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Your grade will be determined as follows:
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MA 117 Mathematical Concepts I
Spring 2003, Arcadia University
Peter Appelbaum
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 each of the following things as soon as possible:
1. Go to the Franklin Institute before February and check out the Risk exhibit -- awesome way to think about mathematics and everyday life in an unusual way! Info at http://sln.fi.edu/tfi/info/current/
2. Go to the Studio 360 Website and listen to the recent program excerpts on Numbers, Theorems, Truth. Wow!
3. 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 (horror flick)
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 cliched gender depictions)
Fermat's Last Tango (hard-to-find videotape of an interesting "opera")
Proof (Nothin's better than broadway for a dose of math fun!)
Burger, Edward & Starbird, Michael. 2000. The Heart of Mathematics. Emeryville, CA: Key College Publishing.
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. But 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.
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: You will do two of these this semester: 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 the section we are studying.
Theme Investigations:
You will participate in three theme 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). 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.
Quizzes and Examinations:
There will be three quizzes and a final exam.
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Your grade will be determined as follows:
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Taylor 312A 215-572-4476 appelbaum@arcadia.edu
Mondays & Thursdays 2:00-3:30
Thursdays at lunchtime -- campus dining hall
& by appointment
| Date | Primary Topics | Reading | Due Today |
| Jan 14 | Welcome! Surfing the book; Mancala & Human Knots | Don't leave without knowing at least three names! | |
| 16 | Problem solving, problem posing, mathematizing and making conjectures | Surf the book some more. | Strategies for mancala; conjectures for human knots. |
| 21 |
Jasper adventure; more mathematizing |
Too busy working on mancala and knots to read anything | Problem solving/posing booklets on mancala and human knots due |
| 23 |
Jasper analogous problems; Silly Stories |
Chapter 1 <DO NOT READ 1.3 or you are cursed!> | Start 1.1#1,3,4,5,7,8 |
| 28 | Numbers: what can we say about them? | Chapter 1 -- all of it | Finish 1.1 #1,3,4,5,7,8; also do #2,6, and 1.4 #6,7,9,14 |
| 30 | Pigeons and interesting numbers | Section 2.1 | Mindscapes 2.1 I.1, 2,3,4,9 |
| Feb 4 | Number patterns | Section 2.2 | 2.1 I.6,8; II.1,2; 2.2 I.1,2,5,10,13 |
| 6 | Patterns; Factoring and prime numbers | Section 2.3 | 2.1 III.1; 2.2 I.17,19; II 1,4,5; 2.3 I.2,3,7,9 |
| 11 | Primes galore | Re-read 2.3; Read 2.4 for fun | 2.2 II.7; III.1; 2.3 I.10,18,19; II.1,4,7; 2.4 I.1,3 |
| 13 | Irrational Numbers | Section 2.6 | 2.3 II.10; III.1; 2.4 I.8; II.1,2; 2.6 I.1,2,5 |
| 18 | Really looking at real numbers | Section 2.7 | 2.4 II.4; III 3; 2.6 II.5; III.5; 2.7 I.2,5,7,15,18,20; Thematic Investigation Action/Event |
| 20 | Quiz | Study for quiz | |
| 25 | Archaeology of Number | First "In your own words" due | |
| 27 | Infinity: What do we mean? | Think about infinity | |
| Mar 4 | Beyond numbers | Section 3.1 | 3.1 1,2,4,5; II.3,4; 2.7 II.8,9; III.2, 3 |
| 6 | Comparing infinities | Section 3.2 & 3.3 | 3.1 II.5; III.1; 3.2 I.6,9,11,12,13; 3.3 I.1,2,6,7 |
***REVISED TENTATIVE SCHEDULE***...***REVISED TENTATIVE SCHEDULE***
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18 |
Comparing
infinities |
Section
3.2 & 3.3 |
3.1
II.5; III.1; 3.2 I.6,9,11,12,13; 3.3 I.1,2,6,7 |
|
20 |
Stratospheric
infinities |
Section
3.4 |
3.2
II.5,7,10; III.1,2; 3.3 I.4,8; II.1,4; 3.4 I.1,2,8 |
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25 |
Geometric
infinities |
Section
3.5 |
3.3
II.4,5; III.1; 3.4 I.3,4; II.1,2; III.1; 3.5 I.1,4,5; II.3,5 Thematic
Investigation Action/Event |
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27 |
Quiz |
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study
for quiz |
***NEW
AND IMPROVED REVISED TENTATIVE SCHEDULE***
4/1/2003
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Apr
1 |
Archaeology
of Infinities |
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Second
"In your own words" due |
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3 |
Geometric
Patterns and chaos |
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Think
about how you could start with one of several shapes, and change each
into other shapes. Now do the same change to a shape multiple times
until you can predict a pattern. |
|
8 |
Pythagorean
playfulness |
Section
4.1 |
4.1
I.2,3,7,10; 3.5 II.1 |
|
10 |
Art
galleries and sexy rectangles |
Sections
4.2 and 4.3 |
4.1
II.1; 4.2 I.1,2,9; 4.3 I.2,4,5 |
|
15 |
Tilings;
Art and Change |
Section
4.4, 6.1 and 6.2 |
4.2
II.1; III.2; 4.3 II.1,3; 4.4 I.1,2,3,4 |
|
17 |
Predetermined
Chaos |
Sections
6.3 and 6.5 |
4.3
II.5; 4.4 II.1,2,4; 6.3 I.1,4,7,8,9;6.2 II.3 |
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22 |
Quiz |
Self-scheduled study group for quiz |
Study
for quiz |
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24 |
Our Mathematical Selves |
Visit the Math Lab to start preparing for the
final exam |
Thematic
Investigation/Event |
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Meet with study partners |
Meet with study partners |
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29 |
Reading
Day -- no class |
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Meet with study partners |
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May
6 |
Final
Exam 9:00 AM |
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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/activities/index.html
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.math.ilstu.edu/~day/courses/old/305/contentpigeonhole.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/ and a curious lesson plan
Mancala on the net: http://www.nrr.co.uk/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
Create Fractal Music http://www.discovery.com/stories/technology/fractals/create.html
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.htm
Fractal deigns using pattern blocks, by Jim Millar: http://home.attbi.com/~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/
Spring
Vacation 