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- Contributed By: TorquedEllipse (NYC)
These are lecture Notes for Week 1 of Combinatorics - The Fine Art of Counting.
Topics include:
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
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are homework assignments for Week 1 of Combinatorics -The Fine Art of Counting. Solutions are posted as a separate file, labeled "Homework Solutions, Week 1"
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are solutions for the homework assignment given in Week 1 of Combinatorics: The Fine Art of Counting.
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are lecture Notes for Week 2 of Combinatorics - The Fine Art of Counting.
Topics include:
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
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are homework assignments for Week 2 of Combinatorics -The Fine Art of Counting. Solutions are posted as a separate file, labeled "Homework Solutions, Week 2"
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are solutions for the homework assignment given in Week 2 of Combinatorics: The Fine Art of Counting.
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are lecture Notes for Week 3 of Combinatorics - The Fine Art of Counting.
Topics include:
Set theory and Boolean logic
Inclusion/exclusion - Easy as PIE
How many handshakes?
This resource is part of the Combinatronics – The Fine Art of Counting collection.
"The Final Challenge - Part One": is an in-class assignment composed of a set of 26 word problems, to be given to students during Week 3 of Combinatorics: The Fine Art of Counting.
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are homework assignments for Week 3 of Combinatorics -The Fine Art of Counting. Solutions are posted as a separate file, labeled "Homework Solutions, Week 3"
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are solutions for the homework assignment given in Week 3 of Combinatorics: The Fine Art of Counting.
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are lecture notes for Weeks 4 and 5 of Combinatorics - The Fine Art of Counting.
Topics for Week 4 (Counting Subsets) include:
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
Topics for Week 5 (Problem Solving) include:
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
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are homework assignments for Week 4 of Combinatorics -The Fine Art of Counting. Solutions are posted as a separate file, labeled "Homework Solutions, Week 4"
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are solutions for the homework assignment given in Week 4 of Combinatorics: The Fine Art of Counting.
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are homework assignments for Week 5 of Combinatorics -The Fine Art of Counting. Solutions are posted as a separate file, labeled "Homework Solutions, Week 5"
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are solutions for the homework assignment given in Week 5 of Combinatorics: The Fine Art of Counting.
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are lecture Notes for Week 6 of Combinatorics - The Fine Art of Counting.
Topics include:
Sample spaces and events
Probability measures
Sampling with and without replacement
Conditional Probability
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are sample problems for Week 6 of Combinatorics: The Fine Art of Counting.
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are homework assignments for Week 6 of Combinatorics -The Fine Art of Counting. Solutions are posted as a separate file, labeled "Homework Solutions, Week 6"
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are solutions for the homework assignment given in Week 6 of Combinatorics: The Fine Art of Counting.
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are lecture notes for Week 7 of Combinatorics: The Fine Art of Counting. Topics include: The Bernoulli process The Infinite Bernoulli process Analyzing games Solving problems
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are group activities for Week 7 of Combinatorics: The Fine Art of Counting. Included are the following activities: Chinese Dice "Craps" "Set" Winning Streak
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are lecture notes for Week 8 of Combinatorics - The Fine Art of Counting.
Topics include:
A whirlwind tour
Vertices, edges, degree, paths, cycles
Connectivity and components
Acyclic graphs - Trees and forests
Directed graphs
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are homework assignments for Week 8 of Combinatorics -The Fine Art of Counting. Solutions are posted as a separate file, labeled "Homework Solutions, Week 8"
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are lecture notes for Week 9 of Combinatorics: The Fine Art of Counting. Topics include: Eulerian tours Graph coloring Ramsey Theory Turan's Theorem
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are homework assignments for Week 9 of Combinatorics -The Fine Art of Counting. Solutions are posted as a separate file, labeled "Homework Solutions, Week 9"
This resource is part of the Combinatronics – The Fine Art of Counting collection.
This is the classroom assignment for Week 10 of Combinatorics: The Fine Art of Counting. Solutions published here separately as "Class Contests, Week 10: Solutions"
This resource is part of the Combinatronics – The Fine Art of Counting collection.
These are solutions for the in-class assignment for Week 10 of Combinatorics: The Fine Art of Counting.
This resource is part of the Combinatronics – The Fine Art of Counting collection.
