M W 3:00 -- Bradley Hall 250
This course will probably be quite unlike any math course you have had before. We will use a method called guided discovery. This method fosters creativity and independent thinking. It is also fun. I will give you lists of questions and theorem statements without proofs. You will answer the questions and prove the theorems. You will then present your results to the class. These presentations are a major part of the course.
Try to settle the questions and prove the theorems independently and write up your results before we discuss them in class. Do not consult books, the internet or other sources. You may collaborate with each other, with a couple of conditions: you should make a serious independent attempt at answering a question or proving a theorem before discussing it with another student, and the discussion should consist of ideas and hints rather than complete solutions. Of course, if you are stuck on a question or theorem, you should not hesitate to ask me for help outside of class. Work far enough ahead of the classroom presentations that there is time for this consultation.
Each day, I will select students to present their results in class. Be prepared! When you are presenting your answer or proof, strive to make your explanation clear and organized. When you are observing a presentation, it is your responsibility to follow the logic and verify that it is correct for yourself. If you cannot follow the reasoning, you should ask a question of the student presenting. I may ask you during class to re-explain an argument that you just heard.
Your standing homework assignment is to write up solutions to all the questions and theorems, preferably before they are presented in class. I will collect your solutions on a semi-regular basis and may ask you to revise them. Please make every effort to keep your solutions neat and clean, and leave space for comments. Keep a notebook containing all your notes and solutions; this will serve as your personal textbook for this course, and will help you study for exams. Writing up the proofs and solutions is an excellent way for you to learn the mathematics.
We use this format because it is directly aimed at our objectives, particularly the first and second. It gets you involved in doing and creating mathematics, rather than watching and imitating. This may be among the most challenging math courses you take, and I think you'll find the experience worthwhile.