MTH 108 Topics in Mathematics - Fall 2003

Section 10 meets Thursday, 9-11:45
Shepard Bldg, Providence

Instructor: Dr. Nancy Eaton, 874-4439,
Office:  Tyler Hall, Rm 222, Kingston

Course Description Class work Schedule
Text Home work World wide web
Writing assignments Quizzes Evaluation
Keys to quizzes Keys to exams MATH TUTOR

Students who require accommodations and who have documentation from
Disability Services (874-2098) should make arrangements with me as soon as possible.

Course Description and goals:  Math 108 is a special topics course that satisfies the general education requirement for math at the University of Rhode Island.  It introduces the non-mathematics student to the spirit of mathematics and its applications.  The content of the course varies from section to section and semester to semester.

In this section of this course, you will be introduced to some exciting ideas in mathematics that come from a wide variety of disciplines such as voting theory, graph theory, game theory, scheduling, counting, algebra, and fractal geometry. These topics will be presented along with real world applications such as voting schemes, fair division schemes, street networks, planning and scheduling, pattern recognition, and fractals in nature.

I hope that you will have a better understanding and appreciation for mathematics by the time you finish this course,   that you will no longer think that math is only about balancing a check book and designing rockets, and that you will be proud to say that you LIKE math.  You may be surprised to find that taking further math courses is both possible and desirable.

We will use reading, writing, discussion, and world-wide web assignments as methods of learning the topics covered in this course. You will discuss and work in groups in class as well as do some short presentations. Because of the high level of knowledge that will be imparted and assessed during class time, attendance will be mandatory. During class time, topics will be presented, examples given and then you will be given the opportunity to work examples on your own.

Text: The text for the course is:  Excursions In Modern Mathematics, 5th edition, by Peter Tannenbaum and Robert Arnold.  We will cover all or part of the following chapters.
1:    The Mathematics of Voting
3:    Fair Division, The Mathematics of Sharing
5:    Euler Circuits
6:    The Traveling Salesman Problem
7:    The Mathematics of Networks
8:    The Mathematics of Scheduling
11:  Symmetry
12:  Fractal Geometry

Note: There is much more material in our text than we could possibly cover this semester, so I will let you know specific pages that you are responsible for and that will accompany what we cover in class. Read as much of the rest as you like.

Additional Readings:   In addition to the textbook, I will present excerpts from the following books.  These are also suggested for you to read on your own.
Conquering Math Anxiety by Arem, Brooks/Cole, A self-help workbook if you feel anxious when it comes to math.
Multicultural Mathematics, by Nelson, Joseph and Williams, Oxford Univ. Press, to investigate the rich cultural heritage of mathematics.
Women in Mathematics, by Osen, MIT Press,  to discover the role some women played in mathematics.
The Puzzling Adventures of Doctor Ecco, by Shasha, Dover, to apply what we learn in class to math puzzles.

Class work:Examples and exercises will be worked on in class.  There will be some class discussion and working in groups.  This is a very important time to absorb the information and begin to understand how to apply it to problems.  This work will count as 10% of your grade.

World wide web assignments:I will use e-mail to send you world wide web assignments. These will consist of the names of web sites.  You are to visit this sites and respond to my e-mail with your comments. If you are unfamiliar with "surfing the web", visit a computer lab and ask for help.  Once you get started, you will find that it is a very easy thing to learn to do. To start this process off, as soon as possible, send me e-mail just saying hello. Once I have e-mail from everyone, I will send out the first assignment.  This work will count as 10% of your grade.

Writing Assignments:    Short writing assignments will given throughout the course.  You will be given specific problems from the book to write up in detail, including the complete question and the solution written in a logical manner.  Your work should be neat and proper use of grammar should be followed.  Emphasis will be placed on proper use of logic in your explanation. NOTE: write neatly.  In your header, put your name and writing assignment number,  include only the problems that I asked you to hand in,  put them in order, labeled clearly,  only write on one side of the paper,  and leave enough room for me to write comments.  This work will count as 15% of your grade.

Homework:   Problems are assigned from the book.  You are responsible to do all problems that are assigned.  We will work on some in class and you will hand some in as writing assignments.  It is best if you collect all of your homework in a loose leaf notebook.  This is because you can more easily keep it in order.  Often, one individual problem will take many passes before it is worked up completely correctly.  You need to see that you understand each problem completely.  Many problems will be presented in class.  Take notes and compare it to what you wrote.  The quizzes will be based on the homework.  If you understand every homework problem then you should have no trouble on the quizzes.

Tutors are available at both the providence and kingston campuses.  Assistance with all levels of mathematics is available on a walk-in basis in Room 240. Hours are posted each semester.  Also, you can make individual appointments with me.  For this, contact me by phone, e-mail, or ask me during class.  You  can even e-mail some of your questions to me and I can answer by e-mail.

Home work assignments:
Homework assignments will be given when we start a new topic and are due when the next topic begins. You will receive feedback from me on these homework assignments.

