22M:151:002 Discrete Mathematical Models, 1:30P - 2:20P MWF 105 MLH, Spring 2004
Instructor: Isabel Darcy
Office & Phone: Department of
e-mail: idarcy@math.uiowa.edu
web-page http://www.math.uiowa.edu/~idarcy/COURSES/151/SPRING04/151.html
Office hours: MWF 2:30-3:00, Wednesday ?, Friday: 10:30-11:20 (tentative), or by appointment
Textbook: Discrete Mathematical Models by Fred Roberts
Out of print, but IMU bookstore has special copies for this course.
Prerequisites: 22M:27 or
equivalent (Students must know matrix algebra, eigen-values/vectors.)
Goals and objectives: To study discrete mathematical models arising from various fields. Construction, interpretation, analysis, simulation and testing of models through Graphs, Pulse processes and Markov chains. Understanding, writing and correcting proofs are also an integral part of the course.
Students are expected to attend all 3 hours of lectures every week. Lectures will occasionally contain material not covered in the textbook, for example, trees, depth-first and breadth-first searches, Eulerian paths and chromatic polynomials. You are responsible for the material of all lectures, the sections covered in the textbook and the prerequisites. You must take both of the 2 midterms, the final exam and submit a project. You are strongly encouraged to go to your lecturer’s office hours, if you need additional help. Additional office hours can be arranged if requested before or after lectures.
Make-ups may be given for exams missed due to unavoidable circumstances and compelling reasons which are documented in writing. If you have a conflict or a medical problem, discuss your situation with your lecturer as soon as possible. No make-ups for homework. We will drop the lowest two homework grades.
Rational for Projects The subject of discrete mathematical models is a broad one that is rich in significance and applications. There is much more than can be communicated in a 3-sh course. In order to motivate each of you to explore discrete mathematical models further, you will be assigned to submit a report to present both orally and in written form at the end of semester. Everyone is expected to work in a team of three students.
Guidelines and list of possible topics for written and in-class reports will be handed out in the first few weeks of classes.
Grades: Plus/minus grading will be used.
50% 2 midterms, tentatively on Mondays March 1 and April 12, in class.
25% Final exam, May 11, 4:30 pm and place to be announced
20% Homework, assigned by Fridays and due the following Friday
5% Project
+/-5% Attendance and class participation
PLEASE TURN THE PAGE OVER
22M:151, Discrete Mathematical Models, Spring
2004 Page
2
Tentative Syllabus: Chapters 1-5 of the textbook, and
*: additional material on trees and search algorithms, chromatic polynomials
2-5 Jan 26 2 Graphs, Connectedness, Strong components, Matrices, and
(*: Eulerian paths, Trees, Spanning trees, Depth-first @ Breadth-first searches, Weighted graphs, Minimal spanning trees, Kruskal’s and Prim’s algorithms)
5-9 Feb 20 3 Applications of graphs, and *: Chromatic polynomials
9-11 Mar 26 4 Pulse Processes, stability and applications
12-13 Apr 14 5.1-6 Markov chains, Classification, Absorbing, Regular, Ergodic chains
14 Apr 28 5.7-10 Applications of Markov chains
15 May 3 Presentations of projects
Notes: 1. All students in the College have specific rights and responsibilities. You have the right to adjudication of any complaints you have about classroom activities or instructor actions. Information on these procedures and your responsibilities is available in the Schedule of Courses and on-line in the College's Student Academic Handbook, (http://www.clas.uiowa.edu/students/academic_handbook/). In summary, first see the person you wish to complain about, and then see his/her immediate supervisor. The chain is: graduate or undergraduate assistants, then Prof. Darcy, then the Chairman of the Department of Mathematics, Prof. Manderscheid, then an appropriate Dean. The Department of Mathematics has offices in 14 MLH (MacLean Hall). To make an appointment to talk to the chairman of the department call 335-0714 or contact the departmental secretary in 14 MLH.
2. I would like to hear from anyone who has a disability which may require some modification of seating, testing, or other class requirements so that appropriate arrangements may be made. Please contact me during my office hours, in the beginning of the semester and far in advance of the exams. You should notify the Office of Student Disability services and obtain the forms. The necessary modifications will be made available to you.
3. This course plan may be modified during the semester. All changes will be announced in class in advance. It is solely the student’s responsibility to be informed of such announced changes.
4. You may collaborate with other students on the homework; however,
each individual student is responsible for turning in your own homework in your
own words. Copying is not collaboration and will be prosecuted under scholastic
dishonesty. Any significant collaboration should be acknowledged.
5. Policy on Scholastic Dishonesty: Students who
violate University rules on scholastic dishonesty are subject to disciplinary
penalties, including the possibility of failure in the course and/or dismissal
from The University. Since such dishonesty harms the individual, all students
and the integrity of The University, policies on scholastic dishonesty will be
strictly enforced.