MAT115: Math for Liberal Arts

Begin your first IMath assignment. This one is partly just to get you familiar with IMath, and how it will work. Low pressure!:) Everyone should get a perfect on this one, because I allow you to repeat the questions until you get them right.

You're going to need to do the following: visit imath.nku.edu, and

1. Create an account (if you don't already have one); then "Enroll in a new class" with this info:
2. Course ID:
   1. Section 002 (in-person): 493
   2. Section 003 (on-line): 495
3. Enrollment Key: 3.1415

1. Read Chapter 2 (Rock Groups);
2. Read the start of Chapter 25 (The Loneliest Numbers, pp. 201-204);
3. Watch this video to get a better understanding of false negatives and false positives (and sensitivity and specificity) of tests.

Word of the day: binary! Try out the Fraudini trick on an unwitting victim; make sure that you can do it.

1. For each of the following composite numbers, draw the unique binary tree corresponding to its prime factorization:
   1. 32 (primes can be repeated!)
   2. 441
   3. 2310

2. Imagine that you're playing Fraudini's trick with a friend: for each of the following numbers, indicate which cards contain that number by writing each number as a sum of powers of 2 (you might use a tree to create the factorization):
   1. 53
   2. 49
   3. 31

3. For the following use the method of "primitive counting" described in class:
   1. Turn the following into the appropriate string of 1s and 0s by drawing the appropriate ternary tree:
      1. 32
      2. 63
      3. 97

   2. Turn the following strings of 1s and 0s into the appropriate number of sheep, drawing the ternary tree is desired:
      1. 1,0,1,0,1,0
      2. 1,0,1,0,1,0,1
      3. 1,0,1,1,0,0,0,1

Please submit those on Canvas by Monday, 3/14, at midnight.

Homework: to be handed in on Wednesday, 3/23:

1. Demonstrate Egyptian multiplication by multiplying the following (write out the table, and check your work):
   1. 13*34
   2. 23*79
   3. 81*123
   4. 255*256
2. Demonstrate Egyptian division by dividing:
   1. 9/4
   2. 13/7
   Try these using the same sort of "doubling/halving" table that we use for multiplication.

3. Demonstrate Egyptian division by dividing:
   1. 4/9
   2. 7/13
   Try these using the Unit Fraction Table method, and Fraudini's trick (writing a number as a sum of distinct powers of 2).

You might check out this great video by Vi Hart, featuring Fibonaccis in Nature.

1. Read this symmetry handout (pages 1-6, 8).

   Carry out the following exercises on that page, to submit on Canvas by Wednesday of next week:

   1. A1, A4 (p. 1)
   2. B1, B3, B4 (p. 2)
   3. C1 (p. 3)

2. Also read this article (from The New York Times, March 22, 2022), as we move into geometry: Is Geometry a Language That Only Humans Know? (here's the source -- the New York Times). Neuroscientists are exploring whether shapes like squares rectangles and and our ability to them recognize are part of what makes our species special.

   (There are two fun games to play in this article, to test your instinctual geometric abilities. Look for them on the left side-bar.)

For homework, make a set of the Platonic solids from paper. Write your name on each one, or decorate them in some interesting way (just printing them off on the right paper might work!), take a photo, and upload it to Canvas.

• You have a new IMath assignment.
• Please check out these videos by Vi Hart:
  1. The first is called Snakes and Graphs. She's always got something really interesting to share.
  2. The second is Mobius Music Box
  3. The other video referenced in our reading for this week is the love story of Wind and Mr. Ug, told in a Mobius world....

Please create your very own Spiral Fractal, and submit it on Canvas. (Due Wednesday, 4/27) 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!

1. Read Chapter 30: The Hilbert Hotel (for next class!)
2. Check out this summary of our work today: Knots: a handout for math circles.

You must print off and put your answers on a copy of the knots (or else draw each one meticulously by hand). Otherwise it's a zero. No exceptions.