handouts/notes/topics.md

• 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