Instructor:

Shane Scott

Jack Olinde

Email:

Hours:

T,Th 4:30-6

W 12-1 & 5-6

Homework 8: Read 12
and
Postman Addendum.
Excercises
§ 12.5 #5,7,10,12,
and
A) Find a minimal weight closed walk which contains every edge
of the graph in
Figure 12.22.
Due 12 April.

Homework 7: Read Lynn's very good write up of hexagonal necklace counting.
Excercises
§ 15.6 #4,11
Due 29 March.
Did you know
Sage can compute Polya indices?
The Burnside TicTacToe video is a great hint for 11.

Homework 6: Read § 8 or Levin 5.1.
Excercises § 8.8 #2bkl, 3beh, 6, 10 Due 15 March.
This Sage CoCalc sheet might help you with polynomial algebra.

Homework 5: Read § 6.1-3 § 7 . Excercises § 5.9 #40 § 6.10 #3, 8
§ 7.7 #3,8,14. Due 1 March.

Homework 4: Read § 5.4-8. Excercises § 5.9 #15, 24, 29, 34. Due 22 Feb.

Homework 3: Read § 5.
Excercises § 4.6 # 1.a,d,j,m, § 5.9 # 4,7,9

Problem A: The Enigma Machine (watch) was used during WWII to encrypt messages character by character. Decrypting a message requires using the same machine setting as the encryption. Determine the bigO complexity class of decrypting an Enigma encoded message by trying every possible setting in terms of the input alphabet size n=2k. (For English letters n=26, k=13). The setting cosists of 1) a choice of 1st, 2nd, and 3rd rotor from 5 rotors, each of which has n-rotary starting positions corresponding to the letters and 2) a 'plug setting' which swaps 10 pairs of letters with exactly one partner.

Due 15 Feb.

Problem A: The Enigma Machine (watch) was used during WWII to encrypt messages character by character. Decrypting a message requires using the same machine setting as the encryption. Determine the bigO complexity class of decrypting an Enigma encoded message by trying every possible setting in terms of the input alphabet size n=2k. (For English letters n=26, k=13). The setting cosists of 1) a choice of 1st, 2nd, and 3rd rotor from 5 rotors, each of which has n-rotary starting positions corresponding to the letters and 2) a 'plug setting' which swaps 10 pairs of letters with exactly one partner.

Due 15 Feb.

Homework 2: Read § 3 & 4.
Excercises: § 3.11 #3,4,12.

Problem A: Ten points are chosen inside a square with sidelength 1. Prove that it is always possible to find a pair of points that are at most √2/3 apart. (Hint: Make some square holes for your pigeon-points.)

Due 1 Feb.

Problem A: Ten points are chosen inside a square with sidelength 1. Prove that it is always possible to find a pair of points that are at most √2/3 apart. (Hint: Make some square holes for your pigeon-points.)

Due 1 Feb.

Homework 1: Read § 2.
Excercises: § 2.9 #3, 8, 18, 20, 30.
Due 25 Jan.

Homework 0: Introduce yourself by replying to this note on Piazza.
Read Backgroupd material sections § B.1-6 of Keller and Trotter.
B7+ is optional, but fun.
Create a CoCalc Account.

Numberphile: My favorite math videos

The Infinite Monkey Cage: An episode on numbers from a great science podcast.

CoCalc: Python based math programming.
Try Sage Cloud