Discrete Mathematics A is only offered during the first semester. Students do not have to take Discrete Mathematics A before taking Discrete Mathematics B.
Students enrolled in this course will use rigorous thought and reasoning skills to explore areas of mathematics not traditionally covered in the algebra-precalculus-calculus sequence. Topics include secret codes and encryption, infinity and different levels of infinity, different geometries, topology, chaos and fractals and probability. Discrete mathematics lends itself to a wide variety of “real world” applications. Problems discussed will range from determining if there are two people on earth with the exact same number of hairs on their bodies to devising secret codes to examining the probability of winning the lottery.
Grade Levels: 11th-12th Grades
Related Priority Standards (State &/or National): K-12 Mathematics Missouri Learning Standards
Enduring Understanding/Big Ideas:
- Students will determine expressions and values using mathematical operations, procedures and rules.
- Students will translate mathematical information from a single representation or across multiple representations in order to develop processes to problem solve.
- Students will recognize mathematical reasoning requires justification of both process and solution.
- Students will use correct notation, language and mathematical convention to classify concepts and communicate results or solutions.
Course Level Scope & Sequence (Units &/or Skills):
Unit 1: Problem Solving
- Students will solve puzzles
- Students will use inductive reasoning to solve puzzles
- Students will use deductive reasoning to solve puzzles
Unit 2: Number Theory
- Students will be able to apply the pigeonhole principle
- Students will be able to apply properties of Prime numbers
- Students will be able to apply the properties of the Fibonacci Sequence
- Students will be able to apply properties of Rational numbers
Unit 3: Mods and Codes
- Students will be able to calculate remainders in mod n
- Students will be able to perform different operations using modular
- Students will be able to solve equations using modular arithmetic
- Students will be able to decipher messages
Unit 4: Fractals
- Students will be able to model real life with fractals.
- Students will be able to apply Algebra to fractals.
- Students will be able to apply Geometry to fractals.
Date Last Revised/Approved: 2008