• Course Description

Discrete Mathematics B is only offered in the second 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.

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 Revisited

• Students will solve puzzles
• Students will use inductive reasoning to solve puzzles
• Students will use deductive reasoning to solve puzzles

Unit 2: Probability

• Students will be able to calculate basic probability.
• Students will be able to use the fundamental counting principle.
• Students will be able to calculate expected value.
• Students will be able to understand the prisoner’s dilemma.
• Students will be able to use probability to analyze misleading situations.

Unit 3: Geometric Gems

• Students will be able to construct geometric figures.
• Students will be able to solve problems in Euclidean Geometry.
• Students will be able to solve problems in Spherical Geometry.
• Students will be able to solve problems in Taxi – Cab Geometry.
• Students will be able to solve problems in Hyperbolic Geometry.

Unit 4: Graph Theory

• Students will be able to identify key Graph Theory concepts.
• Students will be able to color a map.
• Students will be able to apply the vertex coloring algorithm.
• Students will be able to apply the shortest route algorithm.
• Students will be able to create flowcharts.
• Students will be able to apply knowledge of graph theory to a new situation.

Unit 5: Topology

• Students will be able to identify key topological concepts.
• Students will be able to solve topological puzzles.

Unit 6: Flatland and the Fourth Dimension

• Students will be able to describe the 4th Dimension.

Unit 7: Number Bases

• Students will be able to convert numerals to different bases.
• Students will be able to do operations in different bases.

Course Resources & Materials: Math Medic, Desmos, Textbook: The Heart of Mathematics

Date Last Revised/Approved: 2008