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Math 415/515: Combinatorics and Graph Theory; Fall 2017.




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. 28: Day one.
• Sep.4: No class on Labor day.
• Chapter 2: Counting
• Chapter 5: Pascal’s Triangle
• Sep. 11: Last day to drop.
• Chapter 6 : Inclusion Exclusion
• TEST 1. Wednesday Oct. 11.
Here is some additional review for the first exam. Also study quizzes and hw!
Here's the Map of Parma (see page 2).
Answers will be given in class.
• Oct. 16: Last day to w/draw.
• Chapter 7: Recurrence and Generating Functions
• Chapter 11: Graphs
• TEST 2. Monday Nov. 20
• Nov. 23-24: Thanksgiving.
• Dec. 8: Last day.
• Dec. 15: Final Exam12:15PM - 2:15PM, Crouse 209


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.
  • Homework 1: Not to be turned in. Quiz based on these problems: Fri. Sep. 8 (take home, due Sep. 11).
    • Chapter 2: 1, 4, 7, 8, 9, 13, 14, 23, 28(a)
    • For those in 515: Also Chapter 2: 26

  • Homework 2: Not to be turned in. Quiz based on these problems: September 15 (take home, due Sep. 18).
    • Chapter 2: 21, 26, 28 (b), 32, 33, 34, 37, 38, 43, 45, 55
    • For those in 515: Also Chapter 2: 48, 49,

  • Homework 3: Not to be turned in. Quiz based on these problems: September 22 (take home, due Sept 25).
    • Chapter 5: Problems 6, 7, 8, 9, 15
      (hint - use the binomial theorem and differentiate something!), 23, 24, 38, 40.
    • For those in 515: Also Chapter 5: 18 (hint: don’t use differentiation , use...),

  • Homework 4: Not to be turned in. Quiz due October 4.
    • Chapter 6: Problems 2, 3, 5, 6, 8, 9

  • Homework 5: Not to be turned in. Quiz based on these problems: October 13 (take home due 10/16).
    • Chapter 6: Problems 11, 15, 25, 26, 27
    • For those in 515: Also Chapter 6: 21

  • Homework 6: Not to be turned in. Quiz based on these problems: October 20 (take home, due Oct. 23).
    • Chapter 7: 13 (in part c, let alpha be a whole number > n), 14, 17, 18, 19, 20, 24, 25,
    • For those in 515: No extra problems this time!

    No HW, Quiz for week of October 23-27. Project outline due on 10/31.
  • Homework 7: Not to be turned in. Quiz based on these problems: (take home, due Nov 8.)
    • Chapter 7: 31, 32, 35, 43, 44, 48 a,b,c, 51
    • For those in 515: Also Chapter 8: 1

  • Homework 8: (not collected) No quiz: test review will include some of these.
    • Chapter 11: 3, 4, 9, 15, 29 (constructing a trail is optional), 30, 39, 44, 49


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.

Due dates:
  • Oct 31: outline.
  • Nov 28: Rough draft.
  • Dec 9: Final draft.



Exams
There will be two in-class tests and a final.
  • Test 1: Wednesday, October 11, in class.
  • Test 2: Monday, Nov. 20 in class
    Here are the answers to the review questions.
  • Final Exam: 12/15/2017, Friday 12:15PM - 2:15PM, Crouse 209.

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.