**A new kind of math course!**

What if you don't have mathematics core requirements set by your major? We have the course for you! Here's the catalog description:

MATH 125 Mathematical Perspectives

Exploration of easily accessible, engaging, and thematically connected mathematical ideas as a vehicle to lead students to experiences which are characteristic of the mathematical enterprise.

What does that mean for *you*?

**Exploration**means hands-on activities.**Easily accessible**means you can understand it, no matter what your mathematical background is!**Engaging**means that it will be*fun*. We want to engage your*mathematical imagination*.

What more do you need? What more could you ask for? (Okay, so you could ask for an automatic A. We can't promise that in advance, sorry. The grade is mostly up to you.)

Different sections of this course may have different subtitles. Every section
will have its own themes. This means we intend that **you will be able
take MATH 125 twice**, and fulfill all six of your core mathematics credits!
Discuss these options with your advisor; MATH 125 may be the right course for
you.

Here's **what students said** about the Spring 2004 Mathematical
Perspectives courses: (follow this link)

**Courses Offered in Spring 2005:**

MATH 125 Mathematical Perpsectives: Mathematics and Music

MATH 125 Mathematical Perspectives: Devilish Number Investigations

MATH 125 Mathematical Perpsectives: Strategies for Cooperation
and Competition (Honors)

MATH 125 Mathematical Perpsectives: Mathematics and Creativity

MATH 125 Mathematical Perpsectives: Dimensionality

**Courses Offered in Previous Semesters:**

MATH 125 Mathematical Perpsectives: Women in Mathematics

MATH 125 Mathematical Perpsectives: Knots and Other Visual Mathematics

**Course Descriptions for Spring 2005:**

**Mathematical Perspectives: Devilish Number
Investigations **email the instructor
course webpage

The general objective of Mathematical Perspectives is to provide students with
experiences characteristic of the mathematical enterprise, and to do so at a
depth that allows successful students to appreciate the aesthetic beauty of
mathematical truth as well as its timeless and user-independent nature. In Devilish
Number Investigations, we will be exploring many mathematical topics which arise
simply from playing with numbers. These topics include the elementary mathematics
of prime numbers, Fibonacci numbers, sequences, permutations/combinations, and
the golden ratio. We will read the text, *The Number Devil* (which is
mainly a work of fiction), and extrapolate mathematical statements from the
discussion of the characters. Using this as our base, we will learn how to generate
examples, use these to find patterns, make conjectures, and investigate them.
Some of the chapters in the book focus on deep understanding of elementary and
secondary school mathematics, some introduce very different approaches to mathematics,
and some describe the social structure of the mathematical community. Over the
course of the novel, the main characters discuss various aspects of the way
that mathematicians think about numbers, which is what we will be learning and
doing in class as well.

**Mathematical Perspectives: Strategies
for Cooperation and Competition** email
the instructor

The overarching objective of Mathematical Perspectives is to provide students
with experiences characteristic of the mathematical enterprise, and to do so
at a depth that allows successful students to appreciate the aesthetic beauty
of mathematical truth and its timeless, user-independent nature. This proposed
course explores the power of mathematics to address important questions in the
social sciences:

- How can we better understand the motivations of actors in situations of conflict by means of game-theoretic analyses?
- How can we better understand the consequences (many of which are unintended) of voting situations in which groups of individuals make decisions that reflect the preferences of each of the participants?
- Can we measure the power held by certain players in voting situations (i.e. the degree to which they can influence the outcome with their vote)?

**Mathematical Perspectives: Mathematics and Music**
email the instructor

The general objective of Mathematical Perspectives is to provide students with
experiences characteristic of the mathematical enterprise, and to do so at a
depth that allows successful students to appreciate the aesthetic beauty of
mathematical truth as well as its timeless and user-independent nature. The
connection between mathematics and music has fascinated great thinkers and entire
cultures for millennia starting in recorded history with the Pythagoreans. Many
great mathematicians have also been musicians. Research today shows that students
who have had difficulty with mathematics in school improved in mathematics after
learning to play a musical instrument. The most basic connection between mathematics
and music is that of rhythm and timing. But mathematics can also be used to
explain why some notes sound higher than others, why instruments are tuned the
way they are, and why some notes sound better in chords than others. Composers
have used mathematical transformations in writing musical compositions. Relatively
new on the scene is digital music and algorithms being used to create music
electronically.

