MCS 115 --  Finite Math
Spring 2003

Overview
The true title of this course is "The Art of Mathematical Thinking: An Introduction to the Beauty and Power of Mathematical Ideas". In this course we will consider some of the great mathematical ideas, ideas comparable to the works of Shakespeare, Plato and Michelangelo. We will experience what mathematics is all about by delving into some beautiful and intriguing issues. There are three basic goals for this course:

• To attain a better understanding of some rich mathematical ideas.
• To develop thinking skills that can be used to analyze issues that transcend mathematics.
• To develop a new perspective on mathematics and the way it is used in the world.

I hope you will come to see that mathematics is a human activity that requires both creativity and imagination. My goal in teaching the course is to help you learn to appreciate mathematics and to discover the power of mathematical thinking. The course will likely be quite different from mathematics courses you had in high school. There the emphasis was on technique and computational skills. I will ask you to think and analyze rather than to work routine exercises.

Prerequisites
The formal prerequisites are high school plane geometry and algebra. In fact, the only prerequisites for this course are an open and curious mind and the willingness to put aside any preconceived prejudices or dislikes for mathematics.

Course web site: The best source of information about this course is available at gustavus.edu/go/mcs115/. There you will find a complete syllabus, course description, current homework assignments, and so on.

Text

The Heart of Mathematics: An invitation to effective thinking, by Edward B. Burger and Michael Starbird, Key College Publishing, 2000.

This book is intended to be read.  You will find it engaging and fun. The authors have several suggestions on how to read the book on p. xi. which you should read.

You should also have the accompanying Manipulative Kit and access to a basic calculator for use on exams and occasionally for homework and in class. You do not need a graphing calculator.

Quizzes and Exams
We will have three quizzes/tests during the semester and a test during final exam period.
The final exam will be given Friday, May 23, 8:00-10:00am.

Academic Integrity
You are expected to work together in an honorable way in this course. This means that while you can discuss problems and their solutions, each of you should make a real effort to solve each problem by yourself, and you should give credit to any people or texts that helped you find solutions. Needless to say, you are expected to work completely by yourself on tests.

Cheating is not allowed in this course. If we find someone has cheated, then we will take action ranging from giving a zero for the assignment in question to giving a grade of F for the entire course. We will also notify the Dean of Students.

The academic honesty policy can be found in the 2002-2003 college catalog.

Classes
We learn by thinking and doing, not by watching and listening.  Learning is an active process:  it is something we must do, not have done to us.  Classes will be used for lectures, problem solving, discussions, and other fun activities. You should prepare for classes by doing the reading beforehand (reading assignments are posted on the Web),  thinking about the problems in the text, and formulating questions of your own.  You should also participate as much as possible in class.  Class meetings are not intended to be a complete encapsulation of the course material.  You will be responsible for learning some of the material on your own.

Attendance, both physical and mental, is required.

Should you need to miss a class for any reason, you are still responsible for the material covered in that class. This means that you will need to make sure that you understand the reading for that day, that you should ask a friend for the notes from that day, and make sure that you understand what was covered. If there is an assignment due that day, you should be sure to have a friend hand it in or put it in your instructor's departmental mailbox (in Olin 324).

Homework

I hear, and I forget;
I see, and I remember;
I do, and I understand.
                               - Proverb

Homework will be assigned regularly from the text, collected and graded. Clarity of expression is important, and you should strive for well written, polished solutions. For the most part collaboration on homework with other members of this class is allowed, although solutions must be individually written up and collaborators should be acknowledged. It will be made clear when collaboration is not permitted. There will also be several short writing assignments throughout the semester. See the homework guidelines for further suggestions.

Research Project/Poster Session
The only way to really understand mathematics is to learn and discover it on one's own. Thus students will select a mathematical topic outside of those covered in our class, read and teach themselves any necessary background to understand it and then investigate the topic. Students will work together in groups of two or three on this project. By working together, the individuals can learn from each other and share the experience. Each group will write a final paper on their findings and present a poster display during a class poster session at the end of the semester. Also, each student will write a short individual statement regarding the experience. Various interim reports will be collected throughout the term. Students are invited and encouraged to discuss all phases of the project with their instructor.

Syllabus

• An introduction to mathematical thought
• Geometry
• Numbers
• Infinity
• Topology
• Chaos and Fractals
• Probability and Statistics

Evaluation
Your final grade will be assigned using the following percentages as a guide:

BONUS POINTS FOR ATTENDANCE AND CLASS WORK: Attendance, though not mandatory, is essential to learning mathematics. We also know that many students try hard in math classes and still have a hard time succeeding (or passing). Therefore, each person in class begins the semester with 25 BONUS POINTS for attendance and class participation. Attendance will be taken periodically and class work will be collected occasionally. You will receive two unexcused absences. For every successive absence when attendance is taken or class work is collected, you will lose 5 of your attendance bonus points. Please note: these are EXTRA points. NO ONE IS PENALIZED FOR MISSING CLASS. You will just get fewer or no bonus points. Bonus points will be added to your highest test score.

Accessibility:  Please contact me during the first week of class if you have specific physical, psychiatric, or learning disabilities and require accommodations. I will do my best to facilitate the  necessary arrangements.  All discussions will remain confidential.

Area D: Finite Math (MCS-115) satisfies the Quantitative Reasoning criteria of Area D.

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