Syllabus for MTH 481 Discrete Mathematics I, Summer 2013 Instructor: Yang (Louis) Liu, Ph.D. Office: Phone: Email: Office Hours:

C318 Wells Hall (517) 353-0844 [email protected] TuWF 2:30 PM-3:30 PM or by appointment.

Course: Lecture: Web Page:

TuWF 12:40 PM - 2:30 PM in 120 Berkey Hall http://www.math.msu.edu/˜yliu/teachh.htm

Textbook: Combinatorics and Graph Theory, 2nd edition, by Harris, Hirst, Mossinghoff. Coverage: 1. Graphs and Their Relatives 2. The Basics 3. Special Types of Graphs 4. Definitions and a Few Properties of Distance in Graphs 5. Graphs and Matrices 6. Graph Models and Distance 7. Definitions and Examples of Trees 8. Properties of Trees 9. Spanning Trees 10. Counting Trees 11. The Bridges of Konigsberg 12. Eulerian Trails and Circuits 13. Hamiltonian Paths and Cycles 14. Definitions and Examples of Planarity 15. Euler’s Formula and Beyond 16. Regular Polyhedra 17. Kuratowski’s Theorem 18. Definitions of coloring 19. Bounds on Chromatic Number 20. The Four Color Problem 21. Chromatic Polynomials 1

22. Some Essential Problems 23. Binomial Coefficients 24. Multinomial Coefficients 25. The Pigeonhole Principle 26. The Principle of Inclusion and Exclusion 27. Double Decks 28. Counting with Repetition 29. Changing Money 30. Fibonacci Numbers 31. Recurrence Relations 32. Catalan Numbers Exams: There will be a midterm exam and a final exam. Students are expected to take all exams. Attendance: Students are expected to attend all class meetings unless there is a special reason, for example, medical appointment or family emergency. Note that class participation and attendance take 17.5% of your final grade, and in order to earn class participation points, you need to attend the classes. Due to the strong connections among the topics in this class, attendance is very important. Also, there may be some important class announcements that are announced during class meetings. If you have five absences, your final grade may be reduced by one letter grade. Grading:

Final exam Midterm exam Homework assignments Class attendance and participation

35% of final grade 25% of final grade 22.5% of final grade 17.5% of final grade

Academic Honesty: Students are expected to be aware of the University’s policies on academic integrity and uphold MSU’s honor code as it is written. Academic dishonesty is considered a serious offense at MSU. In this course, you may discuss the homework with others, but the writeup solutions should be in your own. However, for exams, you are not allowed to discuss with others until the exam is graded. Academic Accommodation: Students in need of academic accommodation should contact Resource Center for Persons with Disabilities and let the instructor know. Standard Disclaimer: This syllabus provides a general guideline for this course; however, deviation may be necessary. Useful Resources and and Links: • Math Learning Center • Academic Calendar

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