Course Title: Discrete Math
Length of Course: Full Year
Prerequisite: B or better in Algebra II or, C or better in Pre-Calculus
Fulfills UC/CSU Requirements: Yes
Test books: For All Practical Purposes 5th edition, Freeman
Discrete Mathematics with Applications; Susanna Epp
This course explains and explores the concepts of probability, formal and informal logic, social theories, fair division, apportionment theories, voting theories, coding, linear programming applications, financial models, circuit theories (Hamilton and Euler), general math proofs (deductive, inductive and by negation), the nature of proofs, the exploration of the origins of numbers and number systems as well as some history of math topics. The course will be taught through projects, testing and evaluating hypotheses.
The general focus of the course is broken down into these concepts:Logic, Probability, Number Sense, Mathematical Reasoning and analysis, Induction/Deduction0 Business applications and History of Math
Course outline (in block days):
LOGIC (14 days)
Subjects include definitions, vocabulary of logic, arguments, uses of logic, fallacies, deduction, induction, universal quantifiers (for all and there exists) as well as Boolean and circuit logic.
PROBABILITY (14 days)
Subjects include displaying data, number crunching of data, the basic framework of probability (cars, dice, applications), vocabulary of probability, permutations, combinations as well as independent and non-independent events. This topic could be used for one of the projects for this course.
SOCIAL THEORIES (14 days)
Subjects would include setting up and breaking down of word problems, such as the Election Theory, Apportionment theories, voting theories, game theory and Fair Division
MATHEMATICAL REASONING, MATHEMATICAL ANALYSIS and INDUCTION/DEDUCTION (scattered throughout the course)
The main topics in this unit are proofs, inductive reasoning and deductive reasoning. Time could be devoted to the history of these subjects to allow students to explore their importance. This is another good section for a project.
LINEAR ALGEBRA with a focus on business applications (15 days)
The focus of this section is on business related applications such as linear programming. This is another section that can be enhanced by both guest speakers and projects, both written and oral.
GENERAL MATH TOPICS
We explore financial models and coding, circuit theories (Euler and Hamilton), Symmetry and patterns (including sizing, types of shapes and basic tiling techniques)
HISTORY OF MATH
This is interspersed throughout the course. I also use it for semester projects. One as a written project one as an oral presentation.
So far the kids like the practical nature of the class. They like seeing math as it exists in the world around them.
Most find the formal logic unit very challenging. It forces them to think differently as well as making them articulate their knowledge in a clear and concise manner.