07-401/Homework Assignment 4

07-401/Navigation Panel   # Week of... Links 1 Jan 10 About, Notes, HW1 2 Jan 17 HW2, Notes 3 Jan 24 HW3, Photo, Notes 4 Jan 31 HW4, Notes 5 Feb 7 HW5, Notes 6 Feb 14 On TT, Notes R Feb 21 Reading week 7 Feb 28 Term Test 8 Mar 7 HW6, Notes 9 Mar 14 HW7, Notes 10 Mar 21 HW8, E8, Notes 11 Mar 28 HW9, Notes 12 Apr 4 HW10, Notes 13 Apr 11 Notes, PM S Apr 16-20 Study Period F Apr 24 Final Add your name / see who's in! Register of Good Deeds

Reading

Read chapters 15 and 16 of Gallian's book three times:

• First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
• Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
• And then a third time, again at a quicker pace, to remind yourself what bigger all those little details are there to paint.

Doing

Solve problems 53, 54 and 62# in Chapter 15 of Gallian's book and problems 1, 2, 3#, 9, 10, 11, 12#, 13#, 15, 30 and 45# in Chapter 16 of the same book, but submit only the solutions the problems marked with a sharp (#).

Solutions

Due Date

This assignment is due in class on Wednesday February 7, 2007.

Just for Fun

Take a large integer and write it in base 10. Cut away the "singles" digit, double it and subtract the result from the remaining digits. Repeat the process until the number you have left is small. Prove that the number you started from is divisible by 7 iff the resulting number is divisible by 7. Thus the example on the right shows that 86415 is divisible by 7 as 0 is divisible by 7. (I learned this trick a few months ago from Bradford Hovinen). Find a similar criterion for divisibility by 17 and for all other divisibilities and indivisibilities. Note that the word "indivisibilities" has the largest number of repetitions of a single letter among all words in the English language (7 i's). I've known this fact for years but this exercise is the first time that I'm finding a semi-legitimate use for that word! (It is tied with the word honorificabilitudinitatibus for seven 'i's. You can read more about it here: http://en.wikipedia.org/wiki/Honorificabilitudinitatibus)

86415 10 ---- 8631 2 --- 861 2 -- 84 8 - 0