Instructor : Justin Mears
Department : Department of Mathematics, Statistics, and Physics
Office Location : Jabara Hall Room 329
Telephone : (316) - 978 - 3954
E-mail : justin.mears@wichita.edu
Discord Server : Discrete Structures II
Preferred Method of Contact : in-person or any of the above electronic options
Semester : Fall 2022
CRN # : 11210
Classroom : Jardine Hall, Room 309
Days and Times : Monday and Wednesday from 1:30 PM to 2:45 PM
Student Hours : Monday and Wednesday from 3:00 PM to 4:00 PM and by appointment
This syllabus provides you with information specific to this course, and it also provides information about important university policies. This document should be viewed as a course overview; it is not a contract and is subject to change as the semester evolves.
Cross-listed as CS 322. Continuation of Discrete Structures I. Includes relations, graphs, trees, Boolean algebra and automata.
Prerequisites : MATH321 (Discrete Structures I) with grade point of 2.0 (C) or better
Primary Textbook
Discrete Mathematics and Its Applications, (eighth edition) by Kenneth Rosen;
McGraw-Hill Higher Education, 2018 (ISBN 978-1-259-67651-2)
This can be purchased as a physical (loose-leaf) textbook, as an eBook, or rented as a hardback and/or eBook from McGraw-Hill along with other online retailers.
Supplementary Textbooks
Foundations of Computation by Carol Critchlow and David Eck
Applied Discrete Structures by Al Doerr and Ken Levasseur
Discrete Mathematics: An Open Introduction, (third edition) by Oscar Levin
Other Equipment/Materials
This class requires daily access to a computer with sound capabilities and high-speed internet.
Through graded coursework, upon successful completion of this course, students will demonstrate the ability to:
- Demonstrate knowledge and fluency in Binary and n-ary Relations and their applications.
- Draw and describe representations of relations and apply their operations.
- Demonstrate knowledge and fluency Equivalence Relations and Partial Orderings.
- Demonstrate knowledge and fluency in Graph Theory, its models, and operations.
- Draw and describe graphs and their connectivity properties.
- Apply theorems on paths within graphs, including shortest path problems, Euler paths, Hamilton paths.
- Demonstrate knowledge and fluency in Trees.
- Represent various tree applications.
- Apply tree traversals to move between different symbolic representations of mathematical expressions.
- Demonstrate knowledge and fluency in Boolean Algebra.
- Model computing with grammars, languages, Finite-State Machines, and Turing Machines.
This course will consists of the following:
- Two in-person meetings per week that will be streamed and recorded for the online section,
- Regular homework assignments throughout the semester along with multiple exams including a cumulative final, and
- Meaningful discussions about the course topics and ideas.
In order to have meaningful discussions, student participation is crucial. "Participation" involves the student
- Attending every scheduled class,
- Contributing to any and all class discussions in a respectful manner,
- Reading the assigned sections thoroughly prior to coming to class,
- Reading through any provided lecture notes and watching any videos suggested by the instructor throughout the semester,
- Actively participating in the Discourse forum associated with Discrete Structures II, and
- Completing all recommended exercises, projects, and exams.
In addition to attending class, a student who wants to be successfull will be spending at least 15 to 20 hours per week, outside of class,
- Reading every assigned section in the textbook prior to coming to class,
- Doing all provided textbook examples in each section,
- Completing all recommended exercises and projects in a timely manner,
- Studying thoroughly for every exam, and
- Checking their email for important announcements.
Forthermore,
- If the student is having difficulty with course material (including homework problems), they should promptly seek help. The instructor can be reached by email and by appointment.
- Electronic aids (e.g. calculators, cell phones, google glasses, etc.), notes, etc. are not allowed during any quiz or exam; using such aids during an exam constitutes cheating. (Devices approved by the Office of Disability Services (DS) for use during exams should be brought to the attention of the instructor, who will communicate with the DS office.)
Although the student may attempt to reach the instructor by phone, in-person or electronic communication is always preferred.
When e-mailing the instructor with any questions or concerns, please use the following these guidelines:
- Always use the course name in the subject line of the email.
- The student should always remember to sign their name.
- The student should always email the instructor from their WSU email address. Email sent from personal email servers like Gmail, Yahoo, etc., have a tendency to end up in spam folders and thus, are never see them.
- The student should NOT contact the instructor for technical support.
- Any technical problems involving student's computer, or issues regarding file uploading or sharing, should go through the OneStop. They can be contacted at 316-978-3909. Additionally, the student can also fill out a request for help form at their website.
- However, if there is a problem with access or uploading assignments, the student should let the instructor know before the assignment is due. It is a good idea to accompany this notification with the file in question, so that the instructor can verify that it is completed by the due date/time.
