[Acmsmajors] 300-400 level course offerings for 2008-2009
miller at math.washington.edu
Tue Nov 4 10:24:50 PST 2008
To help you plan your class schedules for the rest of this academic
year, here is a list of what the Math Department will be offering at
the 300 and 400 level for Winter and Spring quarters. In all cases,
you should pay attention to the prerequisites listed in the catalog:
A couple of special notes: Math 465 and 466 will not be offered this
year. Also, there will be three topics courses, Math 480, offered in
Spring. And, there are two additional courses for those interested in
teaching, Math 421/422 and Math 497. Descriptions for all of these
307, 308, 309
300, 324, 326
381A MWF 10:30
390A MWF 2:30
394A MWF 8:30
395A,B MWF 8:30, 10:30
403A MWF 9:30
407A MWF 9:30
408A MWF 10:30
412A MWF 1:30
425A MWF 11:30
428A MWF 1:30
442A MWF 12:30
462A MWF 9:30
492A WF 12:30
Two courses for those interested in teaching:
Conceptual Calculus for Teachers
Instructor: Ken Bube
This two-quarter course is intended for students interested in
becoming Secondary School mathematics teachers.
There are three main goals in this class. The content goal
is that you gain a more comprehensive understanding of two
of the fundamental concepts of calculus: the mathematics of
change (Math 421) and reasoning about infinite processes
(Math 422). The communication goal is that you learn to
communicate your understanding and insights about calculus.
The learning process goal is that you reflect on your
experience as a student in a way that increases your
effectiveness as a math teacher.
The text for this course is a draft of the book "Making Sense
of Calculus" by Stephen Monk, a national leader in mathematics
education and recently retired mathematics professor at UW.
These courses will be similar in tone to Math 411/412 (Algebra
for Teachers) and Math 444/445 (Geometry for Teachers).
You should have completed the Mathematics Basic Requirement
for the Teacher Preparation Option (Math 124, 125, 126, 307, 308)
before taking Math 421.
Math 497, Topics for Teachers
Title: Beyond the Quadratic Formula
Instructor: Ron Irving
The principal subject of algebra is the solution of polynomial
equations. The familiar solution of a quadratic or degree two
polynomial equation by the quadratic formula was discovered
independently in several cultures many centuries ago. It is now a
standard part of secondary mathematics education, but typically
students do not study higher degree polynomial equations from the same
perspective. In this course we will do so, as we take a close look at
the most central results in the early history of algebra. These include:
• The solution of quadratic polynomial equations. The quadratic
formula will be examined from three different perspectives.
• The solution of cubic, or degree three, polynomial equations. This
was obtained in the sixteenth century by several Italian
mathematicians and represents the most dramatic advance in algebra to
have taken place for centuries.
• The solution of quartic, or degree four, polynomial equations.
This was also obtained by Italian mathematicians, later in the
• The fundamental role of complex numbers in the solution of cubic
equations. Even if one is interested only in real number solutions to
cubic equations with real number coefficients, the method of solution
developed in the sixteenth century led inevitably to the introduction
and study of complex numbers. We will see why this was so and learn
how to use them.
• The attempt to solve polynomial equations of higher degree,
culminating around 1800 with Gauss's proof of the Fundamental Theorem
Underlying these topics is the idea that the coefficients of a
polynomial encode information about that polynomial's roots. Our goal
is to learn how to use the coefficient data to unravel this hidden
Another goal of the course is the development of experience in
grappling with mathematical argument. There will be weekly assignments
in which students will be asked to read mathematical arguments,
develop an understanding of the arguments, write out the arguments in
more detail, and write arguments from scratch. Some class time each
week will be dedicated to small group discussions of these
assignments. We will not cover a large amount of material, aiming
instead for an in-depth understanding of a few key results.
Entry code required. Please contact Math Advising Office, C-36 PDL,
307, 308, 309
300, 324, 326
390A MWF 2:30
395A MWF 8:30
396A MWF 10:30
404A MWF 9:30
409A MWF 11:30
426A MWF 11:30
443A MWF 12:30
TOPICS COURSES - SPRING 2009
Math 480 COURSE DESCRIPTION Spring 2009
INTRODUCTION TO DYNAMICAL SYSTEMS.
TEXT: R. Devaney, A First Course in Chaotic Dynamical Systems, Addison-
WHAT IS A DYNAMICAL SYSTEM? Dynamical systems is a branch of mathematics
that attempts to understand processes in motion. Such processes occur
in all branches of
science. For example, the motion of planets is a dynamical system, one
that has been studied
for centuries. Some other systems are the stock market, the world’s
weather, and the rise and
fall of populations.
Some dynamical systems are predictable, whereas others are not. The
reason for this un-
predictable behavior has been called “chaos.” One of the remarkable
discoveries of the modern
mathematics is that very simple systems—even as familiar as quadratic
chaotic and behave as unpredictably as the stock market or as wildly
as a turbulent waterfall.
ABOUT THIS COURSE: The aim of the course is to show a “window” into
recent mathematics. The emphasis will be on mathematical ideas and
This is a course in discrete dynamical systems, which is basically
iteration, or composing
a function with itself over and over. We are interested in the long-
term behavior of a system.
Often complexity of the system calls for qualitative reasoning as
opposed to looking for speciﬁc
analytic solutions. Continuous dynamical systems, which arise from
are closely related to, and have many common features with, discrete
The plan is to cover most of the book, which will be supplemented by
handouts and material
from other sources. One of the main themes will be the dynamics of the
Qc (x) = x2 + c depending on the parameter c, ﬁrst when c and x are
real, and later when c and
x are complex. We will study how the long-term behavior of the system
changes from stable
and predictable to chaotic.
PREREQUISITES: Math 327/8 or Math 334/5/6, or permission of the
of an issue is general “mathematical maturity.” This will be a
(mostly) proof-based course, so it
is highly desirable to be familiar with proof methods, such as proofs
by induction, contradiction,
and contraposition; basics of set theory (set algebra, countable and
uncountable sets); ϵ-δ
deﬁnitions of convergence and other elements of Introductory Analysis.
480B MWF 2:30
TIME: MWF at 2:30pm
Instructor: William Stein
TITLE: Algebraic, Scientiﬁc, and Statistical Computing, an
Open Source Approach Using Sage
DESCRIPTION: This is a course about using free open source
software to support computation in the mathematical sciences.
Topics include Sage, Python, Cython, debugging and profiling code,
computing with algebraic structures (groups, rings and fields),
exact and numerical linear algebra, numerical optimization, basic
statistical computing, and 2d and 3d graphics.
> 480C MW 2:30-3:50
> Math 480: The Mathematical Theory of Knots.
> Time: MW 2:30-4:20.
> Instructor: Judith Arms
> Prerequisites: Math 310 and 326, OR Math 335, OR permission of
> Text: The Knot Book, by Colin Adams.
> Topics: Knot and link presentations and Reidemeister moves;
> prime, composite, and altenating knots; tabulating knots;
> knot invariants such as colorability, stick number, genus,
> and knot polynomials; selected additional topics, if time permits.
> One highlight of the course will be the proof of Tait's conjecture
> on alternating knots using polynomial invariants that were
> discovered in the 1980's.
> Grades will be based on homework, classwork (some in groups), a take-
> home midterm, and a project.
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