Principles of Math
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
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
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
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'
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
No late homeworks! (Incomplete homeworks will be accepted,
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:
- Chs. 1,2 : Fri., 2 Oct.
- Chs. 1-4: Fri., 6 Nov.
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.
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.
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
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.