Math 3103: Combinatorial and Discrete Mathematics, Spring 2014

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Math 3103: Combinatorial and Discrete Mathematics, Spring 2014. Date. Section. Topic. Recommended Homework*. Jan 13. 1.1. Set theory, basic counting. —.
Math 3103: Combinatorics, Fall 2017 Date

Sectiona

Aug 21 Aug 23 Aug 25 Aug 28 Aug 30, Sep 1 Sep 6 Sep 8 Sep 11 Sep 13 Sep 15, 18 Sep 20

1.1 1.2 1.3 1.4 8.1 8.2, 8.3 8.4 8.5 9.1 9.2 9.3, 9.5

Set theory, basic counting Permutations Combinations Combinations with repetition Inclusion and exclusion Generalizations, derangements Rook polynomials Forbidden positions Generating functions Examples, formulas and calculations Partitions of integers, summation

Sep 22 Sep 25

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Review Test on Chapters 8 & 9

Sep 27 Sep 29, Oct 2 Oct 4, 6 Oct 9 Oct 11 Oct 13 Oct 18, 20 Oct 23

10.1 10.2 10.3 10.4 14.1 14.2 14.3 14.4

Recurrence relations, first order Second order relations Nonhomogeneous recurrence relations Generating function method Rings: Definition and examples Properties and structure Integers modulo n Homomorphism and isomorphism

Oct 25 Oct 27

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Review Test on Chapters 10 & 14

Oct 30 Nov 1 Nov 3 Nov 6 Nov 8 Nov 10 Nov 13 Nov 15 Nov 17 Nov 20 Nov 27

16.1 16.1 16.2 16.3 16.4 16.5, 16.6 16.7 16.8, 16.9 16.10 16.11 16.12

Groups: definition, examples Groups: properties Homomorphisms and cyclic groups Cosets and Lagrange’s theorem Public key cryptography Coding theory Parity and generator matrices Group codes, Hamming matrices Counting equivalence classes The cycle index Pattern inventory

Nov 29 Dec 1

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Review Test on Chapter 16

Dec 4, 6



Review

Dec 13



Final Exam, 8:00–10:00am

a b

Recommended Homeworkb

Topic

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

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— 1–27, 31–37 1–33 1–17 1–27 1–7, (8.3) 1–11 1–11 1–5 1–15, 29, 33 (9.3) 1, 3, 5; (9.5) 1, 3, 5, 7

1, 3, 5 1, 3, 9–15, 23–31 1–13 1, 3 1, 3, 5, 9bcd, 13, 15 3–7, 13–21 1–5, 9–15, 19, 21 1–15

1–17 1–17 1–15 1–11 (16.5) 1, 3 1–9 1–7 1, 2, 3, 5–13 1–7 1–9

Other Information Instructor: Daniel H. Luecking

Office: SCEN 354

Telephone: 575-6327

Email: [email protected]

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. Web page: http://comp.uark.edu/~luecking/classes/3103.html 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, preferably 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. Page 2 of 2