Course Detail
MATH 301 Discrete MathematicsMATH 301 IS Sec 1, University of Mississippi 3 credit hours |
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Instructor Information: |
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Instructor name: Instructor Information: 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 sheppard@olemiss.edu. Please include your course number in the subject line for a quicker response. |
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Contact Information: |
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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 Phone: (662) 915-7313, toll-free (877) 915-7313 |
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Course Description |
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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. |
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Textbook Information: |
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Textbook information will be provided upon enrollment in your iStudy course. |
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Course Objectives: |
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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:
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Course Outline: |
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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. |
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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: |
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Grading Scale:
FAILURE TO TAKE THE FINAL EXAM WILL RESULT IN FAILURE OF THE COURSE. 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. |