, after ai-math-101. Its
final lesson, gradient descent on a parabola by hand, is the series
linchpin: pytorch-101 replays the exact same minimization with the
derivative automated by .backward(), so autograd arrives as relief rather
than magic. The evaluation discipline seeded here (seeds, trial counts,
base rates) becomes ml-101's core subject.