Discrete Math < School Computer Curriculum
4.3 (6 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
48 students enrolled

Discrete Math < School Computer Curriculum

High School and Middle School - Learn the "Math of Computer Science and Technologies"
4.3 (6 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
48 students enrolled
Created by Hesam Samimi
Last updated 4/2018
English
English
Current price: $12.99 Original price: $19.99 Discount: 35% off
10 hours left at this price!
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This course includes
  • 5.5 hours on-demand video
  • 7 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll learn
  • Prepare your mind for future technical knowledge you will encounter in college or many careers in systems, engineering, computer science, business, and economics
  • Find inspiration about future technology and other career interests by encountering new topics from a different kind of applied math
  • Improve upon your critical thinking and problem solving faculties
Requirements
  • Basic Algebra
Description
  • School Computer Curriculum - Suitable for part of a semester for high school or middle school grades

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 several hands-on 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.

Topics covered in this course include:

  1. Logic

    1. Operations

    2. Truth Tables

  2. Graphs

    1. Shortest Path Algorithm

  3. Sets

    1. Venn Diagrams

    2. Operations

  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.

Who this course is for:
  • High School and Junior High students interested in the "other" Math beyond Algebra, Geometry, Calculus
  • Students who want to preview and learn about the application of Discrete Math in technology, numerous fields and careers
Course content
Expand all 18 lectures 05:17:38
+ Introduction
1 lecture 02:17
  • Instructor Intro
  • Discrete Math Intro
  • Course Format
Preview 02:17
+ Class 1: Logic
3 lectures 55:46
  • Have I lied Game
  • Propositional Logic Operations
    • OR
    • AND
  • Truth Tables
Preview 19:07
  • Have I lied Game
  • Propositional Logic Operations
    • NOT
    • IMPLIES
  • Truth Tables
  • Simplifying Statements
Preview 20:48
  • Truth Tables
  • Equivalence Laws
  • Simplifying Statements




Preview 15:51
+ Class 2: Graphs
3 lectures 54:01
  • Graph Theory Introduction
  • Facebook Friends
  • Coloring Problem
  • Shortest-Path Algorithm
Class 2: Graphs - Part One
19:26
  • Shortest-Path Algorithm (Cont.)
Class 2: Graphs - Part Two
16:57
  • Shortest-Path Algorithm (Cont.)
Class 2: Graphs - Part Three
17:38
+ Class 3: Sets
2 lectures 43:33
  • Sets
  • Concepts
  • Venn Diagrams
  • Set Operations
Class 3: Sets - Part One
22:45
  • Set Operations
  • Set Logic
Class 3: Sets - Part Two
20:48
+ Class 4: State Machines
2 lectures 43:39
  • State Machines
  • Example: Vending Machine
Class 4: State Machines - Part One
18:36
  • Exercise: Traffic Light
  • Exercise: Bank ATM
Class 4: State Machines - Part Two
25:03
+ Class 5: Number Theory
2 lectures 32:04
  • Motivation
  • Primes
  • Coprimes
  • Remainder Classes / Congruence Modulo
  • Exercises
Class 5: Number Theory - Part One
19:15
  • No Encryption
  • RSA Algorithm
  • RSA Example
  • Message Encryption with RSA
  • Message Signing with RSA
Class 5: Number Theory - Part Two
12:49
+ Class 6: Counting
3 lectures 59:18
  • Combinations
  • Permutations
  • Probability
  • Exercises
Class 6: Counting - Part One
21:37
  • Exercises
Class 6: Counting - Part Two
18:34
  • Exercises
Class 6: Counting - Part Three
19:07
+ Class 7: Proofs
2 lectures 27:00
  • Historical Proofs
  • Direct Proof
  • Contrapositive Proof
Class 7: Proofs - Part One
13:48
  • Contrapositive Proof (Exercise)
  • Proof by Cases
Class 7: Proofs - Part Two
13:12