[Acmsmajors] 300-400 level course offerings for 2008-2009

[Brooke Miller]

>


Dear Students,

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:


> http://www.washington.edu/students/crscat/math.html


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  
follows.


WINTER 2009

307, 308, 309
300, 324, 326
327, 328

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:

MATH 421/422

Math 421/422
Conceptual Calculus for Teachers

Instructor: Ken Bube
Winter/Spring 2009
MWF 11:30

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

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  
sixteenth century.
	• 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  
of Algebra.

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  
information.

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,  
543-6830.

SPRING 209

307, 308, 309
300, 324, 326
327, 328'

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 480A

Math 480 COURSE DESCRIPTION Spring 2009
INTRODUCTION TO DYNAMICAL SYSTEMS.
TEXT: R. Devaney, A First Course in Chaotic Dynamical Systems, Addison- 
Wesley, 1992.
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  
functions—may be
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  
some fairly
recent mathematics. The emphasis will be on mathematical ideas and  
concepts.
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  
differential equations,
are closely related to, and have many common features with, discrete  
dynamical systems.
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  
quadratic family
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  
instructor. More
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  

> instructor.

>

> 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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