MTH 101 -- The Art of Mathematical Thinking

Sec 1 -- MWF 12 -- Bradley Hall 340

Description

This course will probably be different from other math courses you've taken.
In a way, it will be more similar to survey classes you take in disciplines like philosophy, art or literature.
There you encounter the masterworks of the likes of Plato and Kant, Michelangelo and Picasso, Shakespeare and Dickens;
you learn to appreciate, analyze and perhaps apply their ideas and modes of thought.
In this class we will investigate some of the great ideas of mathematics and get a feel for the way mathematicians think.
This way of thinking can enrich many areas of life, not just the college classroom.

Prerequisites

According to the catalog, you need high school algebra.
Really, the main prerequisites are an open mind, curiosity, and the willingness to put aside prejudices about mathematics.
Other than that, this course should be fairly self-contained.

Objectives

The primary goal of the course is to develop your ability to solve problems.
Note that this means doing things you haven't already been shown how to do.
If you know ahead of time how to do something, it's an exercise, not a problem.
With new things, you should expect your first attempts to fail some, perhaps much, of the time.
Don't be surprised by this. More importantly, don't be discouraged.
Try something. If it doesn't work, try something else.

The secondary goal of the course is to attain understanding of some beautiful mathematics.

Finally, I hope you will broaden your perspective so you can view the world through the lens of mathematics and appreciate and use its power.

Text

The Heart of Mathematics: An Invitation to Effective Thinking, fourth edition, by Burger and Starbird.

I expect you to actually read this book, not just use it for homework assignments or to hold open a door.
Don't worry, though. This expectation isn't unreasonable. This is a great book.
Not only is it about interesting ideas, it's also pretty amusing.
One of the authors has even done stand-up comedy. Find out which by ... wait for it ... reading the book.
I wouldn't say that this will be like Sports Illustrated or a romance novel, but it won't be dull.

Homework

I will assign reading and questions on a regular basis.
I expect you to complete these assignments, but I will not collect them.
Don't fall behind or skip this work, though, because without it you won't understand the material or be able to handle the ...

Exams and Quizzes

We will have two hour-long in-class exams and a two-hour final.
The in-class exams are on 16 February and 30 March. The final will be on 8 May at 14:30 in the same room as the class.
Mark all of these dates on your calendar and schedule around them.
Each Friday that we don't have an exam, we will probably have a quiz.
We may also have other quizzes, either in class or to take home.

Grades

Each in-class exam counts for 20% of your grade.
The combination of your quizzes, of which I will discard the lowest, counts for 25%.
The final counts for the remaining 35%.
Totals correspond to letter grades as follows: 100-85%=A, 84-70%=B, 69-55%=C, 54-40%=D, 39-0%=F.
If you're unsure of your standing, ask me.

Getting Help

It is your responsibility to learn the material for this course.
I am interested in your success, though, and have a couple suggestions for the times when you don't understand everything.

Talk to me.
Really.
I expect you to talk during class.
If there are still things you don't get, come to my office hours. Those are Monday at 10 and 2, Wednesday at 11 and 3, Thursday at 12. (These are subject to change. The current ones will always be listed on my web site.)
If you need different office hours, make an appointment.
Talk to your classmates.
I encourage you to work together on homework and other problems outside class.
You need to spend plenty of time alone with the material, but lone wolves tend not to do as well as people with support systems.
Note that when someone explains a concept or problem to someone else, the explainer often benefits as much as the explainee.

Rules

Keep phones and other electronic communications devices silent and out of sight.
No matter how good you think you are at multitasking, you can't understand math well while wondering if the picture your friend just posted is of a real puppy.
More importantly, your use of these items is a distraction to others.
If you miss a class, you should arrange to get notes from a classmate.
During quizzes and exams, you may look at your paper, the front of the room or the ceiling, but please don't look anywhere near your classmates' papers.
Even if you're really just staring off into space, your eyes facing such a direction gives a very uncomfortable impression.
For quizzes and exams, besides the quiz or exam itself and maybe some blank paper, the only thing you should have out is a writing utensil.
There are no make-up quizzes or exams.
Your Bradley email is considered an official communication medium.
Be sure to check it regularly.
Feel free to send me email whenever, but don't count on it being answered in the evenings, on weekends, etc.
I believe that cheaters should be expelled from the university.

The Most Important Rule

While you're in class, this section of MTH 101 is in every conceivable way the best thing in the history of the universe.

A Final Note

Keep in mind that time spent on classwork is generally more productive when it's balanced with good nutrition, sufficient sleep, and a bit of exercise.