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Highlights for High School Home

High School Courses Developed by MIT Students

Lecture Notes

The lecture notes for lectures 4 and 5 are combined and appear in lecture 4 only.

Lecture notes files..
WEEK #	TOPICS
1	Introduction (PDF) Platonic solids - Counting faces, edges, and vertices Planar graphs, duality Euler's formula for planar graphs - A constructive proof Non-existence of a sixth platonic solid Proving non-planarity by counting
2	Counting 101 (PDF) First Law of Counting - Multiplying the possibilities Shepard's Law - To count the sheep, count the feet Counting by cases - Break it down and add it up Counting by subtraction - Cases to exclude
3	Counting Sets (PDF) Set theory and Boolean logic Inclusion/exclusion - Easy as PIE How many handshakes?
4	Counting Subsets (PDF) Binomial coefficients The wonders of Pascal's triangle Counting by block walking Counting by committee The most useful combinatorial identity known to man - "The Hockey Stick" The n days of Christmas
5	Problem Solving Applying what we know - Examples of counting How to recognize an apparently unfamiliar problem What to do when you are lost in the forest - How to get unstuck More examples - kids and candy, flower arrangements
6	Discrete Probability (PDF) Sample spaces and events Probability measures Sampling with and without replacement Conditional Probabiliity
7	More Probability (PDF) The Bernoulli process The Infinite Bernoulli process Analyzing games Solving problems
8	Graph Theory (PDF) A whirlwind tour Vertices, edges, degree, paths, cycles Connectivity and components Acyclic graphs - Trees and forests Directed graphs
9	More Graph Theory (PDF) Eulerian tours Graph coloring Ramsey Theory Turan's Theorem
10	Contest Problems A chance to tackle some real contest problems