Exercises from chapter 1:  starting on page 28:  1,9,17,19,20,27,31,33,34,35,37,41,43,45,49,51
Writing Assignment #1:  20, 34

Exercises from chapter 3:  starting on page 112.  1-17 (Odd)  39, 41, 43 47, 51
Writing Assignment #2:  10, 42  Be sure to give reasons.

Exercises from chapter 5:  starting on page 203.  1, 5-11 (Odd), 15-19 (Odd) 23-29(Odd), 41,43, 63
Writing Assignment #3:  54  Be sure to draw the picture and the graph models.

Exercises from chapter 6:  starting on page 247.  1,3,7,9,11, 19, 23-29 (Odd), 37-41 (Odd)

Exercises from chapter 7:  starting on page 293.  1-7 (Odd), 11-15 (Odd), 19, 21, 25

Exercises from chapter 8:  starting on page 342.  7-11 (Odd), 17-21 (Odd),25-29 (Odd) 35,36,39, 47, 50
Writing Assignment #4:  36 (to make sure you understand, do 35 and check the answer before doing 36)
                                        and 50 (do 47 first to check your understanding)

Exercises from chapter 11:  starting on page 453.  1, 3,13,15,29-39 (Odd), 45,47

Exercises from chapter 12:  starting on page 500.  1,2a,3a,5a,b,9,10a,11a,15
Writing Assignment #5:  9, 10a, 11a (Use graph paper and start with a very large square - Do not trace solution)

Quizzes:   Short quizzes will be given each class based on the homework.  Problems will be selected at random from the homework to demonstrate your understanding of the material. Complete solutions to the quizzes will be handed out to demonstrate the proper write up of a problem.  You should study these as examples for the writing assignments.   If you miss a quiz, no makeup will be given, instead, the two lowest quiz grades will be dropped and the rest will be averaged to give 15% of the grade for the course.  You are responsible to get a copy of the quiz and its solution.

Exams:   Three short exams will be given on the material from the chapters indicated.  The exam questions will be based on the homework questions.  To prepare, make sure you understand homework and quiz solutions.  Exactly 1 hour will be allowed for each exam.  Solution keys will be given.

Final exam:   The final will be cumulative.  2 sections will be new, the rest will be covered in previous exams.  The questions given from sections covered in previous exams will be similar to those given before.  So prepare by going over the solution key to each exam.

Course schedule:    The following is the schedule of events.  We will use the entire class period each day of class. 

Date Begin Covering Chapter Homework Due Exam
Thurs. Sept 4 chapter 1

Thurs. Sept 11 chapters 3 WA#1, on chapter 1

Thurs. Sept 18
  quiz 1 on chapter 1
Thurs. Sept 25 chapter 5
WA#2, on chapter 3 quiz 2 on chapter 3
Thurs. Oct. 2

EXAM 1 (on 1 & 3)
Thurs. Oct 9 chapter 6

Thurs. Oct 16 chapter 7 WA#3, on chapter 5 quiz 3 on chapter 5
Thurs. Oct 23
quiz 4 on chapter 6
Thurs.  Oct 30 chapter 8   EXAM 2 (on 5 & 6)
Thurs. Nov 6

quiz 5 on chapter 7
Thurs. Nov 13 chapter 11 WA#4, on chapter 8 quiz 6 on chapter 8
Thurs Nov 20 chapter 12 WWW#2
EXAM 3 (on 7 & 8)
Thurs Dec 4
WA#5, on chapter 12
quiz 7 on chapter 11
Thurs Dec 11

Final Exam (on 1,3,5,6,7,8)

Evaluation:The following percentages are given to compute your grade for the course.  Each category is described above.

10% - Class participation.

10% - World wide web assignments

15% - Writing assignments

15% - Quizzes

30% - Three 1 hr exams  (10% each)

20% - Final Exam

Tuesday 11-12, There will be a note on room 222 saying where to find him.
Tuesday 12-3, Room 222
Thursday 6-9, Room 222
Saturday 9-12, Room 222

Quiz keys:

Exam keys:

Key to Exam 1

Key to Exam 3

Dear Class,

Here is your WWW Assignment number 2.  A couple of these sites may require JAVA to be
installed on your computer.  Try to use a computer that has JAVA.  HAVE FUN!

1)  Chaos Theory and Fractal Geometry:  Explore this site, especially the buttons along the bottom of the page.   Write a paragraph describing something interesting that you learned.

2)  Graph Theory Glossary - take the tutorial and tell me what you learned.  Just a paragraph or two.

3)  Sierpinski's Carpet.  Check out this fractal and report what you learned, a sentecence will do.

3)  Fractals:  An Introductory Lesson.-  Explore and report on a couple of things - 2 paragraphs.

4)  Play the The Chaos Game and tell me what you learned.

5)  Explore this site, What is Tiling.   It is new.  Write 2 paragraphs.