Exploring Mathematical Patterns
January Term, 1997
Instructor: Jennifer Galovich
Office Hours: 1 - 3 every day. Please feel free to make an appointment at another time if this doesn’t work for you.
Phone: Office 363-3192
Course Materials: Math Explorations Problem Collection (available in bookstore)
Teaching Assistant: Matt Maurer
The goal of this course is to provide you with an opportunity to practice doing mathematics. “Doing” mathematics includes not only the use of the traditional tools--proof and formal manipulation--but especially the variety of ways in which mathematicians think about their subject -- experimentation, educated guessing, etc. This course will emphasize mathematical thinking by challenging you to take these steps for yourselves.
The context for our explorations is Combinatorics--the branch of mathematics concerned with describing and exploring the properties of patterns. Sometimes these patterns involve objects which are obviously mathematical, but sometimes not. The good news is that you (yes, you!) can solve many interesting combinatorial problems without having to know a lot of specialized vocabulary or techniques ahead of time. On the other hand, you will need to be persistent yet open-minded--willing to try new approaches when old ones don’t work, but not giving up too easily or too soon.
Since the goal is for you to do as much mathematics as possible, there will be very little lecture and LOTS of discussion and group work. Each class day we will begin with a problem for everyone to work on together but which will provide a context to introduce new problem solving ideas, techniques and (occasionally) vocabulary or helpful notation. We will end the first half of each class with time for questions and comments about the problem of the day. After a short break, we’ll resume with time for everyone to work in groups on problems you will choose from the problem collection.
Attendance (25%) Because of the structure of this course, class attendance (on time!) and participation in your groups is mandatory. If you absolutely must miss a class, please call or leave a message on my voice mail or e-mail which explains your absence.
Written work (60%) Each day’s assignment will include
1. Writing up a careful and complete solution of the problem of the day.
2. Writing up, to the best of your ability, complete solutions to two other problems chosen from the problem collection. In most cases, you will have already begun work on these problems in class and should have a good start on the solutions. However, if you cannot complete a problem to your satisfaction, you must at least give a complete account of the work you did, what you tried, what worked, what didn’t work, etc. If you would like to work on more than two problems, I will be happy to read and respond to your work.
3. Rewrites and corrections of problems you have already worked on but not completed. (These are encouraaged and therefore there is no penalty. )
On the average, you should plan to spend about 4 hours each day outside of class on your work for this course. (Doing homework while watching ER does not count!J)
Note: “Writing up” a solution to a problem is like a final draft for a paper. In particular, I expect your work to be legible and organized, and you should write in complete English sentences. However, this does not mean writing “equals” instead of using “=” for example. It is completely OK to use notation but whatever mathematical notation you choose to use should be used appropriately and correctly. If you are unsure, just ask.
Each problem will be graded on a scale of 1 - 10, where 10 means your solution is correct and complete. A score of 4 or below probably means that you’re on the wrong track. My evaluation of your work will be based primarily on its mathematical correctness, but if your presentation is sloppy or incoherent I will not give full credit, even if the solution is correct. I will comment extensively on your work and I expect you to at least consider my suggestions in any rewrite.
Quizzes (15%) Each Friday I will give a short quiz on basic terms and concepts covered in the problems of the day for that week. There will be no other examinations.
One final note: I truly want each of you to do your best in this course, so please do not hesitate to ask for help at any time.