Dr. Sadun's M328K Sections, Spring 2003

Last updated April 16

There will be homework assigned every week, due on Wednesdays, every week except those weeks with exams.

Homework #1: (due January 22)

1.1 p.14: 4, 8, 12, 24, 26.

1.2 p.22: 2, 8, 12, 14, 24.

Recommended additional problems from the textbook

(you don't have to turn these in)

1.1 p.14: 1, 2, 3, 7, 25.

1.2 p.22: 4, 5, 11, 22, 27, 29, 33.

Homework #2: (due January 29)

1.4 p34: 6, 8, 12, 35

3.1 p76: 4, 16,

3.2 p84: 2, 8, 10

Homework #3: (due February 5)

3.2 p84: 14, 24

3.3 p94: 2, 4, 10

3.4 p104: 2, 10, 30, 46, 66

3.5 p117: 2, 4

3.6: 2, 6, 8

4.1: 2, 8, 10, 22, 28, 34

4.2: 2, 6, 10

Homework #5:

There is no written homework due February 19, due to the exam on February 21. However, I recommend that you work the following problems on your own:

4.2: 13, 14, 15, 16

4.3: 1, 3, 7, 9, 12, 15, 33

Homework #6: (due February 28, because of the school closure on February 26)

4.3: 4, 8

4.4: 2, 4, 10

Homework #7: (due March 7)

4.4: 6

4.5: 2

5.1: 2,3,4, 20, 22, 24, 25, 26

Homework #8: (due

(The following problem was assigned in class but wasn't previously listed. If you have not already turned this in, do so now):

Determine,

A year is chosen at random from 2001 through 4800. That is, each of those years has a 1/2800 chance of

being chosen. Prove that the probability of Christmas falling on Sunday in the chosen year is NOT 1/7. (Easter, however, has a 100% probability of landing on Sunday). [Note that you do not have to calculate the probability that Christmas falls on a Sunday -- you just have to show that it can't be 1/7.]

5.2: 2 (skipping (a), (b) and (c)), 6, 10

Homework #9: (due March 26)

5.5: 6, 8, 12, 14, 18, 20

6.1: 2, 4, 6, 10

Homework #10: (due April 2)

Give a

"(n-1)! is congruent to:

-1 (mod n) if n is prime,

0 (mod n) if n is composite and greater than 4, and

2 (mod n) if n=4. "

6.1: 14,18, 20, 22, 24, 40

6.2: 2, 8

Homework #11 (due April 23)

7.1: 2, 4, 6

8.1: 2, 4, 10, 12, 14, 16

Homework #12 (due May 2)

1) solve the CRT problem for ALL values of a and b:

x = a (mod 123)

x = b (mod 25)

2) A message is encoded with the coding

x => x^(125) (mod 8633)

Find the decoding.

3) Give a careful proof of the Chinese Remainder Theorem for 2 moduli, namely:

If (m1,m2)=1, then there is a unique solution, modulo (m1 m2) to the system of equations

x = a (mod m1)

x = b (mod m2)