MA 117 Mathematical Concepts I

Spring 2005, Arcadia University

Peter Appelbaum, Jinell Smithmyer

Welcome!

This is the first semester of a two-part sequence of courses. We will be focusing on problem solving and problem posing. The goal for this semester is that you become actively engaged in mathematical thought! You will discover ideas on your own, grapple with challenging new concepts, and learn various techniques of thought through repeated exposure throughout the semester. Our rollicking ride this semester will be a party for your mind and spirit with these honored guests: numbers, infinities, and geometries.

To get a good sense of the adventure that awaits us, find a way to do some of the following things as soon as possible:

1. Watch Cyberchase  on PBS, and visit the website afterwards to play some games.

2. Watch Numb3rs Sundays at 10:00 pm on CBS ... http://www.cbs.com/primetime/numb3rs/ 

3. Go to the Studio 360 Website and listen to the recent program excerpts on Numbers, Theorems, Truth. Wow!

4. View some of the following with friends and family members, and talk about them:

Donald Duck in Mathmagic Land (classic gem)

Pi (paranoid fantasy)

The Cube  and its sequel, Hypercube (horror flicks)

Enigma (most recent attempt at Hollywood dramamath)

A Beautiful Mind (fictionalized biopic that has interesting and misleading elements) 

Good Will Hunting (images of math support clichéd gender depictions)

Fermat's Last Tango (hard-to-find videotape of an interesting "opera")

Proof is no longer being performed at a "theater near you," but it is available in paperback for your reading pleasure. Sean Penn plays a mathematician in 21 Grams, The Butterfly Effect relates to something we will study toward the end of the semester, and the new sitcom Committed features someone who is supposed to be a "math genius" (but has all sorts of psychotic problems, like the other characters in this list -- why is that?). American Idol raises interesting questions about the use of mathematics in decision-making, but most of the math of this one will be studied next semester in 118.

Required Text

Burger, Edward & Starbird, Michael. 2005. The Heart of Mathematics. Emeryville, CA: Key College Publishing. Make sure you get the second edition! ISBN 1-931914-41-9.

Assignments & Grades

The following assignments are designed to help you meet our mutual goal that you are actively engaged in mathematical thought throughout the semester:

Active engagement: You are assigned to do more than the minimal expectation that you attend every class meeting; more specifically, you are assigned to come to every class meeting prepared to discuss the day's topics, having worked on mathematics problems and generated your own mathematical questions before class. This is the most important assignment, and a challenging one to accomplish. It runs counter to most of your previous experience in mathematics classes, where you probably were told how to do things before you were asked to practice doing those things. Here we want to figure things out together in class. I am confident you can do this if you set your mind to it. Also: during class you must try out mathematical ideas, even if math is not your favorite subject. You are required to ask questions of other class members about what they mean, and to help them to clarify their thoughts. The premise of this course is that the more you jump in and try stuff, the more you will eventually enjoy jumping in and trying stuff. It's a habit that is acquired only through spending time doing it. Official policy: you may miss any two classes for any personal reasons; any more than this will result in a lower course grade.

Mindscapes: These are daily homework assignments that ask you to explore and/or pose mathematical questions. This homework is probably different from homework you have had in previous mathematics courses. It is really more of a log or journal than answers. Please make every effort to understand the criteria listed in your Mindscapes Specification Sheet during the first two weeks of classes. Contact me if you have any questions or concerns.

In Your Own Words Assignments: Our textbook includes suggested writing topics in each section. You will do three of these this semester, two as graded assignments and one as part of your final exam. Each time you may choose any Personal perspectives, With a group of folks, Creative writing, or Power beyond the mathematics assignment from our textbook that appears in sections after section 2 in the chapter we are studying (e.g., 2.3, 2.4, 2.5, etc.; 3.3, 3.4, 3.5, etc.).

