- Telescoping sums
 - Division algorithm
 - Peano axions
 - Proof basics
 - Show that irrational
 - Voting systems
 - Weighings

# Beginners 1
Grades 2 - 4
 - Basic cyphers
 - Modular Arithmetic
 - Numbers in other bases



# Beginners 2:
Grades 4 - 6

 - Pidgeonhole principle
 - Combinatorics
  - N choose K (c and p)
  - stars and bars
 - Induction
   - Boosted induction (cauchy, etc)
 - Compass-and-Ruler constructions



# Intermediate 1:
Grades 5 - 7
 - Graphs
   - Instant Insanity
   - Euler walks and paths
   - Konigsberg
 - Logs & Slide rules
 - Vectors and Applications
 - Probability
   - Monty Hall problem



# Intermediate 2:
Grades 6 - 9



# Advanced 1:
Grades 9 - 10
 - Linear Algebra Basics
 - Graph Theory
   - Algorithms:
     - Ford-Fulkerson
     - Dijkstra
     - Minimal spanning tree
   - Three-color theorem



# Advanced 2:
Grades 11 - 12
 - Logic
   - Exists, forall, not. (Definable sets handout)
   - Mockingbird, lambda
 - Numerical cryptography
 - Group Theory
 - Understand Euler's Number
 - Relations