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 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:
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.
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/academics/mcs/courses/mcs115/2005F/.
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 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.
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. I
will not be proctoring tests, but I will be available periodically to
answer questions. I 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: I 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. I expect that you will write up your work
individually and never copy someone else's writeup. Should I detect
students copying each other's work, I will on the first occasion talk
with the people having similar work. In case of a second infraction, I 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 and Poster: Plagiarism on the project report or the poster
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 onto your poster is
plagiarism.
Accessibility
Please contact me during the first week
of class if you have specific physical, psychiatric, or learning disability
and require accommodation. I will do my best to facilitate the necessary
arrangements. All discussions will remain confidential.
You can provide documentation of your disability to the Advising
Center (204 Johnson Student Union). All discussions will remain
confidential. Call Jane Lalim in Academic Advising (x6124).
General Education
Finite Math (MCS-115) satisfies the Quantitative
and Empirical Reasoning criteria of the Curriculum I area requirements.
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.
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.
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 class.
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/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.
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 and Poster Session | 10% |
| Homework | 20% |
ATTENDANCE AND CLASS WORK: Attendance and participation, though not mandatory, are essential to learning mathematics. Therefore, I reserve the right to reduce your grade should not attend class regularly or participate in the class activities.
The tentative grading scale is: A: 90-100; B: 80-89.99; C: 70-79.99; D: 60-69.99; F: below 60. Although tentative, the final scale will NOT be higher, and may possibly be lower.
Advice from Your Peers
When asked what advice they would give a student about to take Finite
Math, previous students most often responded with the following suggestions:
A complete list of their suggestions can be found here.
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