Day | Date | Activity | Assignment | ||||||||||||||||
Tue | 1/9 | Welcome and Intro; meet the textbook: Mathemalchemy! | What is a number? Read From Fish to Infinity (and make sure you watch the video from Sesame Street!)
Also please begin reading the Mathemalchemy comic book (in particular the part about the chipmonks), which will give you an important mathematical overview of the installation as well as detail on the prime factorizations and the sieve of Eratosthenes. These readings (and video) will be the focus of Thursday's quiz. |
||||||||||||||||
Thu | 1/11 | Chipmonks: Primes and Prime Factorization; busting up rocks with trees |
Read Rock Groups
Try computing the prime factorizations for some numbers (and draw their trees): or are they prime?
|
||||||||||||||||
Tue | 1/16 | Primitive Counting |
Please read Early Concepts of Number and Counting.
Check out Vi Hart teaching us how to Binary hand-dance. See if you can dance along! Then you might continue on, and see how she uses binary trees to prepare her Thanksgiving feast (vegetarians and vegans: serious meat warning....). Word of the day: binary! Try out the Great Fraudini's trick on an unwitting victim; make sure that you can do it. If your victim were thinking of the following numbers, on which cards do the numbers appear, and why?
|
||||||||||||||||
Thu | 1/18 | Binary Factorization, and Quiz! |
Homework:
|
||||||||||||||||
Tue | 1/23 | Pascal's Triangle |
Please check out some readings (found here --
view each image separately for easier reading):
If you want to solve the following problems, we can use particular rows of Pascal's triangle:
|
||||||||||||||||
Thu | 1/25 | Pascal's triangle. |
For more on the development of Chinese positional number system and bamboo
counting rods, take a look at this
reading.
This one-page reading gives a third version of the triangle, from the Arab world, and a little background on the influence of Indian culture on our number systems. |
||||||||||||||||
Tue | 1/30 | Babylonians and Mayans (Other Bases): Nothing solves the place value problem |
Today you received two "artifacts" in class, one Babylonian and one Mayan. Your job: to
"translate" those artifacts into our numbers systems. The Mayan has
been started for you; the Babylonian one shouldn't be too much
trouble, since we pretty well did it in class.
Please read the following from Georges Ifrah's "The Universal History of Numbers": For practice, try writing the following numbers in Babylonian and Mayan:
|
||||||||||||||||
Thu | 2/1 | Quiz! | |||||||||||||||||
Tue | 2/6 | Fibonacci Numbers |
Please read this short description of the Fibonacci numbers.
You must check out this great video by Vi Hart, featuring Fibonaccis in Nature. There are three of them actually, and you'll probably enjoy all three! |
||||||||||||||||
Thu | 2/8 | Quiz! | |||||||||||||||||
Tue | 2/13 | Review | Make sure that you can beat me at Fraudini Nim. (I don't want to take your money....) | ||||||||||||||||
Thu | 2/15 | Exam 1 | |||||||||||||||||
Tue | 2/20 | Symmetry |
|
||||||||||||||||
Thu | 2/22 | More symmetry | Please read this short (and fun) reading on symmetry. | ||||||||||||||||
Tue | 2/27 | Platonic solids |
Please watch the following two videos:
For Thursday: explore the 17 wallpapers patterns, and try to find ways to distinguish them. This site can help out a lot! Distinguishing the 17 wallpaper groups. In particular, take a look at the glide reflection symmetry. |
||||||||||||||||
Thu | 2/29 | Quiz! | |||||||||||||||||
Tue | 3/5 | Spring Break | |||||||||||||||||
Thu | 3/7 | Spring Break | |||||||||||||||||
Tue | 3/12 | Fractals |
Please create your very own Spiral
Fractal, and submit it to me by Thursday (it will be half of your
quiz). You'll need a small square photo (that's best, although the
program allows you to crop to a square portion of an image); but
please use your creativity to create beautiful things!
Email the resulting image to me (taking a screenshot of it may be easiest). Then watch Vi Hart draw fractals! She's always fun to watch.... |
||||||||||||||||
Thu | 3/14 | Quiz! | Please read the article Pi Day: How One Irrational Number Made Us Modern: The famous mathematical ratio, estimated to more than 22 trillion digits (and counting), is the perfect symbol for our species' long effort to tame infinity. | ||||||||||||||||
Tue | 3/19 | Knots and Links |
Please watch Vi Hart
|
||||||||||||||||
Thu | 3/21 | Quiz! |
Prepare a collection of bands, links, and knots.
We'll have another gallery of those, and more prizes.... Mixed media collections are encouraged (you can make them out of fruit roll-ups if you wish...). Please watch this video from Vi Hart, about snakes and graphs.
|
||||||||||||||||
Tue | 3/26 | Review | |||||||||||||||||
Thu | 3/28 | Exam 2 | |||||||||||||||||
Tue | 4/2 | Distinguishing Knots |
Please read this short piece about
the Reidemeister moves and Tri-colorability.
|
||||||||||||||||
Thu | 4/4 | Quiz! | |||||||||||||||||
Tue | 4/9 | Infinity | Please read The Hilbert Hotel. | ||||||||||||||||
Thu | 4/11 | Quiz! | |||||||||||||||||
Tue | 4/16 | Angels and Miracles |
Please watch our friend Vi Hart describe Doodling in Math:
Sick Number Games. In particular, I'm interested in her observation at 2
and a half minutes that Pascal's triangle
lives in a sea of invisible zeros....
Here's another version of that, with a transcript, and links to more of her videos. Then watch the Numberphiles episode which covers the material from today's lecture. |
||||||||||||||||
Thu | 4/18 | Quiz! | Please check out this video An Infinity Paradox - How Many Balls Are In The Vase? | ||||||||||||||||
Tue | 4/23 | Logos | |||||||||||||||||
Thu | 4/25 | and Projects | |||||||||||||||||
Tue | 4/30 | Rest up | |||||||||||||||||
Thu | 5/2 | Final Exam |