The instructor will respond to most e-mails between 8:00 AM and 5:00 PM, Monday through Friday. If a student e-mails the instructor outside of these times, the instructor will respond at their earliest convenience.
- Participation (20% of Final Grade)
- Students are expected to attend every scheduled in-person class meeting and participate in all discussions. Attending classes remotely, if applicable, does not count as attendance for an in-person class. Attendance will be taken and recorded for every class. No excuses will be accepted UNLESS there are extenuating circumstances.
- Additionally, students are required to make at least three (3) discussion posts per week on the Discourse forum associated with Discrete Structures II. These posts can be either the student asking a quesiton related to the material for that week or the student answering a question for their peers.
- Exams (60% of Final Grade)
- There will be four (4) in-class, closed-note, closed-book, exams over the material we cover in class.
- Each exam will be worth 15% of your final grade, accounting for a total of 60%.
- Each exam MUST be taken during the allotted class time on the day they are scheduled UNLESS there are extenuating circumstances.
- Comprehensive Final Exams (20% of Final Grade)
- Format : In-person written exam; closed book and closed note.
- When : Wednesday, December 14, 2022.
- Time : 1:00 PM - 2:50 PM.
- Where : Wichita State University Main Campus
- Room : JH 309
- Due Dates and Schedule
- The list of readings, problems, labs, and exams are available with their due dates on the Tentative Schedule.
- Missed Assignments and Exams
- Late and/or missed assignments will not be accepted.
- Missing any of the exams is highly discouraged. Contact me before the exam, if possible, if you are ill or have a personal reason for not taking a scheduled exam. Makeup exams will not be allowed unless the instructor finds the reason for missing an exam is adequate and sufficient documentation is provided; a note from a medical professional indicating a medical reason for an absence is usually sufficient justification for a makeup exam.
- Extra Credit
- There is no extra credit work for this course, unless otherwise specified during the semester.
WSU uses a +/- grading scale for final grades and to calculate grade point averages. In this class, grades are assigned according to the following. (Other classes might assign grades differently so be sure to understand the different grading scales in all of your classes.)
Percentage | Letter Grade | Grade Points | Interpretation |
---|---|---|---|
91%-100% | A | 4.00 | A range denotes excellent performance |
90% | A- | 3.70 | |
87%-89% | B+ | 3.30 | |
81%-87% | B | 3.00 | B range denotes good performance. |
80% | B- | 2.70 | |
77%-79% | C+ | 2.30 | |
71%-77% | C | 2.00 | C range denotes satisfactory performance. |
70% | C- | 1.70 | |
67%-69% | D+ | 1.30 | |
61%-67% | D | 1.00 | D range denotes unsatisfactory performance. |
60% | D- | 0.70 | |
0%-59% | F | 0.00 | F denotes failing performance. |
Tentative Schedule
- Topics, Readings and Recomended Exercises
- Section 9.1 : Relations and Their Properties
- Exercises : 1, 2, 3 (a,b,c,d), 4, 5, 6 (a,b,d,e,f), 7 (a,b,d,e,f,g), 26, 27, 35 (a,c,e) , 37 (a, b, c, d, f), 44
- Section 9.2 : n-ary Relations and Their Applications
- Exercises : 1, 3, 7, 9, 13, 17, 19, 21, 31
- Section 9.1 : Relations and Their Properties
- Assessed Outcomes : 1 and 2
- Topics, Readings, and Recommended Exercises
- Section 9.3 : Representing Relations
- Exercises : 1, 3, 5, 7, 11 (see exercises in 9.1 for the definition of R-complement), 14, 15 (a), 20, 23, 25, 27, 29, 31, 33 (see exercises in 9.1 for the definition of R-inverse).
