Prerequisite: Intermediate Algebra, Rutgers Math 026, Math 027, or equivalent.

Text: Excursions in Modern Mathematics, 4^th Edition, by Peter Tannenbaum and Robert Arnold.

Course Web page:

http://www.math.rutgers.edu/courses/103/math103.html

Meeting times: MWTH 6:15-8:45

Final Exam: Aug 2, 2001  6:15-7:35

Instructor: Richard Porter
 

Name:	Porter
Office:	HH-B7
Office phone:	445-1155
Messages:	Use e-mail
Email:	rrporter@math.rutgers.edu
Web page:	math.rutgers.edu/~rrporter
Home phone:	use e-mail

 

Office hours: T 1:10-2:10  Th 1:30-2:30

Calculator: A basic calculator capable of computing square roots will be needed for both homework and examinations. Computers and calculators with typewriter keyboards or built-in computer algebra systems, such as the TI-89 and TI-92, will not be permitted on exams.

Course topics: All sections of Math 103 (except section H1) use the same text and will cover 10 chapters, but the selection of the material covered may vary from section to section. This suggested syllabus is based on chapters 1-8, 11, and 12.

Grading: The term grade will be based on the results of the examinations, the scores on written homework, and on class participation.
 
 
 

Quizzes	20
Homework	5
Hour Exam 1	30
Hour Exam 2	30
Final Exam	15
Total	100

Here is more information about the individual components of the grade:

Exams: There will be two hour exams and a final. The hour exams will count 30 points each and the final will count 15 points. The exams will be closed book and student-prepared formula sheets will not be permitted.

Homework: There will be a written homework assignment for each chapter.

Class participation: Students' involvement in the course will be assessed in several ways. In most class meetings there will be a short quiz, usually on some topic mentioned that day.

The following plan for the course is tentative. In particular, dates of the hour examinations are not definite but will be announced in class.

An additional review session will be scheduled during the final exam period.
 
 

Suggested problems for the written homework assignments:

Chapter 1. 8, 10, 20, 26, 40, 50, 52.

Chapter 2. 4, 10, 14, 24, 26, 42, 46.

Chapter 3. 6, 10, 18, 24, 38, 42, 48, 62.

Chapter 4. 2, 8, 14, 18, 26, 28, 46, 62.

Chapter 5. 8, 14, 20, 24, 30, 40(a), 42, 54.

Chapter 6. 4, 14, 22, 24, 32, 40, 44, 56.

Chapter 7. 4, 14, 20, 30, 44, 52, Supplemental problem.

Chapter 8. 4, 18, 28, 30, 32, 34, 52.

Chapter 11. 2, 14, 24, 34, 44, 70, 71, 72, Supplemental problem.

Chapter 12. 2, 4, 6, 8, 38, 50, 58, Supplemental problem.

Supplemental problem for Chapter 7. (Hand in a photocopy of this page.)

Let G be the weighted graph obtained by taking the complete graph determined by the following six points in the plane, where the weight of an edge is its length in centimeters measured between the centers of its endpoints. (The edges have not been drawn in the picture to keep the figure from getting cluttered.)

(a) Use Kruskal’s algorithm to find a minimal spanning tree for G and sketch this spanning tree on the diagram.

(b) Find the total length of this spanning tree by measuring the lengths of the edges used. Be sure to measure between the centers of the printed dots! Use centimeters and try to make your measurements accurate to the nearest tenth of a centimeter.
 
 

(c) On the following copy of the diagram, sketch as short a network linking these six points as you can find by introducing Steiner points

(d) What is the length of this network? By what percentage has the length of the spanning tree in (a) been reduced by adding Steiner points?

Supplemental problem for Chapter 11.

For each of the following diagrams, describe the nature of the rigid motion that takes point a to point A, point b to point B, and point c to point C. Is the motion a translation, a rotation, a reflection or a glide reflection? If the motion is a rotation, locate its center. If the motion is a reflection or glide reflection, locate its axis. Attach a photocopy of this page with these features indicated.

(a)

(b)

Supplemental problem for Chapter 12.

Create a number a as follows: Put a decimal point in front of the last four digits of your student ID number and multiply the result by -1. For example, if your student ID number is 123-45-6789, then your number a will be -.6789.

Now find a number b such that the complex number s = a +bi is not in the Mandelbrot set but is very close to that set. The sequence defined by s should take at least 500 terms to "escape" outside the circle of radius 2 around 0 in the complex plane.

To experiment with possible values of s, you should use the program available on the course Web page. Go to the Web page for Math 103, the address for which is

http://www.math.rutgers.edu/courses/103/math103.html

and click on "Mandelbrot Set Experiment".

In the box provided, type in various complex numbers s. The number of terms should be at least 600.

The results of an experiment are displayed in a separate window. You should delete the window for one experiment before running another.

Note to AOL users: The program available on the Web page does not seem to be compatible with AOL’s interface to the World Wide Web. Students should use a Rutgers University computer or an Internet service provider other than AOL to work on this problem.