Virginia Discrete Math

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Select the number of each type of objective: (Selecting Random will randomly generate all subtypes) Click on any title to see the free sample worksheet. (only the first few samples are free) (Random) DM.1 Graphs: Using Graphs in Modeling a. Define a graph and its parts b. Finding Bridges, Loops, and Multiple Edges c. Using and Identifying Complete Graphs d. Using and Identifying Trees e. Directed Graph (Digraph) Terminology f. Apply Adjacency Matrices g. Apply the Leslie matrix model to population models h. Apply the Markov chain to probability models i. Apply the Leontief model to economic situations j. Reading Venn Diagrams k. Identifying Union, Intersection, Complement, Etc. Venn Diagrams l. Highlighting Correct Parts of a Venn Diagram m. Drawing A Venn Diagram to Represent Logical Statements (Random) DM.2 Graphs: Euler and Hamilton a. Identifying if Graph has an Open or Closed Unicursal Tracing b. Applying Euler's Graph Theory c. Creating Eulerizations and Semi-Eulerizations d. Solving Euler Path/Circuit Word Problems e. Finding Hamilton Circuits and Paths f. Solving the Traveling Salesman Problem (Brute Force) g. Solving the Traveling Salesman Problem (Nearest Neighbor) h. Solving the Traveling Salesman Problem (Repetitive Nearest Neighbor) i. Solving the Traveling Salesman Problem (Cheapest Link) (Random) DM.3 Graphs: Coloring a. Find the chromatic number of a graph b. Find the chromatic index of a graph c. Identifying Snarks d. Identifying Planar Graphs e. Coloring Graphs vs. Maps f. Use Graph Coloring for Scheduling Problems g. Directed Graph (Digraph) Terminology (Random) DM.4 Graphs: Trees a. Find the Number of Spanning Trees (simple cases) b. Find Minimum Spanning Trees Using Kruskal's Algorithm c. Find Minimum Spanning Trees Using Prim's Algorithm d. Find Minimum Spanning Trees Using Dijkstra's Algorithm e. The Shortest Network and Steiner Points (Random) DM.5 Election Theory and Fair Division: Apportionment (Food/Items) a. Fair Division: The value of things b. Divider-Chooser Method c. Lone-Divider Method d. Lone-Chooser Method e. Last Diminisher Method f. Method of Sealed Bids (Knaster Inheritance) g. Method of Markers (Random) DM.6 Election Theory and Fair Division: Voting a. Creating a Preference Schedule b. Using Plurality c. Using Borda d. Using Plurality with Elimination e. Using Condorcet (Pairwise Comparisons) f. Using Extended Rankings g. Using Plurality with Runoff h. Fairness Criterion and Arrow's Theorem i. Using Weighted Voting Systems j. Computing Power Index (Banzhaf) k. Computing Shapley-Shubik Power Index (Random) DM.7 Election Theory and Fair Division: Apportionment (Congress) a. Standard Divisors and Quotas b. Hamilton's Method c. Jefferson's Method d. Adam's Method e. Webster's Method f. Huntington-Hill Method	(Random) DM.8 Computer Mathematics: Coding a. Check Digits b. Weighted Check Digits c. Using Codabar d. Postnet Bar Codes e. Information: ZIP, UPC, and Social Security Numbers f. Using the Soundex Code g. Binary Codes h. Parity Check Sums i. Data Compression j. Cryptograms k. RSA Encryption (Random) DM.9 Computer Mathematics: Logic a. Check Digits b. Weighted Check Digits c. Using Codabar d. Postnet Bar Codes e. Information: ZIP, UPC, and Social Security Numbers f. Using the Soundex Code g. Binary Codes h. Set Notation i. Unions, Intersections, Differences and Complements j. Venn Diagrams k. DeMorgan's Laws and Other Properties l. Subsets m. Partitions n. Power Sets o. Set Cardinality and Inclusion-Exclusion Principle (Random) DM.10 Recursion and Optimization: Scheduling a. Facts about Schedules b. Applying the Decreasing Time Algorithm c. Applying the Critical Path Algorithm (Random) DM.11 Recursion and Optimization: Linear Programming a. Graphing Linear Inequalities b. Linear Programming Problems (Graph Supplied) c. Linear Programming Problems (Random) DM.12 Recursion and Optimization: Recursion and Fractals a. Calculating Compound Interest Word Problems b. Applying Iteration c. Iterative Fractals d. Evaluating Polynomials with Complex Numbers e. The Game of Chaos f. Mandelbrot Set g. Julia Set h. Sierpinski's Triangle and Carpet i. Von Koch Snowflake and Anti-Snowflake j. Menger Sponge k. Cantor Set and Cantor Dust l. Tessellations (Tilings) m. Fibonacci Numbers n. The Golden Ratio o. Fibonacci Numbers and Quadratic Equations p. Gnomons and Similarity q. General Recursive Definitions r. Hand Shake Problem s. The Tower of Hanoi Puzzle t. Using Recursive Relations u. Linear Growth v. Exponential Growth w. Logistic Growth (Verhulst Law of Restrained Growth) x. Percentages of Percentages (Random) DM.13 Recursion and Optimization: Bin Packing and Probability a. Combinations b. Permutations (And other cases where order matters) c. Simplifying Factorial Expressions d. Combinations with Replacement e. Binomial Theorem f. Multinomial Coefficients g. Counting Subsets h. Identifying Bin Packing vs. Scheduling Problems i. Bin Packing Problems
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