# Harbourne's Math 405 Discrete and Finite Math

(List of UNL Campus Buildings, with Links to Maps)

```Time: 4:30-5:45 MW
Room: 104 Bessey Hall

Office: 935 Oldfather Hall
Office Hours:   The half hour after class, or other times by appointment,
but feel free to drop by my office anytime. If I'm busy, we can
make an arrangement for later.
Tel.: 402-472-4476
email: bharbour@math.unl.edu
web: http://www.math.unl.edu/~bharbour/

```

### Homework Assignments

```Due Date        Assignment
Wed Jan 22      p. 179: 4a, 8ab, 10, 20, 22, 26
Mon Jan 27      p. 184: 34, 38b, 42a, 44b,
Find a weighted graph such that the nearest neighbor algorithm does not give
an optimal Hamilton circuit.
Wed Jan 29      p. 218: 2, 10, 14, 32, 70,
36, 42 (for 36 and 42, drop Pittsburgh and St. Louis from the itinerary)
Mon Feb  3      p. 258: 2, 4, 12a, 20
Wed Feb  5      p. 263: 28, 34, 38
Mon Feb 10      p. 302: 2b, 10, 12, 18, 24, 28, 30
Wed Feb 12      p. 306: 26, 28, 30, 34, 42, 50
Read Ch. 8 and problems 68 and 69.
Mon Feb 17      Read Ch 3.1 to 3.5
Determine which players can envy another using
the lone-chooser division strategy, and give
a cake example (as we did in class) showing
how the method works, and showing one player
envying another.
Wed Feb 19      Read Ch. 3
p. 110: 40, 46
Determine how a cake is divided using each of four different algorithms:
lone divider, lone chooser, last diminisher, and Selfridge-Conway (I'll bring in
a handout explaining the last one; it's not in our book), given that
player 1 sees the cake as being 3 horizontal squares followed by a 3 by 3 square
followed by a 2 by 3 rectangle, and player 2 sees the cake as being
a 2 by 9 rectangle, and player 3 sees the cake as being 3 horizontal
squares followed by a 2 by 3 rectangle followed by a 3 by 3 square
Mon Feb 24      Exam 1, on Ch.s 5, 6, 7 and 8
Review Sheet
Wed Feb 26      Meet in Bessey 117 for Joe Gallian's talk on Hamilton circuits on a torus.
Mon Mar  3      Read Ch 1, sections 1 to 5
p. 28: 20, 32, 34, 52
Mon Mar 10      Finish reading Ch 1.
p. 34: 40, 42
Also, determine if the Borda count method satisfies the Independence of
Irrelevant Alternatives criterion. If so, why? If not, give an example.
p. 63: 4, 8, 12, 20
Mon Mar 24      Read Ch 2
p. 63: 24, 30ace, 65
Wed Mar 26      Read Ch 4.1-4.7
p. 141: 2, 4, 8, 10
Mon Mar 31      Read Ch 4
p. 143: 16, 18, 28, 30, 46
Wed Apr  2      Test 2, on Chapters 1 - 4.
Practice Problems
Wed Apr 9       p. 367: 2, 6, 12, 18
Mon Apr 14      p. 367: 24, 26, 34
Also: Determine the payment required for a 250000 mortgage with a 30 year
term at 5% compounded monthly.
```

### Content

We will cover topics in discrete math of possible relevance at the high school level, using the book Excursions in Modern mathematics, 4th edition, by Tannenbaum and Arnold. The topics we cover, and the depth with which we cover them, will depend partly on the interests of the class, and could include topics not necessarily covered by the book (such as map coloring, finite differences, Pascal's triangle, the Pigeonhole Principle, Markov chains, linear programming, and Game Theory).

```               2 hour exams, worth                20% each
homework average, worth            30%
1 class presentation               10%
Final Exam, worth                  20%

Notes:
Homework will be collected daily.
The final is comprehensive.
Date and Time of Final Exam:       Thur., May 8, 3:30-5:30 pm
```

### Class Presentation

Class presentations will allow students an opportunity to think about how material related to the course could be worked into a high school setting. Copies of a written lesson plan, explaining goals, methods and references, will be given to me and to the other students in the class preceding the date of the presentation. The student will carry out the lesson with the class as subjects. The last half hour will be devoted to a discussion of the student's lesson plan and presentation. The next class the other students will then turn in to me two copies of a written evaluation of the presentation, one for me and one to give to the student who made the presentation.

Departmental Grading Appeals Policy: The Department of Mathematics and Statistics does not tolerate discrimination or harassment on the basis of race, gender, religion or sexual orientation. If you believe you have been subject to such discrimination or harassment, in this or any math course, please contact the Department. If, for this or any other reason, you believe your grade was assigned incorrectly or capriciously, appeals may be made (in order) to the instructor, the Department Chair, the Departmental Grading Appeals Committee, the College Grading Appeals Committee, and the University Grading Appeals Committee.