**Mathematical Perspectives: Dimensionality**
email the instructor course
webpage

The general objective of Mathematical Perspectives is to provide students with
experiences characteristic of the mathematical enterprise, and to do so at a
depth that allows successful students to appreciate the aesthetic beauty of
mathematical truth as well as its timeless and user-independent nature. In Dimensionality,
we will be exploring the differences and samenesses between two-dimensional,
three-dimensional, and (primarily) four-dimensional worlds. Happily, many authors
over the last century-plus have created fictional accounts of what it is like
to live in such worlds, and their works raise interesting mathematical questions
about the structure of these worlds. Questions such as "What properties
do two-dimensional objects have?", "What does a four-dimensional triangle
look like?" and "Do 'left' and 'right' have meaning in higher dimensions?"
will drive our class discussions and the principal tool which we will use to
investigate them is reasoning by analogy.

Additionally, we will learn to think like mathematicians in asking new questions
as well as generalizing some questions to more (and more) dimensions. All of
the fictional accounts that we read in class, as well as the nonfictional supplements,
deal with the concept of different dimensions. This is one of the fundamental
themes of mathematics as a whole, and the unifying thread of the investigations
in Dimensionality.

** Mathematical Perspectives: Mathematics and the Creative
Imagination** email the instructor

The general objective of Mathematical Perspectives is to provide students with
experiences characteristic of the mathematical enterprise, and to do so at a
depth that allows successful students to appreciate the aesthetic beauty of
mathematical truth as well as its timeless and user-independent nature. In Mathematics
and the Creative Imagination we will be exploring creativity in Mathematics.
The Heritage Illustrated Dictionary defines creativity as "Characterized
by originality and expressiveness, imaginative". Too many students associate
mathematics with algorithmic thinking and as a pursuit that is abstract for
the sake of abstraction and thus devoid of any real-world meaning. But they
have never considered many of the topics of Mathematics that makes its study
so enriching. We will learn that Mathematics is more than just algebraic manipulation,
but rather that it is marked by originality, imagination, beauty, and the unexpected!

**Course Descriptions for Previous Semesters:**

**Mathematical Perspectives: Knots and Other Visual
Mathematics **email the instructor
course webpage

The general objective of Mathematical Perspectives is to provide students with
experiences characteristic of the mathematical enterprise, and to do so at a
depth that allows successful students to appreciate the aesthetic beauty of
mathematical truth as well as its timeless and user-independent nature. In Knots
and Other Visual Mathematics, we will be exploring mathematics through three
threads, namely knots, graphs, and surfaces. Knots are just what they sound
like (except we fuse the free rope-ends together), graphs are networks of dots
and lines, and surfaces are things like the surface of the earth or the skin
of a bagel. So far, this doesn't sound very thematic, does it? Ah, but these
topics are actually quite interconnected... graphs can be drawn on surfaces,
and so can knots, and one can use graphs to study knots! The text for this course
is written as a guide to investigation. As the back cover says, "By means
of a wide variety of tasks, readers are led to find intereting examples, notice
patterns, devise rules to explain the patterns, and discover mathematics for
themselves." One pattern which ties (ha, ha) together the three mathematical
threads of the course is that of connectivity: How many distinct pieces make
up an object? How do we decide what counts as a 'piece'? Another commonality
between these mathematical ideas is that each is described best by pictures,
and so in some sense we will be learning to do mathematics by drawing it.

**Mathematical Perspectives: Women and Mathematics**
email the instructor

The general objective of Mathematical Perspectives is to provide students with
experiences characteristic of the mathematical enterprise, and to do so at a
depth that allows successful students to appreciate the aesthetic beauty of
mathematical truth as well as its timeless and user-independent nature. Women
and Mathematics partially focuses on the mathematical fields where some of the
famous women mathematicians studied. Those fields include number theory, abstract
algebra (groups), sequences, calculus, and geometry. The course will also include
the mathematics of some of the traditional activities of women such as quilting
and the art of South African women.