Math 2513Discrete Mathematical StructuresSummer 2014 |
Scissor-tailed Flycatcher (Tyrannus forficatus). If you drive down East Lindsey Street on a summer evening, you will probably see a few of these birds perching on fences and telephone wires. Once while I was mowing our lawn, a scissor-tail came and sat nearby on a fence to watch, perhaps interested in the grasshoppers being scared up. This image taken from birdforum.net. |
Assignment |
Due Date |
Problems |
1 | Wednesday, May 14 | 1.2: 4, 7, 9, 11; 1.3: 4, 9, 15. |
2 | Friday, May 16 | 2.1: 8, 11, 13, 16, 40, 48, 52; 2.2: 6, 24, 26, 28, 36, 46. |
3 | Monday, May 19 | 2.3: 6, 7, 23, 29, 38, 42; 3.1: 3, 7, 12, 32. |
4 | Wednesday, May 21 | 3.1: 25(a-d), 28, 31; 3.2: 2, 16, 17, 26, 27, 40, 43; 3.3: 10, 14, 33, 34. |
5 | Friday, May 23 | 4.1: 19, 28, 29 (if you already did #29 in class you don't need to resubmit it), 52, 57, 58. |
6 | Wednesday, May 28 | 4.2: 16, 24; 4.3: 22, 28, 33, 34; the two questions on this handout; and (for 4 points): prove that if m is an integer and m is greater than or equal to 4, then m^2 - 4 is composite. |
7 | Monday, June 2 | 4.3: 44, 48; 4.4: 14, 15, 17, 24, 44. |
8 | Wednesday, June 4 | 4.5: 10; 4.6: 5, 7, 20, 25, 29. Redo 4.4 #24, corrected as follows: Prove that for all integers m and n, if m mod 5 = 2 and n mod 5 = 3, then mn mod 5 = 1. Extra credit: 4.6 #35. |
9 | Friday, June 6 | 4.8: 13, 15, 21. |
10 | Monday, June 9 | 5.2: 5, 7, 11, 13. |
11 | Wednesday, June 11 | 5.2: 2; 5.3: 5, 9, 17, 20. |
12 | Monday, June 16 | 5.4: 9; 5.6: 29; 6.1: 3. |
13 | Wednesday, June 18 | 6.1: 6, 16(a), 25, 27(a, c, d), 30, 33; 6.2: 7, 16, 26. |
14 | Friday, June 20 | 7.1: 2, 13, 17, 25, 42, 43; 7.2: 12, 15, 20, 22. |
15 | Monday, June 23 | 7.3: 9, 16, 18. |
16 | Wednesday, June 25 | 8.2: 1, 2, 13, 18; 8.3: 2, 21, 26, 29. |
As mentioned in class, one of the reasons to learn something about divisibility properties of numbers is that factorization of numbers is the basis for the encryption algorithms used to send information securely on the internet. But were you aware that encryption is also what underlies Bitcoin? Here is a nice article which explains in detail how Bitcoin works. It requires you to learn something about encryption, but I like this kind of article: it doesn't dumb things down, but assumes the reader really wants to know what's going on. It was sent to me by Dr. Kujawa of the OU math department who I'm sure knows quite a bit about it, so if you make a serious attempt to read the article he'd be a good person to ask questions of.
Here are a couple of sites explaining why Fibonacci numbers arise in plant growth patterns (for example in the spiral patterns in the seeds on a sunflower or pinecone): Introduction to Phyllotaxis, Fibonacci Numbers and Nature.
The numbers that I referred to in class, of the form (2 to a power of 2)+1, are called Fermat numbers. You can find some interesting facts about them, and similar numbers called Mersenne numbers, at the Wikipedia articles titled "Fermat number" and "Mersenne prime". There's also a nice discussion of Mersenne primes here.
Please visit the pages for the discrete mathematics courses I taught in previous semesters for copies of the tests and homework assignments for those courses, along with some other interesting links. They are at Math 2513, Summer 2013 and Math 2513, Fall 2012.