MCS-115: The Nature of Mathematics (Fall 2011)
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Course Description
The true title of this course could well be The Art of Mathematical Thinking: An Introduction to the Beauty and Power of Mathematical Ideas. In this course we will consider some 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:

We hope you will come to see that mathematics is a human activity that requires both creativity and imagination. Our 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. We will ask you to think and analyze rather than to work routine exercises.

Topics
We will learn about several topics in the following general areas:

 

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.

Text

The Heart of Mathematics: An invitation to effective thinking, by Edward B. Burger and Michael Starbird, Wiley, 3rd ed., 2010.

This book, our primary text, 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.

We will also be using a secondary text to cover additional material. This book is Mathematics: A Practical Odyssey , by David Johnson and Thomas Mowry, Brooks/Cole, Cengage Learning, 7th ed., 2012. Our ability to provide online access to several chapters for the Fall, 2011 semester has been provided courtesy of Cengage Learning.

Calculator
You should have access to a basic calculator for use on exams and occasionally for homework and in class. You do not need a graphing calculator.

Academic Integrity
As a student at Gustavus you are expected to uphold the Honor Code and abide by the Academic Honesty Policy.

Tests: You will be expected to work by yourself on tests. We will put the standard honor pledge on the front of each exam for you to sign. The first violation of this policy on an exam will result in a 0 on that exam, and the Dean of Faculty will be notified, as mandated by the policy. The second such violation will result in failing the course as well as notification of the Dean of Faculty.

Homework: We encourage you to work on the homework together, but you are expected to work together in an honorable way. 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. We expect that you will write up your work individually and never copy someone else's writeup. Should we detect students copying each other's work, we will on the first occasion talk with the people having similar work. In case of a second infraction, we will give you a 0 for that assignment and notify the Dean of Faculty. Any further violation will result in increasing penalties, up to failing the course.

Project: Plagiarism on the project paper or the presentation will be reported to the Dean of Faculty and will result in a 0 for the assignment. If you are unclear about what plagiarism is, please visit either this useful website (or this one) on how to avoid it. Printing out a webpage and cutting and pasting it without proper citation onto your paper or presentation is plagiarism.

Accessibility
It is the policy of Gustavus Adolphus College to provide for the needs of enrolled students who have disabilities. The Advising Center has a Disabilities Services Coordinator to assist you with reasonable accommodation. If you have a learning, psychological, or physical disability for which a reasonable accommodation can be made, you can provide documentation of your disability to the Advising Center (204 Johnson Student Union) or call Laurie Bickett (x6286). It is generally best if this can be done as soon as possible.

Help for Students Whose First Language is not English
The Writing Center has on staff a part-time tutor with professional training in ESL/ELL instruction. Students can schedule work with this tutor by contacting the Writing Center. Students may bring their instructors documentation concerning their ELL status. Where it is appropriate, faculty may choose to allow such students more time to complete either in- or out-of-class writing assignments. For further information, contact the Academic Advising Office.

General Education
The Nature of Math (MCS-115) satisfies the Quantitative Reasoning criteria of the Curriculum I area requirements for students who matriculated before September 2005. QUANT courses are intended to acquaint the student with the application of quantitative and empirical reasoning both to the study of biological and physical phenomena and to the logic and abstractions of the mathematical and informational sciences. MCS-115 also satisfies the Mathematical and Logical Reasoning (MATHL) requirement of the Curriculum I area requirements for students who matriculate in or after September 2005.

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. Conversely, just studying the book is not enough as class will not be just reiteration of material from the text.

Attendance, both physical and mental, is expected. As noted below, we reserve the right to reduce your grade should you not attend class regularly or participate in the class activities.

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 that you should make sure that you understand what was covered. If there is an assignment due that day, you should have a friend hand it in or put it in your instructor's departmental mailbox (in Olin 324). DO NOT send assignments through the P.O. for any reason.

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. Usually only a representative sample of the problems will be graded for correctness. You will also receive credit for completing the problems that are not carefully 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. See the the Academic Honesty section of this document for additional information about completing homework assignments honorably. See the homework guidelines for further suggestions about homework.

Homework is due at the beginning of class on the day it is due. No late homework will be accepted. In particular, finishing your assignment in class on the day it is due and then attempting to turn it in at the end of class is unacceptable. In general, you should contact your instructor ahead of time if you believe illness, personal/family emergency or documented participation in a college-sponsored activity will prevent you from turning in an assignment by the due date.

Exams
We will have three exams during the semester and an exam during final exam period. The three exams during the semester will be given in the evening, in part to provide flexibility in the time allowed.

Make-up exams will not be given except for medical or family emergencies. In particular, make-up exams will never be given to accommodate travel plans. If you cannot take an exam because of an academic conflict or documented participation in a college-sponsored activity, you must make arrangements with your instructor in advance.

Research Project
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 three on this project. By working together, the individuals can learn from each other and share the experience. Each group will write a paper on their findings and give an oral presentation during one of the designated class days. Students are invited and encouraged to discuss all phases of the project with their instructor.

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

Tests (4) (20% each, lowest counts 10%)

70%

Research Project

15%

Homework

15%

ATTENDANCE AND CLASS WORK: Attendance and participation are essential to learning mathematics. Therefore, we reserve the right to reduce your grade should you not attend class regularly or participate in the class activities.

Advice from Your Peers
When asked what advice they would give a student about to take The Nature of Math, previous students most often responded with the following suggestions:

A complete list of their suggestions can be found here.