Fall, 2000

Monday, Wednesday, and Friday, 2:00-2:50 p.m.

Buttrick G-13

Office Hours. Monday, 10:00-11:00, Tuesday, 10:00-11:00, Thursday, 2:00-3:00. If these hours are not good for you, we can set up an appointment.

Prerequisites. Calculus I and II. While we won’t spend a great deal of time differentiating and integrating, the hope is that these two classes will provide you with enough mathematical maturity for the challenge that follows. In addition, it wouldn’t hurt to have strong English grammar skills and the enthusiasm to find out how much mathematics there is to explore.

Text. An Introduction To Abstract Mathematics by Robert J. Bond and William J. Keane.

Course Content. Chapters 1 through 6 of the text. Topics include logic, set theory, functions, relations, number theory, mathematical induction, and countability.

It should be pointed out that you will learn something far more valuable than just these topics – you will learn what it means to be a mathematician.

More!

Art? Yes, Art. Writing a good mathematics proof is one part logic, one part style. Each is a vital part of a mathematics proof. If the logic is bad, of course the proof will be bad. If the style is bad, no one will understand you, and what good is mathematics if you can’t share it with the world?

All right, I understand why writing a proof is an art form. How will I benefit from this course? Good question, my bold-faced friend.

This course serves as a bridge between more calculation-based courses (e.g. calculus) to more theoretical courses (e.g. abstract algebra). Success in this course will make the trip across the bridge much easier. So, one benefit of this course is that it will help you with future courses.

However, the logic and critical thinking studied here will help you outside the world of mathematics. The reasoning skills acquired in this class will help you make sound logical arguments in other disciplines. Quite a few mathematics students enter law school, where making a reasonable argument can mean the difference between life and death.

Course Goals. By the end of the semester, you should be able to:

• Learn to analyze an abstract definition and to construct examples that illustrate it;
• Learn a group approach to problem solving;
• Learn to analyze a proof critically, examine it for rigor, and detect weaknesses or flaws;
• Learn to fill in the details of a sketchy proof;
• Learn to write mathematical proofs in clear, concise and grammatically sound English;
• Become comfortable presenting mathematical ideas with clear, coherent oral communication and effective blackboard use;
• Learn to listen critically but supportively to the ideas of others;
• In short: learn what it means to be a true mathematician – the need to experiment, the need to fail, and the need to learn from your mistakes.

Attendance. You are expected to attend every class. While attendance during discussion days will directly affect your grade (see below), missing the other days does not have a direct impact on your grade. It will, however, have an indirect impact on your grade. Trust me. Also, you will not be penalized directly for tardiness, however you are expected to arrive to each class on time.

ecademy.agnesscott.edu. A web page has been set up for this course. You can find it at http://ecademy.agnesscott.edu/Mathematics/mathfacpgs/koch,alan/Math204/index.htm, or if that’s too much typing you can just follow the links from the http://ecademy.agnesscott.edu page. Here you will find all the handouts for the course. Most will be .pdf files, so make sure the computer you’re using has Adobe Acrobat installed.

Homework. At the end of each section (roughly every other day), there will be homework problems assigned from the sections covered during the lecture. They will consist (primarily) of odd problems from the book, so you can check your answers in the back. This homework will not be collected, but it is assumed that it will be completed by the start of the next class. While the homework in not graded, it is vital that it is completed – just doing the weekly assignments is not enough. Trust me.

Assignments. There will be weekly assignments that will be turned in. Their purpose is to give you practice with the writing of formal mathematical proofs. You will be graded not only on logic but also clarity and style. Assignments are due by the start of class on the day indicated at the top of the problem set. Late assignments will not be accepted. You are encouraged to discuss these assignments with the others in the class, but your write-up must be your own. If you have any question about this policy, please let me know.

Quizzes. There will be four short quizzes given this semester, one each for chapters 1,2,4, and 5. They will be 15-minute take-home, closed-book, closed-note, overly-hyphenated quizzes. These will be handed to you in class and returned at the start of the following class day.

Participation. Many of the classes are labeled "discussion" classes, and you are expected to participate. If you do, you will receive points. It is hard for a student to know how she is doing, participation-wise, so if you ever want to talk about your standing in the class please don’t hesitate to stop by my office.

Midterm and Final Paper. In lieu of exams, we will use problem sets to act as our midterm and final. These problem sets will be longer than the typical assignment. You may use your book and notes, but no other sources. The midterm paper will be assigned October 18 and will be due at the start of class on October 25. The final paper will be assigned December 11 and will be due at 5 p.m. on December 19.

Honor Code. All students are expected to follow the honor code throughout the semester. Any graded work must be pledged (and signed) in order for it to be graded. Please consult the student handbook for more details.

You should not expect a curve to be applied to the point scale, although plusses and minuses will be added as appropriate.