Principles of Math
Please feel free to come by my office any time during scheduled
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
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 respond to your phone or
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 be prepared for further study of other specific topics in
This is very different from calculus and differential
equations, where you mostly performed computations to solve problems.
Although there is still problem-solving in this course, we will
emphasize proving your answers are correct, and not just
finding answers. This is what almost all your future advanced math
courses will be like.
Chapter Zero, 2nd. ed., Carol Schumacher
We will go through Chapters 1-6, at the rate of
approximately 2-3 weeks per chapter. We may skip a very few of the
sections in those chapters.
This textbook differs from other texts for proof-based courses, in
that the proofs of most of the theorems are not included. The point
of this is for you, the student, to fill in these details, in order to
be more actively involved with the material. Read pages xiii-xiv of
the preface ("A Note to the Student: What This Book Expects from You")
In order to further your active engagement, most class time will be
devoted to student discussions of the material, while I serve
primarily as a moderator.
- Participation (30%):
You will regularly give presentations of proofs of results in the
textbook and present solutions to problems in class. For full credit,
these presentations should be clear and convincing to your classmates.
When you are in the audience, you are still expected to be actively
engaged in the presentation. This means checking to see if every step
of the presentation is clear and convincing to you, and speaking up
when it is not. When there are gaps in the reasoning, the class will
work together to fill the gaps.
At all times, the conversation will be guided by the principles of
"mathematically accountable" talk.
Of the 30% for this part of your grade, 25% will be for the quality
and quantity of your own presentations, and 5% will be for your
participation in others' presentations.
- Homework (10%):
Written homework will be assigned approximately biweekly, announced in class,
and posted on the course website.
Assignments will be due at the beginning of class.
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
You are encouraged to work together on your homework, but you must
write up your solutions by yourself.
- Tests (15% 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: Wed., 20 Feb.
- Chs. 1-5: Wed., 10 Apr.
Makeup tests can be given only in extraordinary and unavoidable
circumstances, and with advance notice.
- Final (30%)
- 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
Mon., 6 May, 4:00-6:45 p.m.
For every two unexcused absences, you will receive a zero for an
in-class presentation. I will usually excuse an absence if you tell
me about it in advance, or, in cases of emergencies, as soon as
The deadline for student-initiated drops with a
W is Fri., 15 Mar. 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.