Curriculum Resources

Unit 1 Logic and Reasoning

Unit 2 Conflict Resolution

Unit 3 Graph Theory

Unit 4 Apportionment, Fair Division, and Voting

Unit 5 Counting, Listing, and Probability

Unit 6 Searching, Sorting, Recursion and Iteration

Semester Review


MathHW.net Discrete Mathematics

The Common Core Standards for Mathematics do not contain frameworks specific to Discrete Mathematics. Some states, such as Indiana and New Jersey have defined (NonCore) standards which can be used for connecting to a one year or one semester course. The standards below are extracted from the state standards from Indiana. The course contents listed are for a one semester course; a full year course would include additional topics sucs as matrices.

Discrete Mathematics Standards Overview
Adopted from Wayne County Public Schools
Matrices and Graphs
Use matrices to model and solve problems.
 Display and interpret data.
 Write and evaluate matrix expressions to solve problems.
Use graph theory to model relationships and solve problems.

Algebra
Use recursion to model and solve problems.
 Find the sum of a finite sequence.
 Find the sum of an infinite sequence.
 Determine whether a given series converges or diverges.
 Write explicit definitions using iterative processes, including finite differences and arithmetic and geometric formulas.
 Verify an explicit definition with inductive proof.

Statistics and Probability
Describe data to solve problems.
 Apply and compare methods of data collection.
 Apply statistical principles and methods in sample surveys.
 Determine measures of central tendency and spread.
 Recognize, define, and use the normal distribution curve.
 Interpret graphical displays of data.
 Compare distributions of data.
Use theoretical and experimental probability to model and solve problems.
 Use addition and multiplication principles.
 Calculate and apply permutations and combinations.
 Create and use simulations for probability models.
 Find expected values and determine fairness.
 Identify and use discrete random variables to solve problems.
 Apply the Binomial Theorem.
Model and solve problems involving fair outcomes:
 Apportionment.
 Election Theory.
 Voting Power.
 Fair Division.

Standards For Mathematical Practice
 Make sense of problems and persevere in solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in repeated reasoning.



Unit  Standard Map 

Unit3 
*DM.1 The student will model problems, using vertexedge graphs. The concepts of valence, connectedness, paths, planarity, and directed graphs will be investigated. Adjacency matrices and matrix operations will be used to solve problems (e.g., food chains, number of paths).
 Unit3 
*DM.2 The student will solve problems through investigation and application of circuits, cycles, Euler Paths, Euler Circuits, Hamilton Paths, and Hamilton Circuits. Optimal solutions will be sought using existing algorithms and studentcreated algorithms.
 Unit3 
*DM.3 The student will apply graphs to conflictresolution problems, such as map coloring, scheduling, matching, and optimization. Graph coloring and chromatic number will be used.
 Unit6 
*DM.4 The student will apply algorithms, such as Kruskal’s, Prim’s, or Dijkstra’s, relating to trees, networks, and paths. Appropriate technology will be used to determine the number of possible solutions and generate solutions when a feasible number exists.
 Unit2 
*DM.5 The student will use algorithms to schedule tasks in order to determine a minimum project time. The algorithms will include critical path analysis, the listprocessing algorithm, and studentcreated algorithms.
 Unit3 
*DM.6 The student will solve linear programming problems. Appropriate technology will be used to facilitate the use of matrices, graphing techniques, and the Simplex method of determining solutions.
 Unit4 
*DM.7 The student will analyze and describe the issue of fair division (e.g., cake cutting, estate division). Algorithms for continuous and discrete cases will be applied.
 Unit4 
DM.8 The student will investigate and describe weighted voting and the results of various election methods. These may include approval and preference voting as well as plurality, majority, runoff, sequential runoff, Borda count, and Condorcet winners.
 Unit4 
DM.9 The student will identify apportionment inconsistencies that apply to issues such as salary caps in sports and allocation of representatives to Congress. Historical and current methods will be compared.
 Unit6 
DM.10 The student will use the recursive process and difference equations with the aid of appropriate technology to generate
a) compound interest;
b) sequences and series;
c) fractals;
d) population growth models; and
e) the Fibonacci sequence.
 Unit6 
DM.11 The student will describe and apply sorting algorithms and coding algorithms used in storing, processing, and communicating information. These will include
a) bubble sort, merge sort, and network sort; and
b) ISBN, UPC, Zip, and banking codes.
 Unit1 
DM.12 The student will select, justify, and apply an appropriate technique to solve a logic problem. Techniques will include Venn diagrams, truth tables, and matrices.
 Unit5 
DM.13 The student will apply the formulas of combinatorics in the areas of
a) the Fundamental (Basic) Counting Principle;
b) knapsack and binpacking problems;
c) permutations and combinations; and
d) the pigeonhole principle.

