MATH 125: Mathematical Perspectives

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?

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:

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.