Discrete Math & Real-World Applications ← School Curriculum

Description

• School Computer Curriculum - Suitable for part of a semester for high school or middle school grades

  • For teacher curriculum bundle see Termeric Education website.

Discrete Mathematics covers many fundamental theories which are the foundation for many fields in systems, engineering, computer science, business, economics, sciences, general problem solving, critical thinking, and more. Roughly, it is the math that is not part of Algebra/Calculus/Geometry which are typically taught in schools.

Sadly, despite its application in higher education and many careers and fields, Discrete Mathematics is seldom taught in the USA high schools, for the unfortunate reason that it is not covered in the SAT examinations.

Learning about topics in Discrete Mathematics can help junior high and high school students in the following ways:

• Find inspiration about future technology and other career interests by encountering new topics from a different kind of applied math

• Prepare their minds for future technical knowledge they will encounter in college or many careers in systems, engineering, computer science, business, and economics

• Improve upon their critical thinking and problem solving skills

In this class series, high school and junior high students get an accessible, hands-on overview to several topics in Discrete Math. We won't go too deep in each subject, but students will get a nice preview of several important subjects in Discrete Math and understand their application to the real world.

Each class includes class-time exercises. The student will be prompted to pause the video, do the exercise, and then resume the video to compare his/her work with the teacher.  Each unit includes take-home exercises and solutions.

Topics covered in this course include:

1. Propositional Logic

   1. Operations

   2. Truth Tables

   3. Simplifying Statements

2. Graphs

   1. Basic Concepts

   2. Shortest Path Algorithm

3. Sets

   1. Basic Concepts

   2. Venn Diagrams

   3. Operations

   4. First-Order Set Logic

4. State Machines 

5. Number Theory

   1. Coprimes

   2. Remainder Classes

6. Counting

   1. Combinations

   2. Permutations

   3. Probability

7. Proofs

   1. Direct

   2. By Contrapositive

   1. By Cases

I have used "Discrete Mathematics: An Open Introduction" by Oscar Levin, a great free online textbook, as an inspiration to create this course.

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