- Section 9.4 : Closures of Relations
- Exercises : 1, 3, 5, 7, 9, 11, 13, 16, 17, 18, 19 (a), 21 (a), 25 (a,b), 27 (a,b)
- Section 9.3 : Representing Relations
- Assessed Outcomes : 1 and 2
- Topics, Readings, and Recommended Exercises
- Section 9.5 : Equivalence Relations
- Exercises : 1, 3 (a,c,d), 5, 7, 9 (a), 13, 17, 21, 23, 26, 35 (a,b), 41, 43 (a,b), 49
- Section 9.6 : Partial Orderings
- Exercises : 1 (a,c,e), 3, 5, 7(a,c), 9, 15 (a), 21, 23 (a), 25, 31*, 33, 43
- Section 9.5 : Equivalence Relations
- Assessed Outcomes : 3
- Topics, Readings, and Recommended Exercises
- Section 10.1 : Graph Models
- Exercises : 3 - 9, 10, 11, 19, 27, 31, 35
- Exam 1 : Relations
- Covers Sections 9.1 - 9.6
- Section 10.1 : Graph Models
- Assessed Outcomes : 1 - 4
- Topics, Readings, and Recommended Exercises
- Section 10.2 : Graph Terminology and Special Types of Graphs
- Exercises : 1 - 4, 7 - 10, 11, 13, 15, 18, 20, (a, d, e), 21, 23, 25, 27, 33, 35, 41, 51, 53, 59
- Section 10.3 : Representing Graphs and Graph Isomorphisms
- Exercises : 1, 3, 5, 9(a,d), 11, 13, 17, 19, 23, 39, 45, 49*, 54*, 63(a)
- Section 10.4 (part 1): Connectivity
- Exercises : 1, 3, 5, 11, 15, 21, 27(a,b), 31, 33, 50 (a,b,d)
- Section 10.2 : Graph Terminology and Special Types of Graphs
- Assessed Outcomes : 4 - 6
- Topics, Readings, and Recommended Exercises
- Section 10.4 (part 2): Connectivity
- Section 10.5 : Euler and Hamilton Paths
- Exercises : 3, 5, 7, 15, 19, 21, 33, 35
- Assessed Outcomes : 5
- Topics, Readings, and Recommended Exercises
- Section 10.7 : Shortest-Path Problems
- Exercises : 3, 7, 17, 25
- Exam 2 : Graphs
- Covers Sections 10.1 - 10.6
- Section 10.7 : Shortest-Path Problems
- Assessed Outcomes : 4 - 6
- Topics, Readings, and Recommended Exercises
- Section 11.1 : Introduction to Trees
- Exercises : 1, 3, 5, 7, 9, 19, 20, 23
- Section 11.2 (part 1) : Applications of Trees
- Exercises : 1, 3, 5, 7, 20 (b), 21, 23, 37
- Section 11.1 : Introduction to Trees
- Assessed Outcomes : 7 and 8
- Topics, Readings, and Recommended Exercises
- Section 11.2 (part 2) : Applications of Trees
- Section 11.3 : Tree Traversal
- Exercises : 3, 5, 9, 12, 15, 17, 19, 22(a,c), 23(a), 24(c)
- Assessed Outcomes : 7 - 9
- Topics, Readings, and Recommended Exercises
- Section 12.1 : Boolean Functions
- Exercises : 1, 3, 5(b,c), 9, 19, 21, 25(b), 28(a,c)
- Section 12.2 (part 1): Representing Boolean Functions
- Exercises : 1, 3, 5, 7, 10, 11
- Section 12.1 : Boolean Functions
- Assessed Outcomes : 10
- Topics, Readings, and Recommended Exercises
- Section 12.2 (part 2): Representing Boolean Functions
- Exam 3 : Trees and Boolean Functions
- Covers Sections 11.1 - 11.3 and 12.1 - 12.2
- Assessed Outcomes : 7 - 10
- Topics, Readings, and Recommended Exercises
- Section 13.1 : Languages and Grammars
- Exercises : 1(a), 5, 6(c), 7, 11, 14(c,d), 17, 19(a), 23(a)
- Section 13.2 : Finite-State Machines with Output
- Exercises : 1, 2 (a,b), 3, 7, 13
- Section 13.1 : Languages and Grammars
- Assessed Outcomes : 11
- Topics, Readings, and Recommended Exercises
- Section 13.3 : Finite-State Machines with No Output
- Exercises : 1, 3, 9, 11, 13, 17, 19, 20, 21, 25, 26, 29, 43, 45, 47, 51, 53
- Section 13.4 (part 1): Language Recognition
- Exercises : 3, 5 (a,b), 7 (a), 13, 15, 17, 19
- Section 13.3 : Finite-State Machines with No Output
- Assessed Outcomes : 11
- Topics, Readings, and Recommended Exercises
- Section 13.4 (part 2): Language Recognition
- Thanksgiving Break
- Be Thankful and Eat Lots of Food
- Assessed Outcomes : 11
- Topics, Readings, and Recommended Exercises
- Section 13.5 (part 1): Turing Machines
- Exercises : 1, 3, 7, 11, 13, 15, 20
- Section 13.5 (part 1): Turing Machines
- Assessed Outcomes : 11
- Topics, Readings, and Recommended Exercises
- Section 13.5 (part 2) : Computability
- Exercises :
- Exam 4 : Modeling Computation
- Covers Sections 13.1 - 13.5
- Section 13.5 (part 2) : Computability
- Assessed Outcomes : 11