Syllabus
MATH 131 Survey of Mathematics Spring
2003
Instructor -- Richard Stark, SB 172, ext. 4371,
email: rkstark@smcm.edu,
rstark@gmpexpress.net
Office Hours -- t.b.a.
Time and Place -- Tu-Th
Text -- Survey of Mathematics, notes
developed by the St. Mary’s mathematics faculty, available in class.
You will also need a straightedge – preferably unmarked –
and a compass – preferably collapsible.
Course Content -- The course will give an
introduction to the mathematical ways of thinking and present a variety of
mathematical topics. We begin by trying
to solve a number of (mathematical) puzzles and discuss how we arrive at
solutions. After that, numbers,
geometrical constructions,
and set
theory are explored. These are
the three main chapters of the notes, however, we plan
to frequently switch from one topic to another (to avoid monotony). The chapter on numbers begins with
introducing the natural numbers 1, 2,
3, . . . , then discusses integers
and fractions and explains why we
need decimal numbers (numbers beyond fractions) to deal with many mathematical
and scientific problems. There are
clearly infinitely many natural
numbers, but are there different sizes of
infinity? Geometrical construction methods stem from the Greeks of antiquity
who allowed only straightedge and compass for their geometrical work. We shall follow the Greeks and explore what
numbers or objects can be constructed with their methods. Sets are
collections of objects and such collections have many interesting
properties. We investigate these
properties and ask questions leading to binomial
coefficients and Pascal’s triangle.
Classes -- There will be lectures, discussions,
and many problems will be investigated and solved in class or as a homework. To keep
up in the course, it is important that you
attend all classes and prepare for
each class. Much of your work should be in writing -- English sentences,
not just formulas or numbers -- and you are encouraged to discuss your work
with other students in the class.
Often, the class will split into small groups to discuss
problems and work examples together. Frequent in-class quizzes will help you
keep up-to-date. Don't hesitate to speak
up, ask questions, and voice your opinion.
Help -- Erica Helland will be teaching assistant for this class. She will attend classes, hold
outside-of-class help sessions, and give some lectures.
Feel free to come to my office for help, or just for a
chat. Bring your questions and discuss
your problems with me or with Erica.
Homework will not be collected but you may
turn in problems that you have worked if you are not sure about your answers or
need some feedback. Homework problems
will be discussed in class at your request.
Evaluation -- There will be frequent
unannounced quizzes, some to be taken in pairs or groups of two or three
persons, three tests, and a final exam.
Quizzes --20%; each test -- 20%; final exam -- 20%.
Test dates -- Thursday, February 27; Thursday, April 3,
Thursday, May 1. For the final see the
exam schedule.