Math 3103: Combinatorics, Fall 2017

Date    Sectiona          Topic Recommended Homeworkb

Aug 21     1.1     Set theory, basic counting -
Aug 23     1.2     Permutations 1-27, 31-37
Aug 25     1.3     Combinations 1-33
Aug 28     1.4     Combinations with repetition 1-17
Aug 30, Sep 1     8.1     Inclusion and exclusion 1-27
Sep 6     8.2, 8.3    Generalizations, derangements 1-7, (8.3) 1-11
Sep 8     8.4     Rook polynomials
Sep 11     8.5     Forbidden positions 1-11
Sep 13     9.1     Generating functions 1-5
Sep 15, 18     9.2     Examples, formulas and calculations 1-15, 29, 33
Sep 20     9.3, 9.5    Partitions of integers, summation (9.3) 1, 3, 5; (9.5) 1, 3, 5, 7

Sep 22     -     Review
Sep 25     -     Test on Chapters 8 & 9

Sep 27     10.1     Recurrence relations, first order 1, 3, 5
Sep 29, Oct 2     10.2     Second order relations 1, 3, 9-15, 23-31
Oct 4, 6     10.3     Nonhomogeneous recurrence relations 1-13
Oct 9     10.4     Generating function method 1, 3
Oct 11     14.1     Rings: Definition and examples 1, 3, 5, 9bcd, 13, 15
Oct 13     14.2     Properties and structure 3-7, 13-21
Oct 18, 20     14.3     Integers modulo n 1-5, 9-15, 19, 21
Oct 23     14.4     Homomorphism and isomorphism 1-15

Oct 25     -     Review
Oct 27     -     Test on Chapters 10 & 14

Oct 30     16.1     Groups: definition, examples 1-17
Nov 1     16.1     Groups: properties 1-17
Nov 3     16.2     Homomorphisms and cyclic groups 1-15
Nov 6     16.3     Cosets and Lagrange's theorem 1-11
Nov 8     16.4     Public key cryptography
Nov 10     16.5, 16.6    Coding theory (16.5) 1, 3
Nov 13     16.7     Parity and generator matrices 1-9
Nov 15     16.8, 16.9    Group codes, Hamming matrices 1-7
Nov 17     16.10     Counting equivalence classes 1, 2, 3, 5-13
Nov 20     16.11     The cycle index 1-7
Nov 27     16.12     Pattern inventory 1-9

Nov 29     -     Review
Dec 1     -     Test on Chapter 16

Dec 4, 6     -     Review

Dec 13     -     Final Exam, 8:00-10:00am

 a Some sections may be omitted.
 b Only odd-numbered problems unless otherwise noted.


Other Information

Instructor: Daniel H. Luecking                     Office: SCEN 354

Office Hours: 10:45-11:35am and 1:30-2:50pm MWF

Textbook: Discrete and Combinatorial Mathematics, R. Grimaldi, 5th ed., Chapters 1, 8-10, 14, 16.

Exams: There will be three regular exams worth 100 points each. Exams will occur on the dates in the above schedule. There will be a comprehensive final exam worth 200 points.

Quizzes: There will be a quiz every few sections, each worth 10 points. Some quizzes may be take-home. If so, they must be turned in at the beginning of class on the day they are due, before you take your seat. I plan to have 12 or more quizzes.

Make-ups: No make-up exams and no make-up quizzes. If you have a reasonable conflict that prevents your taking an exam, you will be excused, and I will give you a grade on that exam equal to the average of all other scores, except the final (but including the quizzes). Conflicts which are known in advance must be reported in advance in order to be excused. Reasonable conflicts include (but are not limited to) required university activities, jury duty, national guard duty, illness or other emergencies, and funerals. Missed exams without an excuse are recorded as 0 points.

All missed quizzes are recorded as 0 points. In compensation, only the 10 best quizzes are counted. Missed deadlines on take-home quizzes may be extended, but only if you have a reasonable conflict (see previous paragraph) and only until the beginning of the next class session.

Attendance: I take attendance occasionally, and I take note of a missed quiz, homework not turned in, or a graded item that is not picked up. Attendance will be taken into account when borderline grades are considered.

Grading: All of your solutions must show enough of the work that I can tell you understand what you are doing in each step; the answer alone will not get you full credit.

Your 10 highest quiz scores will be added for a possible 100 points. Your two highest test scores will be added for another possible 200 points. The final exam is worth another 200 possible points.

Your grade is then determine from this grand total of quizzes, tests and the final, according to this scale: 450-500 = A, 400-449 = B, 350-399 = C, 300-349 = D.

Policy on Class Cancellation: In the event of bad weather, check with the University: if it is open, class will be held.

If I have not arrived by 5 minutes after the class starting time, call my office phone (I may simply be delayed). If I do not answer, wait another 10 minutes (I may be on my way).

Statement on Academic Honesty: Submitting the work of another as your own is a serious violation of the University's policy on academic integrity, and will result in disciplinary proceedings when detected. This includes any take-home assignments unless I say otherwise. Do not accept help and do not offer help to anyone on them. If you are uncertain what constitutes a violation, talk to me before you do it.

Quoting the University: Each University of Arkansas student is required to be familiar with and abide by the University's `Academic Integrity Policy' which may be found at http://honesty.uark.edu/policy/index.php. Students with questions about how these policies apply to a particular course or assignment should immediately contact their instructor.

Miscellaneous: You are not permitted to use any electronic device (unless mandated by a recognized disability) during any test or quiz. In compensation, I never require you to simplify numerical answers or algebraic expressions.

On quizzes you may use only pencils or pens and blank scratch paper.

On exams (including the final), in addition to pencil and paper, you may use your textbook and any handwritten notes you care to bring. A good strategy is to write down the main ideas you have trouble remembering on a single sheet of paper.




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