Principles of Math

Fall 1998

Other resources


Instructor: Dr. Art Duval

Please feel free to come by my office any time during scheduled office hours. You are welcome to come at other times, but in that case you might want to make an appointment, just to make sure that I will be there then. You can make an appointment simply by talking to me before or after class, by calling me at my office or at home, or by sending e-mail.

You may also ask any questions directly via phone or e-mail. If I'm not in when you call, please leave a message on the voice-mail or answering machine with your name, number, and a good time for me to call you back. I will try to repond to your phone or e-mail message as soon as possible.


Upon successful completion of the course, you will be able to construct straightforward proofs in a variety of settings. You will be able to make use of existing theorems, and employ basic mathematical techniques of proof (induction, proof by contradiction, contrapositives, etc.). Your proofs will be in clear and complete English sentences, accompanied by clarifying diagrams where necessary.

You will also be able to analyze moderately complicated proofs in analysis and algebra. You will be able to identify the difficult steps, and to justify each step from previous ones.

You will be prepared for further study of other specific topics in proof-based mathematics.

Textbook: A Transition to Advanced Mathematics, Smith, Eggen, and St. Andre

We will go through Chapter 1 quickly (about 2 weeks), Chapters 2-4 thoroughly (about 2 sections per week), and then the first half or so of each of Chapters 5, 6, and 7 (about 2 weeks for each).


Reading assignments for each class will be announced at the previous class, and posted, more or less simultaneously, on the course website.

I will not "lecture" on material from the textbook, but I will answer any questions about the reading assignment at the beginning of each class. Most of our class time will be spent with either me explaining solutions to problems and how you could discover, develop, and write the proof, or students presenting solutions with constructive criticism and feedback from the rest of the class.


Participation (6%):
I expect you to be actively engaged with the material during the entirety of each class period. Your participation grade will be my subjective evaluation (on a 0-6 point scale) of how well you meet this expectation. Active engagement does not require you to have all the answers all the time, but to make an honest effort at all times. You can demonstrate this engagement in several ways.

I expect you to take your share of the student presentations. Your solution need not be complete or correct, but you should be able to intelligently discuss with me and your classmates any problems you are having. And I expect you to offer your suggestions on other students' presentations.

I expect you to ask questions in class about material you do not understand, and to answer other students' questions about material that you do understand. I expect you to take part in other class discussions as well.

There will be some in-class group activities, and I expect you to do your share towards making your group effective.

Homework (40%):
Homework will be assigned weekly (with exceptions announced in class). Assignments will be due at the beginning of class on Wednesdays. No late homeworks! (Incomplete homeworks will be accepted, though.) If an emergency prevents you from delivering your homework on time (or having someone else deliver it for you), please let me know as soon as possible. Your lowest homework score will be dropped.

You are encouraged to work together on your homework, but you must write up your solutions by yourself.

Tests (12% each):
There will be two in-class, closed-book tests. You will have to recall and explain definitions, reproduce proofs from class, and present short proofs to new problems. These tests will be on the following days:

Makeup tests can be given only in unusual and unavoidable circumstances, and with advance notice.

Final (35%)
The final exam will be comprehensive over all material we discuss in class. It will be similar to the in-class tests, but longer, and may ask you for some more involved proofs. The final will be on
Wed., 9 Dec., 10:00-12:45 p.m.

Attendance Policy:

While I will not take roll, I do expect you in class every day (realizing that emergencies do arise). Attendance will not directly affect your grade, but it will be hard to get a good participation grade if you are absent too often.

Drop date:

The deadline for student-initiated drops with a W is Fri., 16 Oct. After this date, you can only drop with the Dean's approval, which is granted only under extenuating circumstances.

I hope everyone will complete the course successfully, but if you are having doubts about your progress, I will be happy to discuss your standing in the course to help you decide whether or not to drop. You are only allowed three enrollments in this course, so please exercise the drop option judiciously.