Introduction to Combinatorics - Mathematics 413


Section D1U/D1G


11:00-11:50 am MWF, 159 Altgeld Hall


University of Illinois - Fall 2004


Course and Final Exam Grades

Section D1U (html)

Section D1G (html)

Course information

  • The course textbook is Introductory Combinatorics, by Richard A. Brualdi, 4th ed., Prentice Hall, 1999.

  • Office hours: Tuesday 9 am, Wednesday 3 pm, Friday 12 pm, and by appointment.

  • Exam schedule: There will be 3 in-class hour exams and 1 final exam. All exams will be held in class, room 159, Altgeld Hall.
    Exam 1: Wednesday, September 22.
    Exam 2: Wednesday, October 20.
    Exam 3: Wednesday, November 17.
    Final Exam: Saturday, December 18, 8-11 am.

  • The above and all other relevant course information may be found in the syllabus. (pdf) (ps)

    • Sections covered

  • 8/25, 8/27: chessboard covers: 1.1.

  • 8/30-9/3: pigeonhole principle: 2.1, 2.2.

  • 9/8, 9/10: Ramsey Theory, permutations: 2.3, 3.1, 3.2.

  • 9/13-9/17: combinations, permutations and combinations of multisets: 3.3, 3.4, 3.5.

  • 9/20-9/24: Pascal's formula, the binomial theorem, binomial coefficient identities: 5.1, 5.2, 5.3.

  • 9/27-10/1: binomial coefficient identities, the multinomial theorem, Newton's binomial theorem: 5.3, 5.5, 5.6.

  • 10/4-10/8: inclusion-exclusion principle, derangements: 6.1, 6.2, 6.3.

  • 10/11-10/15: linear homogeneous recurrence relations: 7.1, 7.2.

  • 10/18-10/22: linear non-homogeneous recurrence relations, generating functions: 7.3, 7.4.

  • Exam II: Wednesday, October 20, covers 5.1, 5.2, 5.3, 5.5, 5.6, 6.1, 6.2, 6.3, 7.1, 7.2.

  • 10/25-10/29: solving recurrences using generating functions, the recurrence for Catalan numbers, exponential generating functions: 7.5, 7.6, 7.7.

  • 11/1-11/5: exponential generating functions, Catalan numbers (revisited), Difference sequences, Stirling numbers: 7.7, 8.1, 8.2.

  • 11/8-11/12: Difference sequences, Stirling numbers, partitions: 8.1, 8.2, 8.3.

  • 11/15-11/19: Partitions.

  • Exam III: Wednesday, November 17, covers 7.3, 7.4, 7.5, 7.6, 7.7, 8.1, 8.2, 8.3.

  • There is no homework 11/20-11/28.

  • 11/29-12/3: More on partitions, Polya counting: 14.1, 14.2.

  • 12/6-12/10: Polya counting, Burnside's Lemma: 14.1, 14.2.

  • Final Exam: Saturday, December 18, 8-11 am, 159 Altgeld Hall. The exam is comprehensive. It will cover all sections listed above and consist of ~ 12 problems.

    Homework assignments

    homework 1, due 9/3. (pdf) (ps)

    homework 2, due 9/10. (pdf) (ps)

    homework 3, due 9/17. (pdf) (ps)

    homework 4, due 9/24. (pdf) (ps)

    homework 5, due 10/1. (pdf) (ps)

    homework 6, due 10/8. (pdf) (ps)

    NOTE: There is a type in the statement of #27: "2n+1 choose n+1" should be "2n+2 choose n+1."

    homework 7, due 10/15. (pdf) (ps)

    NOTE: The correction I made to the statement of problem #17 was made in haste. The problem is correct as stated, but not completely clear. It should read "the letters of the same type do not ALL appear consecutively".

    homework 8, due 10/22. (pdf) (ps)

    NOTE: The instructions for #21 are incomplete; it should read "01, 10, 00, and 11 never occur".

    homework 9, due 10/29. (pdf) (ps)

    homework 10, due 11/5. (pdf) (ps)

    homework 11, due 11/12. (pdf) (ps)

    homework 12, due 11/19. (pdf) (ps)

    homework 13, due 12/6. (pdf) (ps)

    homework 14, due 12/13. (pdf) (ps)

    Homework 14 will be graded and solutions will be available on Tuesday, 12/14.