Discrete Mathematics
All questions and comments about this curriculum should be directed to the North Carolina Department of Public Instruction.
Goal 1
Number and Operations - The learner will use matrices and graphs to model relationships and solve problems.
Objective 1.01
Use matrices to model and solve problems.
- Display and interpret data.
- Write and evaluate matrix expressions to solve problems.
Objective 1.02
Use graph theory to model relationships and solve problems.
Goal 2
Data Analysis and Probability - The learner will analyze data and apply probability concepts to solve problems.
Objective 2.01
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.
Objective 2.02
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.
Objective 2.03
Model and solve problems involving fair outcomes:
- Apportionment.
- Election Theory.
- Voting Power.
- Fair Division.
Goal 3
Geometry and Measurement - The learner will describe and use recursively-defined relationships to solve problems.
Objective 3.01
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.
