Discrete Mathematics Syllabus

Overview:

Discrete Mathematics introduces students to the mathematics of networks, social choice, and decision making. The course extends students' application of matrix arithmetic and probability. Applications and modeling are central to this course of study. Appropriate technology will be used regularly for instruction and assessment.

Objectives:

The learner will:

· Display and interpret data.

· Write and evaluate matrix expressions to solve problems.

· Use graph theory to model relationships and 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 addition and multiplication principles of probability.

· 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 such as apportionment, election theory, voting power, and fair division.

· 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.

Evaluation

Tests – 70%

Independent Work – 30%

Resources

Discrete Mathematics Through Applications Crisler, Fisher, and Froelich

Understandable Statistics Brase & Brase

Technology Resources

TI-84 Plus Graphing Calculator

Virtual TI Calculator

Interwrite SchoolPad

Document Reader