Added notes

.gitignore

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 *.fls
 *.fdb_latexmk
 *.dvi
-*.xdv
+*.xdv
+
+# Do not ignore any notes
+!/notes/**

notes/TODO.md

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+
+# Game ideas
+ - Math dominos:
+   - Each problem is a domino tile, by difficulty.
+   - Score is sum if 1st try, max if 2nd try. Subtract min if no solution.
+   - Each team can have 2-3 dominos at a time. No free swaps.
+   - Pick up dominos without knowing problem.
+
+ - что-где-когда:
+  - All teams solve one problem at once.
+
+ - Spacewar!:
+   - Two teams, each starts in one root node.
+   - Graph of problems, symmetric across middle
+   - easy problems close, hard problems far.
+   - Goal: capture as many nodes as possible
+     - Solve a problem, capture a node
+     - solve a problem on the other team's side, capture their node.
+     - TODO: a fun way to resolve conflicts?
+
+
+# Topics:
+- Divisibility proofs & properties
+- 1 exists ==> assume 2 exist
+- <= , >= ==> =
+- pidgeonhole
+
+# Handout ideas:
+- Notation toolbox
+- Propositional logic
+- Rubik's group
+- Graph combinatorics
+- Fourier transforms
+- Probabalistic proofs
+- Bayesian / Frequentist probability
+- Data structures
+
+# Handouts to clean up:
+ - Euler's number
+ - Lattices
+ - Nim handout
+ - Stocks
+ - Continued fractions
+
+
+# Problems to record:
+ - Nikita: weight of 100 cows
+ - Seat swapping: everyone wants a seat that's not their own, no two people want the same seat. Each cycle, everyone swaps. Min # of cycles? Solution: 2, reflect. use even and odd cycles. Takeaway: composition of reflections is rotation.
+ - Geometric optimization: ant on cube shortest path, ant on brick shortest path, ribbon on brick (over-under, h-shape) minimal length, Farthest point from corner of brick
+ - 180: Sperner lemma and brouwer theorem
+ - 25 horses. 5 at a time. find top 3? (7 races)

notes/topics.md

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+ - 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