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.
Course web site
The best source of information about this course is available at
http://gustavus.edu/~anienow2/MCS_115/ or http://gustavus.edu/~tjm/ 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, 2nd ed., 2005.
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 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.
A copy of the honor code and academic honesty policy
can be found in the
Academic
Bulletin
and in the
Gustie Guide.
Tests: You are expected to work completely 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 the 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
the 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 the
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 office and will result in a 0 for the
assignment. If you are unclear about what plagiarism is, please visit
this useful website
on how to avoid it or this
one. 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.
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.