# UoPeople Online Syllabus Repository (OSR)

## General Studies

### MATH 1302 Discrete Mathematics

**MATH 1302: Discrete Mathematics**

Credits: 3

Prerequisites: None

Course Description: 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.

Required Textbook and Materials: UoPeople courses use open educational resources (OER) and other materials specifically donated to the University with free permissions for educational use. Therefore, students are not required to purchase any textbooks or sign up for any websites that have a cost associated with them. The main required textbooks for this course are listed below and can be readily accessed using the provided links. There may be additional required/recommended readings, supplemental materials, or other resources and websites necessary for lessons; these will be provided for you in the course's General Information and Forums area, and throughout the term via the weekly course Unit areas and the Learning Guides.

- Al Doerr., & Levasseur, K. (2022).
*Applied discrete structures*(3rd ed.). licensed under CC BY-NC-SA - Jamaloodeen, M., Pinzon, K., Pragel, D., Roberts, J., & Siva, S. (2021).
*Discrete Math*(3rd ed.). licensed under CC BY-NC - Levin, O. (2021).
*Discrete mathematics: An open introduction*(3rd ed.). licensed under CC 4.0

Software Requirements/Installation: There are no special requirements that exceed general internet access.

Learning Objectives and Outcomes:

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

- Describe and apply basic structures of discrete mathematics.
- Identify mathematical arguments, implement logical thinking, and recognize a faulty argument.
- Find suitable solutions for real-world problems.
- Identify and apply different mathematical and logical notations.
- Demonstrate different methods of proof.
- 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

Course Requirements:

Discussion Assignments

Some units in this course require that you complete a Discussion Assignment. You are required to develop and post a substantive response to the Discussion Assignment in the Discussion Forum. A substantive response is one that fully answers the question that has been posed by the instructor. In addition, you must extend the discussion by responding to at least three (3) of your peers’ postings in the Discussion Forum and by rating their posts. Instructions for proper posting and rating are provided in the Discussion Forum for each week. Discussion Forums are only active for each current and relevant learning week, so it is not possible to contribute to the forum once the learning week has come to an end. Failure to participate in the Discussion Assignment by posting in the Discussion Forum and responding to peers as required may result in failure of the course.

**Math Assignment**

Math Assignment is graded by your instructor. The grading rubric is listed under the assignment instructions. The grading rubric is a document that outlines the criteria that your instructor will use to grade your work.

Quizzes

This course will contain three types of quizzes – the Self-Quiz, the Graded Quiz, and the Review Quiz. These quizzes may contain multiple-choice, true/false, or short-answer questions. The results of the Self-Quiz will not count towards your final grade. However, it is highly recommended that you complete the Self-Quiz to ensure that you have adequately understood the course materials. Along with the Reading Assignments, the results of the Self-Quiz should be used as part of an iterative learning process, to thoroughly cover and test your understanding of course material. You should use the results of your Self-Quiz as a guide to go back and review relevant sections of the Reading Assignments. Likewise, the Review Quiz will not count towards your final grade, but should also be used to assist you in a comprehensive review and full understanding of all course material, in preparation for your Final Exam. Lastly, the results of the Graded Quiz will count towards your final grade.

Final Exam

The Final Exam will take place during the Thursday and Sunday of Week/Unit 9, following the completion of eight units of work. The format of the Final Exam is similar to that of the quizzes and may contain a combination of different question types. You will have one attempt to take the exam, and it will be graded electronically. Specific instructions on how to prepare for and take the Final Exam will be provided during Week 8 (located inside the Unit 9 Learning Guide). Final Exams must be taken without the use of course learning materials (both those inside and outside the course). If particular materials are allowed for use during the exam, these will be noted in the exam’s instructions.

**Note:** You are allowed to use a scientific calculator.

Class Introductions

This section provides an opportunity to introduce yourself, connect with your classmates, and foster a vibrant learning community. Through sharing your background, interests, and goals, you will create meaningful connections and discover commonalities with your peers.

**Course Forum**The Course Forum is the place to raise issues and questions relating to the course. It is regularly monitored by the instructors and is a good place to meet fellow students taking the same course. While it is not required to participate in the Course Forum, it is highly recommended.

Course Policies:

Grading Components and Weights

Each graded component of the course will contribute some percentage to the final grading scale, as indicated here:

Discussion Assignments | 15% |

Math Assignments | 45% |

Two Graded Quizzes (2 @10% each) | 20% |

Final Exam | 20% |

TOTAL |
100% |

Grading Scale

This course will follow the standard 100-point grading scale defined by the University of the People, as indicated here:

Letter Grade |
Grade Scale | Grade Points |

A+ | 98-100 | 4.00 |

A | 93-97 | 4.00 |

A- | 90-92 | 3.67 |

B+ | 88-89 | 3.33 |

B | 83-87 | 3.00 |

B- | 80-82 | 2.67 |

C+ | 78-79 | 2.33 |

C | 73-77 | 2.00 |

C- | 70-72 | 1.67 |

D+ | 68-69 | 1.33 |

D | 63-67 | 1.00 |

D- | 60-62 | 0.67 |

F | Under 60 | 0.00 |

Grade Appeal

If you believe that the final grade you received for a course is erroneous, unjust, or unfair, please contact your course instructor. This must be done within seven days of the posted final grade. For more information on this topic, please review the Grade Appeal Procedure in the University Catalog.

Participation

Non-participation is characterized by lack of any assignment submissions, inadequate contributions to the Discussion Forums, and/or lack of peer feedback to Discussion/Written Assignments. Also, please note the following important points about course participation:

- Assignments must be submitted on or before the specified deadline. A course timeline is provided in the course schedule, and the instructor will specify deadlines for each assignment.
- Any student showing non-participation for two weeks (consecutive or non-consecutive) is likely to automatically fail the course.
- Occasionally there may be a legitimate reason for submitting an assignment late. Most of the time, late assignments will not be accepted and there will be no make-up assignments.
- All students are obligated to inform their instructor in advance of any known absences which may result in their non-participation.

Academic Honesty and Integrity

If and when you submit any work that requires research and writing, it is essential to cite and reference all source material. Failure to properly acknowledge your sources is known as “plagiarism” – which is effectively passing off an individual’s words or ideas as your own. University of the People adheres to a strict policy of academic honesty and integrity. Failure to comply with these guidelines may result in sanctions by the University, including dismissal from the University or course failure. For more information on this topic, please review the Academic Integrity Policy in the University Catalog.

Any materials cited in this course should be referenced using the style guidelines established by the American Psychological Association (APA). The APA format is widely used in colleges and universities across the world and is one of several style and citation formats required for publication in professional and academic journals. Refer to the **UoPeople APA Tutorials in the LRC** for help with APA citations.

Code of Conduct

University of the People expects that students conduct themselves in a respectful, collaborative, and honest manner at all times. Harassment, threatening behavior, or deliberate embarrassment of others will not be permitted.

Any conduct that interferes with the quality of the educational experience is not allowed and may result in disciplinary action, such as course failure, probation, suspension, or dismissal. For more information on this topic, please review the Code of Conduct Policy in the University Catalog.

**Submitting Assignments**

Please note that accepted formats for assignments are Microsoft compatible format, PDF, or any other file format that is clearly specified in the course and activity instructions. These files should not be password-protected. Additionally, unless otherwise stated in assignment instructions, screenshots of computer coding, mathematical formulas or images with sentence structures (typed or in handwriting) are not allowed when you submit your assignments in this course.