MATH 301 Discrete Mathematics

MATH 301 IS Sec 1, University of Mississippi
[See UM Catalog for Description]

3 credit hours

Instructor Information:

Dr. Laura Sheppardson

Instructor name:
Dr. Laura Sheppardson

Instructor Information:
I am an Associate Professor and Associate Chair of the Mathematics department. I earned a B.S. in Mathematics with Secondary Teaching certification from the University of Michigan. After several years of industry experience designing and building computer systems, I returned to school to complete an M.S. in Applied Mathematics and a Ph.D. in Mathematics from the Georgia Institute of Technology. My research is in Graph Theory. I have been at the University of Mississippi since 2003. I especially enjoy teaching upper-division undergraduate courses and advising students who are interested in the math major or minor.

During Fall and Spring semesters, I can be reached in my office, 305 Hume Hall, at (662) 915-1463. Outside of these periods you may use my Google Voice number, (662) 205-6997, to text or leave a voicemail. I can always be reached via email at Please include your course number in the subject line for a quicker response.

Contact Information:

If you have questions concerning the content of the course, you may contact the instructor directly using the Email Your Instructor link in the Lessons or Content page. NOTE: Whenever sending email, please be sure to indicate your course title and number in the subject line. You can expect a response within 72 hours, although it may be longer on weekends. Many instructors reply within 24 hours.

For lesson or test administration issues, please contact the iStudy department:

The University of Mississippi
Division of Outreach and Continuing Education
P. O. Box 1848
University, MS 38677

Phone: (662) 915-7313, toll-free (877) 915-7313
Fax: (662) 915-8826

Course Description

Discrete Mathematics is the study of mathematical objects that take on distinct values, often integer values. This is in contrast to the continuous functions you have encountered in Calculus. This course introduces mathematical reasoning and proof in a discrete context, as well as tools for modeling real-world processes. Topics will include elementary counting principles, mathematical induction and other proof methods, relations and functions, and graphs. Our focus will be on logical thinking and problem-solving.

Textbook Information:

Textbook information will be provided upon enrollment in your iStudy course.

Course Objectives:

This course will cover elementary counting principles, mathematical induction and other proof methods, relations and functions, and graphs. This includes selected sections of chapters 1-5 and 9 in the Scheinerman text. Our focus will be on logical thinking and problem-solving.

By the end of this course, you should be able to:

  • apply counting methods to solve a variety of problems
  • explain your solutions to someone who understands basic counting methods
  • read and write statements involving standard mathematical notation, including quantifiers, set operations, and “if…then…” structures
  • write simple proofs using direct methods, mathematical induction, or contradiction
  • read and write a variety of notation for relations and functions, and identify standard properties of relations and functions
  • apply equivalence relations and bijective functions in solving counting problems
  • understand standard graph definitions, and identify examples of such items as subgraphs, trees, and independent sets
  • use graphs to model and solve problems

Course Outline:

Class Format:

Instructional methods used in this course include recorded lectures, reading and writing assignments, online communications, and a final written exam.

The format for this course - both the traditional and the online sections - may be different from what you’ve experienced in Calculus. Your individual participation will be vital to your success.

The course is organized in a series of modules. You will complete these in the order they are presented. Each module will include a reading assignment, a brief reading quiz, and recommended textbook exercises. Many will include short video lectures. Most will include traditional written problem solving and proofs.

This course consists of 15 instructional modules (or lessons). Please note that the suggested Pacing Guide to complete the course in a traditional semester is written for Fall and Spring. Full summer students need to make adjustments due to the significantly shorter time period involved.

Module Reading Assignments Due for Grades Suggested Pacing Guide to complete the course in a traditional semester. *Summer session students will need to make adjustments due to the shorter time period*
Start Here *You MUST complete the syllabus quiz as soon as you have access to your Blackboard course. This is mandatory to verify your attendance.*NOTE: you must pass the Syllabus and Orientation Quiz for the course materials to appear on the Lessons page. Syllabus Quiz Week 1
0 Introduction Introduce Yourself, Journal Entry, Quiz Week 1
1.1 Mathematical Reasoning: Definitions and Proofs Quiz, Written Homework Week 1
1.2 Counting Ordered Selections: Lists and Factorials Quiz, Written Homework Week 2
1.3 The Language of Sets: Subsets, Sets, and Quantifiers Quiz, Written Homework Week 3
1.4 Operations on Sets Quiz Week 4
Proctored Course Exam 1 Covers Module 1 To be scheduled
and completed
before proceeding
Week 4
2.1 The Language of Relations Quiz, Journal Entry Week 5
2.2 Using Relations in Counting: Partitions and the Division Principle Quiz, Written Homework Week 6
2.3 Counting Unordered Selections: Binomial Coefficients and the Binomial Theorem Quiz, Written Homework Week 7
MIDPOINT OF COURSE If you are a semester student, you must reach the midpoint of your course by the date specified in your information.

If you are a Flex UM student, you CANNOT WITHDRAW from this course after the lesson has been submitted.
All lesson assignments or exams needed to reach the midpoint of the course The exact date semester students are required to reach the midpoint is specified in your information.
2.4 Proof by Counting: Combinatorial Proof Quiz, Written Homework, Journal Entry Week 8
2.5 Counting with Repeated Elements: Multiset Counting Quiz, Written Homework Week 9
2.6 Counting the Complement: Inclusion/Exclusion Quiz, Written Homework Week 10
Proctored Course Exam 2 Covers Module 2 To be scheduled
and completed
before proceeding
Week 10
3.1 Writing Proofs: Contrapositive, Contradiction, and Mathematical Induction Quiz, Written Homework Week 11
3.2 Function Properties and Applications: Functions, Pigeonhole Principle Quiz, Written Homework Week 12
3.3 Modeling the World with Graphs Quiz, Journal Entry Week 13
3.4 Graph Properties: Connection, Trees, Euler Tours Quiz, Written Homework Week 14
Proctored Course Exam 3 Covers Module 3 To be scheduled
and completed
before proceeding
Week 14
3.5 Graph Coloring Quiz, Written Homework Week 15
Proctored Final Exam Comprehensive exam from all chapters (ensure all work is completed and graded prior to scheduling this exam) To be scheduled
and completed
to finalize credit
Week 15


Grading Scale:

Score % Minimum Grade
465 93% A
450 90% A-
435 87% B+
415 83% B
400 80% B-
385 77% C+
350 70% C
300 60% D


You must submit the lessons required to take the course exam(s). Lessons required but not submitted will receive a grade of zero. For the final exam, all coursework must be submitted and graded.