Thematic Investigations:

You will participate in three thematic investigations during this semester -- one for each of the main topics that we will explore. These may be individual or group investigations. You are encouraged to formulate your investigations based on your interests. You will find that others may share those interests, and therefore that it can be valuable to work together. Some class time will be provided for formulating the ideas and methods of investigation, but you are expected to pursue the investigation outside of class. Each investigation will result in some sort of "event" (performance or presentation) that you schedule for yourself outside of class. The purpose of the performance of our work is to practice sharing some aspect of our recent mathematical encounters with others. We have had little experience in doing this with mathematics in the past, and that is sad, for us and for the lovely and enchanting world of mathematics. Possible formats include: a dramatic, puppet, musical or other creative performance; an illustrated graphic novel or comic book; a scholarly magazine article; an interactive museum exhibit; a "math action" that generates awareness of an issue at the dining hall; others are possible and you are encouraged to be creative. For class, in addition to your records of investigation work,  I only need a short description of your "performance" plans and some comments on what you learned from the experience.

Math & Snack Time

Meetings will be scheduled at a time that is possible for a large majority of class members. The location will be determined with the registrar's office based on the time, and will be announced in class as soon as possible. Jinell Smithmyer will prepare supplementary activities to help you understand course material, be available to explain stuff that is harder to understand, and help groups work together on mindscapes and thematic investigations. Attendance will automatically raise your grade proportional to the number of meetings you attend; this could be as much as the next highest grade (e.g., it could raise your grade from a B- to a B). For extra help beyond Math & Snack times, you are strongly encouraged to visit my office, the Math Lab (Boyer 116 8:00-8:00 weekdays), and the Academic Enhancement Center (second floor of Taylor).

Quizzes and Examinations:

There will be three quizzes and a final exam.

Grades:

Your grade will be determined as follows: Active Engagement 10% Mindscapes 15 In Your Own Words  15 Thematic Investigations 30 Quizzes 18 Final Exam 12 100% Math & Snacks extra credit

Office Hours

Tentative Schedule

  Spring Vacation 

Helpful Links

Review of our textbook http://www.maa.org/reviews/heartmath.html 

Another review of our textbook http://www.williams.edu/Mathematics/eburger/monthlyreview.pdf 

Edward Burger's Homepage http://www.williams.edu/Mathematics/eburger/index.www.html (Starbird is less visible on the net: homepage; picture)

Heart of Mathematics Activites on-line: http://www.heartofmath.com/first_edition/activities/ 

Welcome to the Hotel Infinity! http://www.c3.lanl.gov/mega-math/workbk/infinity/inhotel.html

What's a Number? http://www.cut-the-knot.com/do_you_know/numbers.shtml 

Ron Knott's Site on Fibonacci Numbers, the Golden Ratio, and the Golden String http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html ... and  another nice Fibonacci page

Awesome Fibonacci Spirals http://www.moonstar.com/~nedmay/chromat/fibonaci.htm

Pigeonhole Principle http://www.cut-the-knot.com/do_you_know/pigeon.shtml ; http://www.ma.umist.ac.uk/avb/Pigeon.html 

The Prime Pages http://www.utm.edu/research/primes/ and another nice prime numbers page

Goldbach Conjecture mystery page http://plus.maths.org/issue2/xfile/

Mancala on the net: http://imagiware.com/mancala/,, http://www.jgames.com/mancala/, http://www.rocketsnail.com/mancala/ 

Fractals, by Cynthia Lanius http://math.rice.edu/~lanius/fractals/ 

Exploring Fractals, by Mary Ann Connors http://www.math.umass.edu/~mconnors/fractal/fractal.html 

Fractal Music http://thinks.com/webguide/fractal-music.htm 

Listen to Indonesian Gamelan music http://www.gamelan.org/AGI/gongcast.html 

African Fractals -- Ron Eglash (fantastic site!) http://www.rpi.edu/~eglash/eglash.dir/afractal/afractal.htm 

Fractal designs using pattern blocks, by Jim Millar: http://home.comcast.net/~patternblock/ 

Peter's list of mathematics education websites: http://gargoyle.arcadia.edu/appelbaum/mathweb.htm

Peter's homepage: http://gargoyle.arcadia.edu/appelbaum/

Ask Dr. Math: http://mathforum.org/dr.math/