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Week of...

Links

1

Jan 9

About, Notes, HW1

2

Jan 16

HW2, Notes

3

Jan 23

HW3, Photo, Notes

4

Jan 30

HW4, Notes

5

Feb 6

HW5, Notes

6

Feb 13

On TT, Notes

R

Feb 20

Reading week

7

Feb 27

Term Test (and solution)

8

Mar 5

HW6, Notes

9

Mar 12

HW7, Notes

10

Mar 19

HW8, Notes, RC (PDF)

11

Mar 26

HW9, Notes

12

Apr 2

FT, HW10, Notes

13

Apr 9

Notes

S

Apr 1425

Study Period: blackboards

F

Apr 28

Final

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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 of the bigger picture all those little details are there to paint.
Doing
Solve problems 19, 20, 30, 35, 39, S50, 53, S54, 62 in Chapter 15 of Gallian's book and problems 1, 2, 3, 9, 10, S11, 12, S13, S15 in Chapter 16 of the same book, but submit only the solutions of the problems marked with the letter "S".
Due Date
This assignment is due in class on Wednesday February 6, 2008.
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 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 semilegitimate 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

Solutions
Here is one set of solutions by LeoDaVinci