MATH 150 - DISCRETE MATHEMATICS
SPRING 2004
MWF 10:00 - 10:50
MC 555
Instructor: Dr. Milan Luki´c
Office: MC 521
Office Hours: MF 2:10-3:00, T 12:00-12:50 or by appointment
Phone: (608) 796-3659 (Office); 787-5464 (Home)
e-mail: lmilan@execpc.com
WWW: http://my.execpc.com/˜lmilan
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: Norman L. Biffs, Discrete Mathematics, Second Edition, Oxford University
Press, 2002.
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 correct mathematical proofs. State definitions and prove theorems.
(2) Communication Skills: Students will . . .
• . . . turn in written solutions to occasional problems.
• . . . communicate solutions to some problems using e-mail.
• . . . typeset an assignment using LATEX
• . . . use oral presentations.
(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 SPRING 2004 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 two-three in-class exams (100 points each), a cumulative final exam (200 points), in-class participation, take-home problems and projects.
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:
• Chapter 1:
Page 11, Exercises 1.6, Problem 4 and Exercises 1.7, Problems 4-7;
• Chapter 3:
Page 21, Exercises 3.5, Problem 3 and Page 24, Exercises 3.7 7-9.
• Chapter 4:
Page 35, Exercises 4.7 3-4, and page 38, all 7 problems.
• Chapter 5: page 45, problems 1-3, 6-7.
• Chapter 6:
Page 49, Exercises 6.2, problems 2-3; Page 50, Exercise 6.3; Page 51,
Exercises 6.4, problem 1-4; Page 53, Exercises 6.5, problems 1-4; Page
54, Exercises 6.6, problems 1-2; Page 55, problems 1, 3,5 and 9-12.
• Chapter 7:
Page 59, Exercises 7.3, problems 3-4; Page 61, Exercises 7.4, problems
1, 3-5; Page 63, Exercises 7.5, problems 3-4; Page 64, Misc. exercises,
1-4.
Rules for the project:
• Each problem is worth 2 points, no partial credit. Any 50 problems from the list above can be chosen. If one is doing real well by the time you are done with 35-40 problems, I will let you drop five more problems.
• You can submit a solution to any problem any time during the semester, but not after the midnight on Thursday April 29. The solutions are to be submitted electronically, as a plain text e-mail - no attachments. Please use the e-mail address given at the top of this syllabus. When you start getting better with these, I will allow you to submit more than one problem at the time, but no more than five.
• Please try to write your solutions so that they are correct and complete. Justify your argument, state your reasoning.
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• 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.
Important dates.
Classes begin: January 12.
Humanities Symposium: February 2-4.
Midterm break: February 28 - March 7.
Easter Vacation: April 8-12.
No classes, due to my conferences: Friday, April 16;
Last day of class: Friday, April 30.
Final Exam: Wednesday May 5, 3:00 - 5:00.
This syllabus is tentative and may be adjusted during the semester.
Have a good semester !