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Math 415/515: Combinatorics and Graph Theory; Fall 2023.

    Preview | Review 1 | Review 2 | Review 3 | Aug 29. | Aug 31. | Sep 5 | Sep 7 | Sep 12 | Sep 14 | Sep 19 | Sep 21 | Sep 26 |
Sep 28 | Oct 3 | Oct 5 | Oct 10 | Oct 12 | Oct 17 | Oct 19 | Oct 24 | Oct 26 | Oct 31 | Nov 2 | Nov 7, project | Part 2 |


Instructor: Dr. Stefan Forcey Textbook: Required: Introductory Combinatorics (5th edition) by Richard Brualdi, Prentice Hall.

Course Syllabus.
The syllabus will include information about grading policies. You should definitely read it.
Here's an approximate schedule of what we'll be doing this semester. Emphasis on the "approximate".

Course Outline:
• Aug. 29: Day one.
• Sep. 4: No class on Labor day.
• Chapter 2: Counting
• Chapter 5: Pascal’s Triangle
• Sep. 10: Last day to drop.
• Chapter 6 : Inclusion Exclusion
• Oct. 15: Last day to w/draw.
• TEST 1. October 19, Review .
Also study quizzes and hw!
Here's the Map of Parma (see page 2).

Here's some additional chapter 5 solutions.

• Chapter 7: Recurrence and Generating Functions
• Chapter 11: Graphs
• TEST 2. Tues Nov. 21
• Nov. 23,24: Thanksgiving.
• Dec. 7: Last day.
• Final Exam TBA

Homework and Quizzes
Homework will be posted here on this webpage, along with either the due date for the
homework to be turned in or more usually the date for the quiz (if the hw is not turned in.)
No makeup quizzes will be given, but 15 quiz/homework points will be dropped.


    Preview (3 videos)Top menu | Previous | Next.
  • Quick review of MacLaurin power series:





  • Preview of basic counting:




  • Review of set theory 1:


    Review 1 (4 videos)Top menu | Previous | Next.
    Download pdf here: Notes: Review 1 posted Aug 24

    Then watch the explanations!
    In the next 4 short videos I talk through the introduction to set theory.









  • Review of set theory 2:


    Review 2 (5 videos)Top menu | Previous | Next.
    Basic set operations. Download pdf here: Notes: Review 2 posted Aug 24

    Then watch the explanations!











  • Review of set theory 3:


    Review 3 (2 videos)Top menu | Previous | Next.
    More set operations. Download pdf here: Notes: Review 3 posted Aug 24

    Then watch the explanations!

    Additional notes:
    1) The complement of the empty set is the whole set U ( universe).
    Complement of {} = U.
    2) Subtracting works even when there is no overlap: it is just the whole first set, since there is nothing to subtract.
    A - B = A, when A intersect B = {}.
    3) A - {} = A.
    4) A union {} = A.
    5) A intersect {} = {}
    6) {} - A = {}





    Download: Practice quiz Not to turn in.
    Key to Practice quiz


    Week 1 part 1 (6 videos)Top menu | Previous | Next.
  • Homework 1: Not to be turned in.
    • Chapter 2: 1, 4, 7, 8, 9, 13, 14, 23, 28(a)
    • Chapter 2: 21, 28 (b), 32, 33, 34, 37, 38, 43, 45, 55
  • Basic Counting. Download pdf here: Notes: Basic Counting posted.

    Then watch the explanations.

  • Duplicate notes of above, with answers. Download pdf here: page 1 and page 2

    Here is the second part. Download pdf here:
    Basic Counting 2. Notes posted.
    Practice problems.
    Then watch the explanations.




    ***Correction: at the very last line, should have read...({7,q},4),({7,q},5),({7,q},q)...










    Week 1 part 2 (5 videos)Top menu | Previous | Next.
    Download: Take home quiz 1a. Due Sep 7 .


    Here is the lecture. Download pdf here:
    More counting: Notes posted.

    Then watch the explanations.









    And the final answer did turn out to be 22,134.

    Here is the second part. Download pdf here:
    Part 2: Notes posted.

    Then watch the explanations.





    Week 2 part 1 (1 video)Top menu | Previous | Next.
  • Download: Take home quiz 1b. due Sep 14 .
    Key here: Key to quiz 1b.

