Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete in nature. This course is designed to provide some basic fundamental concepts in Discrete Mathematics that will help the students in their technical field, more specifically in computer science. This course includes the concepts of sets, combinatorics, number theory, and functions to develop the skills of counting, formulating.  And also, this course will enable the student to apply logical reasoning, problem-solving, and visualization of problems through the concepts of logic, recursions, relations, and Graph Theory.

Learning Objectives and Outcomes:

By the end of this course students will be able to:

1. Describe and apply basic structures of discrete mathematics.
2. Identify mathematical arguments, implement logical thinking, and recognize a faulty argument.
3. Find suitable solutions for real-world problems.
4. Identify and apply different mathematical and logical notations.
5. Demonstrate different methods of proof.
6. Apply different concepts of relations and number theory.

Course Schedule and Topics

This course will cover the following topics in eight learning sessions, with one Unit per week.

Week 1: Unit 1 – Set Theory and Basics of Counting

Week 2: Unit 2 – Functions and Sequences

Week 3: Unit 3 – Combinatorics

Week 4: Unit 4 – Recursion and Solutions of Recurrence Relations

Week 5: Unit 5 – Introduction to Logic

Week 6: Unit 6 – Partial Ordering and Mathematical Induction

Week 7: Unit 7 – Graph Theory

Week 8: Unit 8 – Introduction to Algebraic Structures

Week 9: Unit 9 – Course Review and Final Exam

Learning Guide

The following is an outline of how this course will be conducted, with suggested best practices for students.

Unit 1: Set Theory and Basics of Counting

• Read through the Learning Guide and the Reading Assignment
• Complete the Discussion Assignment by posting in the Discussion Forum
• Respond to three of your fellow classmates’ posts in the Discussion Forum
• Complete and submit the Math Assignment
• Take and submit the Self-Quiz

Unit 2: Functions and Sequences

• Read through the Learning Guide and the Reading Assignment
• Complete the Discussion Assignment by posting in the Discussion Forum
• Respond to three of your fellow classmates’ posts in the Discussion Forum
• Complete and submit the Math Assignment
• Take and submit the Self-Quiz

Unit 3: Combinatorics

• Read through the Learning Guide and the Reading Assignment
• Complete the Discussion Assignment by posting in the Discussion Forum
• Respond to three of your fellow classmates’ posts in the Discussion Forum
• Complete and submit the Math Assignment
• Take and submit the Self-Quiz
• Take and submit the Graded Quiz

Unit 4: Recursion and Solutions of Recurrence Relations

• Read through the Learning Guide and the Reading Assignment
• Complete and submit the Math Assignment
• Take and submit the Self-Quiz

Unit 5: Introduction to Logic

• Read through the Learning Guide and the Reading Assignment
• Complete the Discussion Assignment by posting in the Discussion Forum
• Respond to three of your fellow classmates’ posts in the Discussion Forum
• Complete and submit the Math Assignment
• Take and submit the Self-Quiz

Unit 6: Partial Ordering and Mathematical Induction

• Read through the Learning Guide and the Reading Assignment
• Complete and submit the Math Assignment
• Take and submit the Self-Quiz
• Take and submit the Graded Quiz

Unit 7: Graph Theory

• Read through the Learning Guide and the Reading Assignment
• Complete the Discussion Assignment by posting in the Discussion Forum
• Respond to three of your fellow classmates’ posts in the Discussion Forum
• Complete and submit the Math Assignment
• Take and submit the Self-Quiz

Unit 8: Introduction to Algebraic Structures

• Read through the Learning Guide and the Reading Assignment
• Complete the Discussion Assignment by posting in the Discussion Forum
• Respond to three of your fellow classmates’ posts in the Discussion Forum
• Complete and submit the Math Assignment
• Take and submit the Self-Quiz

Unit 9: Course Review and Final Exam

• Read the Learning Guide and take the Review Quiz
• Prepare for, take, and submit the Final Exam
• The Final Exam will take place during the Thursday and Sunday of Week/Unit 9 (UoPeople time); exact dates, times, and other details will be provided accordingly by your instructor