2007-08 - Pitzer College

156 MATHEMATICS
at least two of which must be upper-division, to be chosen by the student in consultation
with a member of the Mathematics faculty. Students who satisfy the requirement for
Calculus II and/or III by placement or by AP credit may constitute the 6 required lettergraded
courses by additional mathematics courses (which cannot include course designed
to prepare students for calculus), by computer science courses, or by courses with
mathematics prerequisites in science, economics, or history and philosophy of mathematics.
A catalogue, “Mathematics Courses in Claremont,” which lists all mathematics courses
offered in The Claremont Colleges, is prepared each year by the Mathematics Field
Committee. Students who want mathematics courses other than those listed below
should consult this catalogue. Copies are available in the office of the Registrar, from the
Mathematics faculty, and on the World Wide Web.
Honors: Students will be recommended for Honors at graduation if their overall gradepoint
average is 3.5 or above, if their grade-point average in Mathematics is 3.5 or above,
and if they satisfactorily complete a Senior Exercise of honors quality. The Senior Exercise
will be designed by the students and their Pitzer mathematics adviser, with the
cooperation, if appropriate, of mathematics faculty elsewhere in Claremont.
AP Credit: A student who has a score of 4 or 5 on the Mathematics Calculus AB
examination will receive credit for Mathematics 30 after passing Mathematics 31.
Similarly, a student with a score of 4 or 5 on the Calculus BC exam will receive credit for
Mathematics 30 and 31 after passing Mathematics 32.
1. Mathematics, Philosophy, and the “Real World.” Throughout history, mathematics
has changed the way people look at the world. This course will focus on two examples:
Euclidean geometry (which suggested to philosophers that certainty was achievable by
human thought), and probability and statistics (which gave scientists a way of dealing
with events that did not seem to follow any laws but those of chance). Readings and
problems will be taken from three types of sources: (1) Euclid’s Elements of Geometry; (2)
modern elementary works on probability and its applications to the study of society and
to gambling; (3) the writings of philosophers whose views were strongly influenced by
mathematics, such as Plato, Aristotle, Pascal, Spinoza, Kant, Laplace, Helmholtz, and
Thomas Jefferson. Prerequisite: high school algebra and geometry. Enrollment is limited.
Fall, J. Grabiner.
6. Pencil and Paper Games. This class will focus on the analysis of games in which
chance is not a factor. Familiar examples range from tic-tac-toe to chess. This analysis
leads to direct applications to the social sciences, as well as to such mathematical oddities
as surreal numbers. Offered in alternate years. Prerequisite: high school algebra. Spring,
D. Bachman.
7. The Mathematics of Games and Gambling. An introduction to probability and game
theory. Topics will include combinations, permutations, probability, expected value,
Markov chains, graph theory, and game theory. Specific games such as keno, roulette,
craps, poker, bridge, and backgammon will be analyzed. The course will provide
MATHEMATICS
excellent preparation for statistics courses as well as for uses of game theory in the social
sciences. Prerequisite: high school algebra. Fall, J. Hoste.
10. The Mathematical Mystery Tour. I saw a high wall and as I had a premonition of an
enigma, something that might be hidden behind the wall, I climbed over it with some
difficulty. However, on the other side I landed in a wilderness and had to cut my way
through with a great effort until-by a circuitous route-I came to the open gate, the open
gate of mathematics. From there well-trodden paths lead in every direction…. (M.C. Escher).
Many beautiful and exciting topics in mathematics are accessible to students having only
a minimal background in mathematics. Study knots in 3-dimensional manifolds, learn
that some infinities are bigger than others, discover surreal numbers and write home
about it on 1-sided postcards. Topics will vary from year to year and the course may be
repeated for credit. Little mathematical experience required.
10B. Cartography. We will study various aspects of the history and mathematics of map
making. Topics include surveying, finding longitude and latitude, globe projections and
spherical trigonometry. D. Bachman. [not offered 2007-08]
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10G. Mathematics in Many Cultures. Mathematical ideas are found in many cultures,
among both literate and non-literate peoples. We will study both the mathematics and the
role it plays in the cultures. Examples will be chosen from the mathematical ideas of
present-day peoples of Africa, Asia, Oceania, and the Americas, as well as historic Egypt,
Mesopotamia, Greece, Islam, and China. Students will learn the modern mathematical
concepts necessary to understand the examples. Spring, J. Grabiner.
10H1. Dynamical Systems, Chaos, and Fractals. By means of computer experimentation,
this course will explore the basic concepts of dynamical systems and the strange world of
fractals. Topics ill include fixed points, periodic points, attracting and repelling sets,
families of functions, bifurcation, chaos and iterated function systems. We will investigate
several famous examples including the Quadratic Family, the Henon map, Julia sets and
the Mandelbrot set. No previous computer experience requires. Some knowledge of
calculus will be helpful but not required. J. Hoste. [not offered 2007-08]
10H3. Topology. This course explores the shape of 1,2,3, and 4-dimensional space. Is the
universe curved or flat? Could an astronaut return from a long journey as the mirrorimage
of her former self? What do knots have to do with this? The subject is extremely
visual-we will draw pictures and make models in order to gain insight. Enrollment is limited.
J. Hoste. [not offered 2007-08]
11. Theories of Electoral Systems. (See also POST 111). In this course we will analyze
various voting procedures (majority rule, Borda counts, instant runoff voting,
proportional representation, etc.) as well as ways of assessing voting power and other
kinds of power. We will also consider the U.S. Electoral College, the use of the initiative
in California and the election for governor in California. This course satisfies Pitzer’s
formal reasoning objective. J. Hoste/J. Sullivan. [not offered 2007-08]