    Here is the lecture. Download 2 pdfs here:
    Problems posted.
    Solutions posted.
    Then watch the explanations.





    Week 2 part 2 (3 videos)Top menu | Previous | Next.
    Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanations.









    Week 3 part 1 (5 videos)Top menu | Previous | Next.
    Here is the lecture. Download notes here:
    Notes posted part 1
    Part 2:
    Notes posted part 2
    Then watch the explanation.







    Take home quiz 1c .
    Download here:
    Quiz 1c

    Key here: Key to quiz 1c.

    Download practice problems here:
    Practice problems posted.

    Then watch the explanations.







    Week 3 part 2 (4 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.

  • Take home quiz 2 .
    Download here:
    Quiz 2

    Key here: Key to quiz 2.











    Week 4 part 1 (5 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.













    Week 4 part 2 (5 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.

  • Take home quiz 3 due Oct 5.
    Download here:
    Quiz 3

    Key here: Key to quiz 3.













    Week 5 part 1 (4 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.

  • Take home quiz 4 due Oct 12 .
    Download here:
    Quiz 4

    Key here: Key to quiz 4.











    Week 5 part 2 (4 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.










      Book problems
    • Chapter 5: Problems 6, 7, 8, 9, 15
      (hint - use the binomial theorem and differentiate something!), 23, 24, 38, 40.
    • Chapter 6: Problems 2, 3, 5, 6, 8, 9

    Week 6 part 1 (10 videos)Top menu | Previous | Next.
  • Download practice problems here:
    Practice problems posted.
    and Answers to the problems
    Also study quizzes and hw!
    Here's the Map of Parma (see page 2).

    Here's some additional chapter 5 solutions.


    TEST 1 ENDS HERE.



    Week 6 part 2 (2 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.







    Week 7 part 1 (2 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.

  • Take home quiz 5 due: Oct 31 .
    Download here:
    Quiz 5

    Key here: Key to quiz 5.





  • Chapter 6: Book Problems 11, 15, 25, 26, 27


  • Week 7 part 2 (2 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.







    Week 8 part 1 (7 videos) Top menu | Previous | Next.

  • Here is the lecture, review of Calculus 2. Download pdf here:
    Notes posted pt1.

  • Part 2 of the lecture. Download pdf here:
    Notes posted pt2.

  • Take home quiz 6a due
    Download here:
    Quiz 6a

    Key here: Key to quiz 6a.

















    Week 8 part 2 (3 videos) Top menu | Previous | Next.

  • Here is the lecture. Download pdf here:
    Notes posted.

  • Take home quiz 6a due
    Download here:
    Quiz 6a

    Key here: Key to quiz 6a.









    Week 9 part 1 (5 videos) Top menu | Previous | Next.

  • Here is the lecture. Download pdf here:
    Notes posted.

  • Take home quiz 6b due
    Download here:
    Quiz 6b

    Key here: Key to quiz 6b.













    Week 9 part 2 (3 videos) Top menu | Previous | Next.

  • Here is the lecture. Download pdf here:
    Notes posted.









  • Week 10 part 1 (3 videos) Top menu | Previous | Next.

  • Here is the lecture. Download pdf here:
    Notes posted.

  • Take home quiz 7 due
    Download here:
    Quiz 7









    Week 10 part 2 (3 videos) Top menu | Previous | Next.

  • Here is the lecture. Download pdf here:
    Notes posted.









  • Week 11 part 1 (5 videos) Top menu | Previous | Next.

    Projects

    Here is the project description.

    Here are some potential sequences, if you have not already found one you like.

    Here is the grading rubric.

    Here is an example project.

    (MSword version)
    Note that your project must follow this exact outline, using the values that I assign you.
    There is room for additional information in the open problem section.


















Exams
There will be two in-class tests and a final.
  • Test 1:
  • Test 2:
  • Final Exam:

RESOURCES:
H. Wilf: generatingfunctionology

A great resource is wolfram|alpha.
Here is the ordinary generating function for the triangular numbers, n choose 2.
Here is the exponential generating function for the triangular numbers, n choose 2.

Of course the OEIS.
Here is the open question of counting numbers of posets.


CREDIT:
The text of this page was adapted, with permission, from an original course site by J.P. Cossey.