Mathematics in the Modern World
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
or at home, or by sending
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 e-mail message
as soon as possible.
An open mind, a healthy curiosity, and a willingness to learn new ideas.
This course is designed to introduce you to the big picture of what
mathematics is, and what it means to do mathematics. In contrast
(probably) to your previous experiences with mathematics, this means
more than applying rote formulas or watching someone else think. You
will be actively engaged in (guided) discovery, retracing for yourself
the highlights of some of the major developments in mathematics.
Upon successful completion of the course, you will know and
understand the great ideas and recurring themes of mathematics. You
will be able to express this understanding in verbal form, and by
solving problems. You will be capable of applying, in a variety of
settings, mathematical thinking, such as: following assumptions to
their logical conclusions; finding and testing patterns; and
representing the essential information of an involved situation.
Specific topics will come from the broad areas of numbers, infinity,
geometry, and probability. Highlights include (but are not limited
to) answering the following questions: Are there infinitely many
primes? Can all numbers be written as fractions? Are there
different kinds of infinity? What are the most symmetric
3-dimensional shapes we can build with straight lines? What is the
fourth dimension, and how can we describe it? How likely are
The Heart of Mathematics, 2nd ed., Burger and Starbird, Chs. 1,
2, 3, 4, 7. We will skip some sections, and maybe include one or two
sections from other chapters. The textbook is required at all class meetings.
"Welcome!", pages xi-xiv.
Carefully read each section that we cover in class after each class
(taking into account the suggestions of "how to use the book" in the
"Travel Tips - Read the Book" subsection of the "Welcome" section).
I will point out in class and on the web site which parts of each
section, if any, you can skip.
This textbook is extraordinarily readable, and even entertaining,
but also challenging and thought-provoking. The topics in
the text (and the course) are selected to introduce you to deep
mathematical ideas, made accessible by the authors' unique style.
- Participation (5%):
A large portion of class time will be devoted to discussions and
investigations in small groups and with the whole class. Your active
engagement with the material is required at all times. You will not
be able to get a good participation grade if you are absent too much.
- Homework (25%):
Individual homework will be assigned weekly, and will be due
Wednesdays (with exceptions as announced in class). You are allowed
to work together on homework (in fact, I encourage you to do so), but
the paper you turn in you must write yourself. In order to receive
substantial credit for a homework solution, you will need to explain
your steps and reasoning, not just the answer.
Homework is due at the beginning of class (1:30 sharp); if you
cannot make it to class, arrange to either deliver the homework to me
early, or have someone else bring it to class for you. Your lowest
homework score will be dropped.
- Writing assignments (20%):
There will be approximately four writing assignments, where you
will reflect on what you have learned, explain key ideas, and
investigate more involved problems.
- Exams (10% each):
There will be three in-class exams on the following days, covering
approximately the following chapters:
Makeup exams can be given only in extraordinary and unavoidable
circumstances, and with advance notice.
- Secs. 2.1-2.4: Wed. 26 Sep.
- Secs. 2.6-3.3: Wed. 17 Oct.
- Ch. 4: Wed. 14 Nov.
- Final (20%)
- comprehensive (including parts of Ch. 7).
Wed. 12 Dec., 4:00-6:45 p.m.
The deadline for student-initiated drops with a W is Fri., 2 Nov. 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, and new freshmen are only allowed
six withdrawals in their entire academic career, so please exercise the
drop option judiciously.