Optimization for Data Science
Finding the best option among trillions: the engine that schedules airlines, prices markets, and trains models.
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Big Idea
The Math Underneath
Grade bands
K-2 · 3-5 · 6-8 · 9-12
AI literacy pillar
How AI works · Ethics
Lesson overview
Finding the best option among trillions: the engine that schedules airlines, prices markets, and trains models. This module climbs from an everyday intuition to the real mechanism, then names the Stanford course it descends from.
Teacher script · ~45 min
- 0–5
Hook
Optimization is just: get the most of what you want while obeying limits. Most profit, given a budget. Shortest route, given the roads. Once you can write down your goal and your constraints clearly, math can often find the genuinely best answer, not just a good guess.
- 5–15
Explore
Students do the activity in pairs: Graph 'x + y <= 10' and 'x, y >= 0,' then find the point maximizing x + 2y. It's a corner. Always a corner.
- 15–30
Explain
Some problems are 'convex': bowl-shaped, with one bottom you can reliably roll down to. Others are bumpy, full of false bottoms (local minima) that trap you. Knowing whether your problem is convex tells you whether 'just go downhill' will find the true best answer or fool you. ML lives squarely in the bumpy world, which is why training is hard.
- 30–40
Connect to the summit
Show students this is the real thing professionals build: MS&E211DS, the real thing. Finding the best option among trillions: the engine that schedules airlines, prices markets, and trains models.
- 40–45
Check
Run the formative check below. Anyone who can explain a key term in their own words has it.
Student activity
Graph 'x + y <= 10' and 'x, y >= 0,' then find the point maximizing x + 2y. It's a corner. Always a corner.
Slides
Formative check
- 1.In your own words, what is "Objective function"? (Looking for: The single quantity you're trying to make as large or small as possible.)
- 2.In your own words, what is "Constraint"? (Looking for: A rule the solution must obey, like a budget or capacity limit.)
- 3.In your own words, what is "Convexity"? (Looking for: A bowl-shaped problem with one true bottom, so 'go downhill' always works.)
Carry-away concepts
- Objective function
- The single quantity you're trying to make as large or small as possible.
- Constraint
- A rule the solution must obey, like a budget or capacity limit.
- Convexity
- A bowl-shaped problem with one true bottom, so 'go downhill' always works.
- Duality
- A mirror version of a problem that reveals the value of each constraint.
From the summit · the Stanford source
You formulate and solve linear, convex, and integer optimization problems, and connect duality and gradient methods to data science.
This module descends from MS&E211DS at Stanford. Students who climb the full ladder arrive here.