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UoPeople Online Syllabus Repository (OSR)

General Studies

MATH 1302 Discrete Mathematics

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MATH 1302: Discrete Mathematics


Credits: 3

Prerequisites:

Recommended:


Course Description: This course is primarily intended for students majoring in Computer Science. The emphasis will be on the development of technical discrete mathematics skills, rather than rigorous proof. Topics will include sets, logic, induction, elementary counting techniques, functions, graph theory, and number 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.


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:

  1. Identify and define the basic structures of discrete mathematics including sets, combinatorics, logic, graphs, number theory, and functions.
  2. Use methods from logics, combinatorics, and graph theory to perform calculations and solve problems involving discrete structures.
  3. Apply logical thinking to write simple proofs of arithmetical statements.
  4. Apply the tools and methods of discrete mathematics to real-world problems in computer science, especially in the analysis of recursive algorithms 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 - Basic Mathematical Notation and Set Theory

Week 2: Unit 2 - Combinatorics

Week 3: Unit 3 - Logic

Week 4: Unit 4 - Sequence and Series

Week 5: Unit 5 - Recursion

Week 6: Unit 6 - Functions

Week 7: Unit 7 - Graph and Graph Theory

Week 8: Unit 8 - Number Theory

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

  • Read the Learning Guide and Reading Assignments
  • Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
  • Complete and submit the Written Assignment
  • Make entries to the Learning Journal
  • Take the Self-Quiz

Unit 2: Combinatorics

  • Peer assess Unit 1 Written Assignment
  • Read the Learning Guide and Reading Assignments
  • Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
  • Make entries to the Learning Journal
  • Take the Self-Quiz

Unit 3: Logic

  • Read the Learning Guide and Reading Assignments
  • Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
  • Complete and submit the Written Assignment
  • Take the Self-Quiz
  • Take the Graded Quiz

Unit 4: Sequence and Series

  • Peer assess Unit 3 Written Assignment
  • Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
  • Read the Learning Guide and Reading Assignments
  • Make entries to the Learning Journal
  • Take the Self-Quiz

Unit 5: Recursion

  • Read the Learning Guide and Reading Assignments
  • Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
  • Make entries to the Learning Journal
  • Complete and submit the Written Assignment
  • Take the Self-Quiz

Unit 6: Functions

  • Peer assess Unit 5 Written Assignment
  • Read the Learning Guide and Reading Assignments
  • Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
  • Make entries to the Learning Journal
  • Take the Self-Quiz
  • Take the Graded Quiz

Unit 7: Graph and Graph Theory

  • Read the Learning Guide and Reading Assignments
  • Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
  • Make entries to the Learning Journal
  • Complete and submit the Written Assignment
  • Take the Self-Quiz

Unit 8: Number Theory

  • Peer assess Unit 7 Written Assignment
  • Read the Learning Guide and Reading Assignments
  • Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
  • Make entries to the Learning Journal
  • Take the Self-Quiz
  • Read the Unit 9 Learning Guide carefully for instructions on the Final Exam
  • Take the Review Quiz
  • Complete and submit the anonymous Course Evaluation

Unit 9: Course Review and Final Exam

  • Read the Learning Guide and take the Review Quiz, if you haven't already done so
  • 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:

Written Assignments
Some units in this course require that you complete a Programming Assignment. You are required to submit your assignments by the indicated deadlines and, in addition, to peer assess three (3) of your classmates’ assignments according to the instructions found in the Assessment Form, which is provided to you during the following week. During this peer assessment period, you are expected to provide details in the feedback section of the Assessment Form, indicating why you awarded the grade that you did to your peer. Please note that each assignment grade is comprised of a combination of your submission (90%) and your peer assessments (10%). Failure to submit Programming Assignments and/or Assessment Forms may result in failure of the course.

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 inside 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.

Learning Journals
Your instructor may choose to assign specific topics and/or relevant questions as a weekly Learning Journal entry for you to complete, but you are still encouraged to also use it to document your activities, record questions/problems you may have encountered, reflect on the learning process, and draft answers for other course assignments. The Learning Journal must be updated on a weekly basis because its entries will be assessed by your instructor directly as a part of your final grade. The Learning Journal will only be seen by your instructor.

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. Specific instructions on the format and content of the Graded Quiz will be provided by your instructor.

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.

The Final Exam for this course must be done under the supervision of a proctor. Since you already secured your proctor before registering for this course, this is a reminder that you should coordinate with him/her before you take the exam. Please note, you will not be permitted to change proctors during the course. As a reminder, students are required to successfully complete proctored exams spaced throughout their program of study at UoPeople, in order to verify the student’s identity in confirming a degree and diploma upon graduation.

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%
Written Assignments 15%
Learning Journals 10%
Two Graded Quizzes  (2 @15% each) 30%
Final Exam 30%
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. Purdue University’s Online Writing Lab (OWL) is a free website that provides excellent information and resources for understanding and using the APA format and style. The OWL website can be accessed here: https://owl.purdue.edu/owl/purdue_owl.html

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.