MATH 150 - DISCRETE MATHEMATICS
FALL 2002
MWF 9:00 - 9:50
MC 414
Instructor: Dr. Milan Luki´c
Office: MC 521
Office Hours: MTWF 1:10-2:00, or by appointment
Phone: (608) 796-3659 (Office); 787-5464 (Home)
e-mail: lmilan@execpc.com
WWW: http://www.viterbo.edu/personalpages/faculty/MLukic
Course Description: (from the catalog)
A course surveying topics utilized in computer science. Topics include problem-solving, logic, computer arithmetic, Boolean algebra and linear mathematics. Required of Math teaching majors. Prerequisites: acceptable score on placement exam, a grade of C or higher in one year of high school algebra, or a grade of C or higher in 001. Recommended for general education requirements-B.S. degree. Offered as needed.
Text: J.A. Dossey, A. D. Otto, L. E. Spence, C. Vanden Eynden, Discrete
Mathematics, Third Edition, Addison-Wesley, 1997.
Core (General Education) Skill Objectives:: (1) Thinking Skills:
(a) Students will use reasoned standards in solving problems and presenting arguments.
(2) Communication Skills: Students will . . .
(a) . . . read with comprehension and the ability to analyze and evaluate.
(b) . . . listen with an open mind and respond with respect.
(c) . . . access information and communicate using current technology.
(3) Life Value Skills:
(a) Students will analyze, evaluate and respond to ethical issues from an informed personal value system.
(4) Cultural Skills: Students will . . .
(a) . . . understand culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.
(b) . . . demonstrate knowledge of the signs and symbols of another
culture.
(c) . . . participate in activity that broadens their customary way of thinking.
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(5) Aesthetic Skills:
(a) Students will develop an aesthetic sensitivity.
Specific Course Goals:: Those happen to coincide with some of the NCTM
(National Council of Teachers of Mathematics) “standards” for mathematics
education. We have:
The students shall . . .
(1) . . . develop an appreciation of mathematics, its history and its applications.
(2) . . . become confident in their own ability to do mathematics.
(3) . . . become mathematical problem solvers.
(4) . . . learn to communicate mathematical content.
(5) . . . learn to reason mathematically.
General Education Course Objectives:: (1) Thinking Skills: Students will . . .
(a) . . . develop algorithmic skills;
(b) . . . learn combinatorial techniques and solving combinatorial problems;
(c) . . . explore sets, relations, and functions;
(d) . . . study some basic concepts of Graph Theory. For example, consider the most efficient way for a mailman to deliver the mail in a certain part of a city.
(e) . . . study matching problems. For example, assigning bus operators to routes, or a basketball coach must assign a player to guard each player on the opposing team in such a way as to minimize the opponent’s total score.
(f) . . . study network flows problems. For example, a long-distance telephone company must move messages from one city to another.
The number of of telephone calls that the company can handle at a given time is limited by the capacity of its cable and its switching equipment.
(g) . . . learn basic counting principles, Binomial Theorem, and Pascal’s
Triangle.
(h) . . . apply those basic combinatorial concepts in solving some probability problems.
(i) . . . study recurrence relations, difference equations, and generating functions.
(j) . . . learn some fundamentals of mathematical logic and learn to recognize valid and invalid reasoning.
(2) Communication Skills: Students will . . .
(a) . . . collect a portfolio during the course and write a reflection paper.
(b) . . . turn in written solutions to occasional problems.
(e) . . . learn to use the Internet resources and present the findings in class.
(3) Life Value Skills: Students will . . .
(a) . . . develop an appreciation for the intellectual honesty of deductive reasoning.
(b) . . . listen with an open mind and respond with respect.
MATH 150 - DISCRETE MATHEMATICS FALL 2002 3
(c) . . . understand the need to do one’s own work, to honestly challenge
oneself to master the material.
(4) Cultural Skills: Students will explore the importance and the historical development of the topics covered in the course.
(5) Aesthetic Skills: Students will . . .
(a) . . . develop an appreciation for the austere intellectual beauty of deductive reasoning.
(b) . . . develop an appreciation for mathematical elegance.
Content:: This course is aimed at the students who major/minor in Mathematics Education.
Course Philosophy and Procedure: Two key components of a success in the course are regular attendance and a fair amount of constant, every-day study. You should try to make sure that your total study time per week at least triples the time spent in class.
Grading will be based on three in-class exams (100 points each), a cumulative final exam (200 points), class participation, take-home problems, projects, group practice exams and portfolios.
Out of all these assignments, I attach a special importance to the Mathematical Reasoning project. It is a semester long project which consists of doing the following problems:
• Appendix A.3: Problems 1 − 26. You can also try 27 and/or 28 for an extra credit.
• Supplementary exercises, page 537: Do Exercises 9 − 20
• Do also exercises 21 − 24, this time stating some of the basic principles/ formulas hidden in those that are true.
• The last group, still Appendix A.3, Supplementary exercises: Do 37 − 44.
Rules for the project:
• Each problem is worth 2 points, no partial credit.
• You can submit a solution to any problem, or any number of them, any time during the semester. The solutions are to be submitted electronically.
Please use the e-mail address given at the top of this syllabus.
The last day to submit is the last day of class.
• Please try to write your solutions so that they are correct and complete.
Justify your argument, state your reasoning.
• I will look up each of your solutions and return it to you with some comments. I either accept a solution of a problem, and mark down 2 points for you, or will return the problem back to you with some suggestions for correction and improvement.
I will keep returning a problem to you until it is done right. You don’t lose any points for repeated attempts.
My grading scale is
A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.
Americans with Disability Act:: If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and Wayne Wojciechowski in Murphy Center Room 320 (796- 3085) within ten days to discuss your accommodation needs.
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Important dates.
Classes begin: August 26.
Last day to add: Friday, August 30.
Labor Day: Monday, September 2.
Last Day for credit/no credit: Monday, September 9.
Last day to withdraw without a W: Thursday, October 17.
St. Francis Day: Friday, October 4. Classes. 11, 12 and 1 : 10 canceled.
Midterm break: Friday, October 18.
Last day to withdraw with a grade of W: Monday, November 4.
Thanksgiving: Wednesday, November 27-Sunday, December 1.
Last day to request a grade of Incomplete: Thursday, December 5.
Last day of class: Friday, December 6.
Commencement: Saturday, December 14.
Final Exam: Friday, December 13, 12 : 50 − 2 : 50.
This syllabus is tentative and may be adjusted during the semester.
Have a good semester !