Math 510 Discrete Mathematics

Fall 2009
12:30-1:20 PM MWF 129 Cardwell Hall

Course Information ----- Homework ----- Solutions ----- Exam Review

Course Information

Instructor: Dr. Paulhus
Office Hours: Monday 10AM-12PM and Wednesday 2:30-4:30 PM
Office: 125 Cardwell Hall
e-mail: paulhus [at] math [dot] ksu [dot] edu
web site:
Text: Introductory Combinatorics, 5th edition., Richard A. Brualdi

Grading: Your grade in this class will be determined by your performance on homeworks and exams.
  • Homework: Homework will be assigned roughly once a week and will count as 33% of your final grade. The assignments will be posted below. Follow all instructions carefully.
  • In-Class Exams: There will be two exams during the semester on Friday October 2 and Friday November 13. They will count as 34% of your final grade (17% each). Nothing but a writing implement will be allowed for these exams.
  • Final: The final is Thursday December 17 from 4:10-6:00 PM. Do not make plans to go home before this. It will be 33% of your grade for the class. You will be allowed one small sheet of notes for the exam. More instructions on this will be posted later in the semester.
  • The grading rubric for this class may be found here.

  • Some notes:
  • No makeup exams will be given nor late homework accepted unless agreed to beforehand.
  • Cell phone usage is strictly prohibited during class.
  • I encourage you to work together to solve homework problems but everyone must write their own solutions. Copied homework assignments will be given a zero.
  • Any student with a disability who needs an accommodation or other assistance in this course should make an appointment to speak with me as soon as possible.
  • At the bottom of this page* you can find information about the honor code. As stated before, working together on homework is encouraged but the honor pledge does apply to all exams.

  • Syllabus: We will follow the standard syllabus for this class: Chapters 2, 3, 5, 6, 7, 9, 11, 12, and 13.

    Unsolicited Advice:
  • You're not in calculus anymore. "Plug and Chug" or just mindlessly following in-class examples won't cut it. The goal of the class is to teach you how to think about the problems and explain your solutions like a mathematician. Like any new subject, this requires learning the language we use and the conventions for explaining our work. The best way to do this is to practice, practice, practice.
  • Most of you will be challenged a lot during the semester. Be prepared to not "get" everything right away.
  • Work together when you can.
  • Success in this class requires a conceptual understanding of the material, not just the ability to follow proceedure.
  • If you are struggling, come to see me early. If you wait until a week before the final, there isn't much I can do to help you.

  • Homework

    Homework is due at the start of class on the date listed below. Make sure your name, Math 510, and my name are on your homework and please staple your homework. Write in complete sentences and justify all claims. A and B should be turned in separately on the same day. I will grade one, the grader will grade the other

    A sample solution may be found here.

    Homework 1.  Due: September 2:   1.8: 30, 31     2.7: 1, 2, 4, 6, 7, 9
    Homework 2.  Due September 11:  2.7: A = 12, 34, 37, 42     and    B = 14, 20, 24, 47
    Homework 3.  Due September 18:  3.4: A = 3, 5, 8, 9     and    B = 10, 15, 16, 18
    Homework 4.  Due September 28:  3.4: A= 23    5.7: A= 3, 6, 16     and     B = 8, 10, and induction problems found here.
    Homework 5.  Due October 16:  5.7: A=46    6.7: A= 5, 8       and     B= 2, 6, 9
    Homework 6.  Due October 23:  6.7: A= 11, 13, 26, 27       and     B= 14, 17, 21
    Homework 7.  Due November 2:   7.7: A= 13, 14(d and e), 18, 31       and     B=15, 16, 33, 36
    Homework 8.  Due November 11:   7.7: A=48 (bd)   11.8: A=6, 10, 20, 49 (bcf) and (i, iii, iv)   and   B=2, 3, 11, 12, 27, 29, 34, 39
    Homework 9.  Due November 23:  11.8: A=53, 54, 62, 64       and     B=50, 55, 65, 66
    Homework 10.  Due December 4:  13.4: 29   9.4: 6, 7, 8   DO NOT USE ANY RESULTS WE HAVE NOT PROVEN YET. Also, prove:
    Let G be a bipartite graph with bipartition X and Y. Suppose there is a positive integer p such that each vertex in X meets at least p edges, and each vertex in Y meets at most p edges. By counting the total number of edges in G, prove that Y has at least as many vertices as X.
    Homework 11.  Due December 11:  9.4: 9, 11, 16, 17, 19, 20, 25    Also prove this lemma from class.


    Homework Solutions

    Solutions are no longer available online.


    Practice Exams

    Old Exams are no longer available online.


    For the final, you will be allowed 1 sheet of paper with any equations or formula you would like. I will pass out the pieces of paper on the last day of class. You are only allowed to use the piece of paper I pass out. NO WORKED PROBLEMS are allowed on the paper. I will collect the paper at the end of the exam. Anyone attempting to bring different paper or to have worked problems on it will automatically be given a 0 for the final. Still no calculators or other notes and books.


    *Kansas State University has an Honor System based on personal integrity, which is presumed to be sufficient assurance in academic matters one's work is performed honestly and without unauthorized assistance. Undergraduate and graduate students, by registration, acknowledge the jurisdiction of the Honor System. The policies and procedures of the Honor System apply to all full and part-time students enrolled in undergraduate and graduate courses on-campus, off-campus, and via distance learning. The honor system website can be reach via the following URL:

    A component vital to the Honor System is the inclusion of the Honor Pledge which applies to all assignments, examinations, or other course work undertaken by students. The Honor Pledge is implied, whether or not it is stated: "On my honor, as a student, I have neither given nor received unauthorized aid on this academic work." A grade of XF can result from a breach of academic honesty. The F indicates failure in the course; the X indicates the reason is an Honor Pledge violation.

    Last Updated: December 8, 2009