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0. (Random) Pascal's Triangle

1. (Random) Combinatorics

2. (Random) Probability

3. (Random) Graph Theory

      a. Define a graph and its parts
      b. Use a matrix to represent a graph
      c. Using a weighted or directed graph
      d. Describe a path, circuit, or cycle
      e. Apply Euler's graph theory
      f. Chinese postman problem
      g. Apply Hamilton's graph theory
      h. The Traveling Salesman Problem
      i. Construct a Minimum Spanning Tree
      j. Use Kriskal's algorithm to solve minimum spanning trees
      k. Scheduling
      l. Perform critical-path analysis.
      m. Identifying NP complete
      n. Find Steiner points
      o. Probability Tree

4. (Random) Graph Coloring And Examples

      a. Find the chromatic number of a graph
      b. Find the chromatic index of a graph
      c. Identifying Snarks
      d. Use graph coloring for scheduling problems
      e. Using Graph Coloring (4 Color Theorem)
      f. Using Kirkman's Graph
      g. Using Petersen's Graph
      h. Using Schlegel Diagrams
      i. Tree Games
      j. Conflict/Agreement

5. (Random) Voting and Elections

      a. Using Plurality
      b. Using Runoff
      c. Using Sequential Runoff
      d. Using Borda
      e. Using Condorcet
      f. Using Arrow's Theorem
      g. Using Weighted Voting Systems
      h. Computing Power Index (Banzhaf)
      i. Computing Shapley-Shubik Power Index

6. (Random) Apportionment

      a. Fair Division (discrete)
      b. Fair Division (continuous)
      c. Hamilton
      d. Hill-Hunting
      e. Webster
      f. Nongovernment Situations
      g. Sports Salary Caps
      h. Estate Division

7. (Random) Game Theory

      a. Create a game matrix
      b. Determine the value of the game matrix
      c. Identify zero-sum and nonzero-sum games
      d. Prisoner's Dilemma
      e. Game of Chicken
      f. Inspection Games
      g. Duel Games
      h. Equilibrium
      i. Fairness

8. (Random) Matrices

      a. Identify and define terms relating to matrices
      b. Performing Matrix Operations (Addition/Subtraction/Scalar Multiplication)
      c. Performing Matrix Operations (Multiplication)
      d. Finding Matrix Inverses (up to 4x4)
      e. Apply the Leslie matrix model to population models
      f. Apply the Leontief model to economic situations
      g. Apply the Markov chain to probability models

9. (Random) Recursion

      a. Identify and define terms relating to recursion
      b. Solving Recurrence Relations by Iteration
      c. Fibonacci Sequence
      d. Gambler's Ruin
      e. General Recursive Definitions (boolean, functions, etc)
      f. Hand Shake Problem
      g. Tower of Hanoi
      h. Pascal's triangle
      i. Von Kock Snowflake
      j. Sierpinski's triangle, carpet, or gasket
      k. Menger Sponge
      l. Cantor Set / Cantor Dust
      m. Anti-snowflake
      n. Limits
      o. Recurrence Relations
      p. Dynamical Growth / Decay
      q. Verhulst Law of Restrained Growth

10. (Random) Sequences, Series, and Induction

      a. Sequences and Series
      b. Limits
      c. Recursive Relations
      d. Finite Differences
      e. Difference Equations (Creating)
      f. Difference Equations (Identifying)
      g. Cobwebbing
      h. Weak Induction
      i. Strong Induction

11. (Random) Recursion and Fractals

      a. Applying Recursion
      b. Sandefur's drug model
      c. Population Model
      d. Fractals
      e. Chaos Theory
      f. Julia Set
      g. Mandelbrot Set
      h. Tesselations (Tilings)

12. (Random) Coding and Encoding

      a. ISBN
      b. ZIP
      c. Bar Codes
      d. Social Security Numbers
      e. Census Codes
      f. Cryptograms

13. (Random) Modeling

      a. Explicit Formula
      b. Linear
      c. Quadratic
      d. Exponential
      e. Bin Packing
      f. Queuing Theory

14. (Random) Number Theory

      a. Clock arithmetic
      b. Properties of Even/Odd Prime/Composite Numbers
      c. Properties of Rational Numbers
      d. Number Bases
      e. Divisibility
      f. Quotient and divisor theorem
      g. Modular Arithmetic (mod)
      h. GCD
      i. Contradiction and Contraposition
      j. The Division Algorithm
      k. The Euclidean Algorithm

15. (Random) Set Theory

      a. Set Notation
      b. Venn Diagrams
      c. Unions, Intersections, and Complements
      d. De Morgan's Laws
      e. Subsets
      f. Empty Set, Partitions, Power Sets, and Boolean Algebra
      g. Russell's Paradox and the Halting Problem
      h. Inclusion - Exclusion

16. (Random) Logic

      a. Truth Tables
      b. Truthtellers and Liars
      c. Logically Equivalent Statements
      d. Conditional Statements
      e. Valid and Invalid Arguments
      f. Digital Logic Circuits
      g. Number Systems and Circuits (Binary)
      h. Universal and Existential Statements
      i. Symbols and Universal Statements
      j. Modus Pollens and Modus Tollens

17. (Random) Functions

      a. Definition of a function
      b. Finite State Automata
      c. One-to-One and Onto, Inverse Functions
      d. The Pigeonhole Principle
      e. Composition of Functions
      f. Cardinality and Computation

18. (Random) O-Notation and Efficiency of Algorithms

      a. O-Notation
      b. Computing Orders of Algorithms
      c. Exponential and Logarithmic Orders
      d. Binary Search and Merge Sort Algorithms
      e. NP Complete

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