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# Homework 10, due Monday April 4, 2016

Note: You may use an elliptic curve calculator (use a search engine to find one) for these problems if you wish.

- Problem 6.14 parts a,b,d.
- Problem 6.16 part b.
- Problem 6.17.
- Problem 6.21 part a.

# Mathematics of Being Human

(Note: one of the authors of the play, Manil Suri, got his PhD from CMU and is an active research mathematician and an active novelist.)

Forwarded from Ivan Yotov:

Dear Colleagues,

As part of Pitt’s “Year of the Humanities,” this week there will be five shows (Wed-Sat) of the play, “The Mathematics of Being Human”. The play is written by University of Maryland professors Michele Osherow (English) and Manil Suri (Mathematics). The purpose of the play is to raise awareness about the interconnections between different fields. It was recently enthusiastically reviewed in the AMS monthly:

http://www.ams.org/publications/journals/notices/201601/rnoti-p42.pdf

Tickets (free) can be reserved at

https://www.eventbrite.com/e/the-mathematics-of-being-human-tickets-22179916728

I would like to encourage all of you to see the play and I ask you to advertize it in your classes.

Ivan

# Homework 9, due Monday March 28, 2016

- 6.1.a
- 6.2
- 6.4.a
- 6.5.a
- 6.7.a
- 6.8

# Homework 8, due Monday March 21, 2016

- Based on the table of number of births each month in the US (for example, birth-data), estimate the entropy of a random variable taking values in days of the year, with probabilities according to the frequency of the birthday).
- Based on a table of letter frequencies in the English language, estimate the entropy of the English language, checking the answer from page 276. (Just use single letter frequencies from table 1.3 on page 6. More accurate measures of the entropy are possible, but are not necessary for this exercise.)
- We are given 80 coins of the same denomination; we know that one of them is counterfeit and that it is lighter than the others. Locate the counterfeit coin by using four weighings on a pan balance. Explain in terms of entropy.
- 5.45 Warning: perfect secrecy is a condition that must hold for all c in C and all m in M.
- 5.46
- 5.56(a)

# Homework 7, due Monday March 14

- 4.2
- 4.6
- 5.20(b)
- 5.23(b)
- 5.24(a)
- 5.25

# Homework 6, due Monday Feb 22

- 3.22 (a) (b)
- 3.23 (a) (d) (f)
- 3.24 (a) (b)
- 3.26 (a)