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

    Preview | Review 1 | Review 2 | Review 3 | Jan 10. | Jan 12. | Jan 17 | Jan 19 | Jan 24 | Jan 26 | Jan 31 | Feb 2 | Feb 7 |
Feb 9 | Feb 21 | Feb 14 | Feb 21 | Feb 28 | Mar 2 | Mar 7 | Mar 9 | Mar 14 | Mar 16 | Mar 28 | Mar 30, 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:
  • Jan 10. Day 1.
  • Jan 15: Last day to add.
  • Jan. 16: No class for MLK day.
  • Chapter 2: Counting
  • Chapter 5: Pascal’s Triangle
  • Jan. 22: Last day to drop.
  • TEST 1: Feb 23? Review

  • Feb. 21: No class on Tues. (Pres. day.)
  • Feb. 26: Last day to w/draw.
  • Chapter 6 : Inclusion Exclusion
  • TEST 2. Apr 7?
    Here is some additional review for the second exam.
    Here are the answers with some work shown. Also study quizzes and hw!.

  • March 20-24: Spring break.
  • Chapter 7: Recurrence and Generating Functions
  • Chapter 11: Graphs
  • April 28: Last day.
  • Test 3: Comprehensive Final Exam.


    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


      Jan 10 (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)...










      Jan 12 (5 videos)Top menu | Previous | Next.
      Download: Take home quiz 1a. Due Jan. 17 .
      Key here: Key to quiz 1a.

      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.





      Jan 17 (1 video)Top menu | Previous | Next.
    • Download: Take home quiz 1b. due Jan 24 .
      Key here: Key to quiz 1b.

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





      Jan 19 (3 videos)Top menu | Previous | Next.
      Here is the lecture. Download notes here:
      Notes posted.
      Then watch the explanations.









      Jan 24 (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 due Jan 31 .
      Download here:
      Quiz 1c

      Key here: Key to quiz 1c.

      Download practice problems here:
      Practice problems posted.

      Then watch the explanations.







      Jan 26 (4 videos)Top menu | Previous | Next.
    • Here is the lecture. Download notes here:
      Notes posted.
      Then watch the explanation.

    • Take home quiz 2 due Feb 2 .
      Download here:
      Quiz 2

      Key here: Key to quiz 2.











      Jan 31 (5 videos)Top menu | Previous | Next.
    • Here is the lecture. Download notes here:
      Notes posted.
      Then watch the explanation.













      Feb 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 Feb 9 .
      Download here:
      Quiz 3

      Key here: Key to quiz 3.













      Feb 7 (4 videos)Top menu | Previous | Next.
    • Here is the lecture. Download notes here:
      Notes posted.
      Then watch the explanation.

    • Take home quiz 4 due Feb 14 .
      Download here:
      Quiz 4

      Key here: Key to quiz 4.











      Feb 9 (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

      Feb 14 (10 videos)Top menu | Previous | Next.
    • Download MORE practice problems here:
      Practice problems posted.
      and Answers to the problems


      TEST 1 ENDS HERE.



      Feb 16 (2 videos)Top menu | Previous | Next.
    • Here is the lecture. Download notes here:
      Notes posted.
      Then watch the explanation.







      Feb 21 (2 videos)Top menu | Previous | Next.
    • Here is the lecture. Download notes here:
      Notes posted.
      Then watch the explanation.

    • Take home quiz 5 due: Feb 28 .
      Download here:
      Quiz 5

      Key here: Key to quiz 5.





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


    • Feb 28 (2 videos)Top menu | Previous | Next.
    • Here is the lecture. Download notes here:
      Notes posted.
      Then watch the explanation.







      Mar 2 (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 Mar 9
      Download here:
      Quiz 6a

      Key here: Key to quiz 6a.

















      Mar 7 (3 videos) Top menu | Previous | Next.

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

    • Take home quiz 6a due Mar 9
      Download here:
      Quiz 6a

      Key here: Key to quiz 6a.









      Mar 9 (5 videos) Top menu | Previous | Next.

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

    • Take home quiz 6b due Mar 16
      Download here:
      Quiz 6b

      Key here: Key to quiz 6b.













      Mar 14 (3 videos) Top menu | Previous | Next.

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









    • Mar 16 (3 videos) Top menu | Previous | Next.

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

    • Take home quiz 7 due Mar 28
      Download here:
      Quiz 7









      Mar 28 (3 videos) Top menu | Previous | Next.

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









    • Mar 30 (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.