Syllabus for MTH 482 Discrete Mathematics II, Spring 2015 Instructor: Yang (Louis) Liu, Ph.D. Office: Phone: Email: Office Hours:
C318 Wells Hall (517) 353-0844
[email protected] TBA
Course: Lecture: Web Page:
MWF 10:20AM-11:10AM in A304 Wells Hall http://www.math.msu.edu/˜yliu/teachh.htm
Textbook: • Combinatorics and Graph Theory, 2nd edition, by Harris, Hirst, Mossinghoff • Generatingfunctionology, Academic Press, New York, 1994. H. S. Wilf (recommended) • Enumerative Combinatorics I, 2nd edition, by Richard Stanley • Proofs from THE BOOK, Martin Aigner and G¨ unter Ziegler (recommended) Coverage: 1. Generating Functions 2. Double Decks 3. Counting with Repetition 4. Changing Money 5. Fibonacci Numbers 6. Recurrence Relations 7. Catalan Numbers 8. Regular Polyhedra 9. Kuratowski’s Theorem 10. Bounds on Chromatic Number 11. The Four Color Problem 12. Chromatic Polynomials 13. Some Essential Problems 14. Binomial Coefficients 15. Multinomial Coefficients 1
16. Permutation Groups 17. Burnside’s Lemma 18. The Cycle Index 19. Polya’s Enumeration Formula 20. Partitions 21. Stirling Cycle Numbers 22. Stirling Set Numbers 23. Bell Numbers 24. Sylvester’s Problem 25. Euler’s Formula and Beyond 26. Sylvester–Gallai Theorem 27. Convex Polygons 28. Infinite Combinatorics and Graphs 29. Language and Logical Axioms 30. Proper Axioms 31. Axiom of Choice 32. Ordinals, Cardinals, and Many Pigeons 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, a student needs 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 a student has five absences in the class meetings set by the university calendar, his or her 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. Academic Accommodation: Students in need of academic accommodation should contact Resource Center for Persons with Disabilities and let the instructor know. 2
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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