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Math n: Combinatorial mathematics and Graph Theory with JavaScript; Summer 2026.

    1.1 JavaScript | 1.2 Games | 1.3 Sets 1 | 2.1 Combinatorics 1 | 2.2 Combinatorics 2 | 2.3 Combinatorics 3 |
3.1 Combinatorics 4 | 3.2 Combinatorics 5 | 3.3 Combinatorics 6 | 3.4 Combinatorics 7 | 4.1 Combinatorics 8 | 4.2 Combinatorics 9 | 4.3 Combinatorics 10 | 4.4 Combinatorics 11 |
    5.1 Combinatorics 12 | 5.2 Combinatorics 13 | 5.3 Combinatorics 14 | 6.1 Graph theory 1 | 6.2 Graph theory 2 |


Instructor: Dr. Stefan Forcey Textbook: Eloquent Javascript by Haverbeke (free, see below), Winning Ways for your Mathematical Plays by Conway, and Introductory Combinatorics by Brualdi.

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 summer.

Course Outline:


Homework and Quizzes
Homework quizzes will be posted here on this webpage, along with the due date for the
quiz to be turned in.
No makeup quizzes will be given, but 15 quiz/homework points will be dropped.

    1.1 JavaScript (n videos)Top menu | Next.

    JavaScript:


    • Reading: I recommend the free book Eloquent JavaScript by Marijn Haverbeke.

    • Easy to get started: just write a program in text (samples follow) and save as .htm. Then just open with any browser.
      JS is still the most popular language among developers.

    • Below are some easy sample programs to get started!
      To run the code, click the link. To see the code, add this term to the beginning of each URL: view-source:
      ...or after clicking on a linked program then click on tools and developer tools, and then look at elements (in Chrome) or script (in Explorer).

      • This one just prints Hello World to the screen and the console. To see the latter, open tools and developer tools, and then look at console.

      • This one calculates the value of sin(x)/x for any input.

      • This demonstrates better output use, and if-statements: test how close to 100 floating points can be.
        What is 100.0000000000000071054273576?

      • This one animates sin(x)/x with zoomability.


      Download quiz J:
      Quiz J
      Due on July 14. Brightspace: turn in work..

    • Here is a great tutorial by Matt Mongeau for writing javascript games.
      Here's the Pvs.P Awesome Pong variation wawesome and I wrote using Mr. Mongeau's code:
      top player uses a-w-s-d, bottom uses arrows; first to 10 points wins.
    Games
    1.2 Games (1 video)Top menu | Previous | Next.

    Download pdf here: Book chapter: games

  • Reading: The classic is Winning Ways for your Mathematical Plays by Conway et.al.

    Games:




    Snaky: winner or loser

  • Is the 6-polyomino Snaky achievable (by player 1) on an infinite grid,
    or can it be blocked by player 2?
  • Combinatorial games [ wiki ]
  • What is the smallest grid on which Snaky can be achieved by player 1? [ wiki ] (Harary)

  • Specific Question: Can Snaky win on a 9 x 9 board?
  • Best known answer: Snaky is a loser on an 8 x 8 board. [ Research Gate ]
    		•

    Download quiz G:
    Quiz G
    Due on July 15. Brightspace: turn in work..

  • Set theory 1:


    1.3 Sets 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.









  • Set theory 2:


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

    Then watch the explanations!











  • Set theory 3:


    Sets 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 = {}

    JSON: sets in JavaScript!
  • This one demos the notation: notice the nested sets!
    • Use view-source to see the code, and tools:developer-tools:console to see the output of this JSON demo .






    Download quiz 0:
    Quiz 0
    Due on July 16. Brightspace: turn in work..


    2.1 Combinatorics 1 (6 videos)Top menu | Previous | Next.
  • Reading: Chapter 2 of Combinatorics by Brualdi.

  • 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)...









    2.2 Combinatorics 2 (5 videos)Top menu | Previous | Next.
    Download Quiz 1a:
    Take home quiz 1a.
    Due on July 18. Brightspace: turn in work..

    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.




    2.3 Combinatorics 3 (1 video)Top menu | Previous | Next.
  • Download Quiz 1b:
    Take home quiz 1b.
    Due on July 21. Brightspace: turn in work..

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




    3.1 Combinatorics 4 (3 videos)Top menu | Previous | Next.
    Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanations.








    3.2 Combinatorics 5 (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.







    Download take home quiz 1c here:
    Quiz 1c
    Due on July 23 Brightspace: turn in work..


    Download practice problems here:
    Practice problems posted.

    Then watch the explanations.






    3.3 Combinatorics 6 (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
    Due on July 24 Brightspace: turn in work..











    3.4 Combinatorics 7 (5 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.












    4.1 Combinatorics 8 (5 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.

  • Take home quiz 3
    Download here:
    Quiz 3
    Due on July 28 Brightspace: turn in work..













    4.2 Combinatorics 9 (4 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.

  • Take home quiz 4.
    Download here:
    Quiz 4
    Due on July 29 Brightspace: turn in work..











    4.3 Combinatorics 10 (4 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.










    4.4 Combinatorics 11 (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.


    5.1 Combinatorics 12 (2 videos)Top menu | Previous | Next.
  • Reading: Chapter 6 of Brualdi.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.






    5.2 Combinatorics 13 (2 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.

  • Take home quiz 5.
    Download here:
    Quiz 5
    Due on Aug 4 Brightspace: turn in work..







    5.3 Combinatorics 14 (2 videos)Top menu | Previous | Next.
  • Here is the lecture. Download notes here:
    Notes posted.
    Then watch the explanation.








    6.1 Graph Theory 1 (2 videos) Top menu | Previous | Next.

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

  • Take home quiz 8.
    Download here:
    Quiz 8
    Due on Aug 6 Brightspace: turn in work..







    Graph Theory 2 (2 videos) Top menu | Previous | Next.

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







    • 6.2 Graph Theory 3 ( 0 videos) Top menu | Previous.

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

Resources.

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