Math 236     Elementary abstract algebra     Spring 2009

Instructor: Sunil Chebolu


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Homework Problems:

Week 15 (Apr 19 - Apr 25)

1. Section 4.4: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17.


Week 14 (Apr 12 - Apr 18)

1. Section 4.3: 1, 2, 3, 4, 5, 6, 7, 9(a), 10, 12, 13(a), 14, 15, 23(a), 26. (These are the problems from last week. Nothing more for this week.)


Week 13 (Apr 5 - Apr 11)

1. Section 4.1: 1, 2, 3, 4, 5(a), 5(c), 6, 7, 11, 12, 17.
2. Section 4.2 : 1, 2, 3, 4, 5(a), 5(d), 7, 8, 10, 14.
3. Section 4.3: 1, 2, 3, 4, 5, 6, 7, 9(a), 10, 12, 13(a), 14, 15, 23(a), 26.


Week 12 (Mar 29 - Apr 4)

1. None yet. The goal is to finish off the problems in Chapter 3. I might assign a few from Section 4 later in the week if we get there.


Week 11 (Mar 22 - Mar 28)

1. Read Section 3.3.
2. Section 3.3: 1, 3, 4, 5, 6, 8, 9, 10, 13, 15, 25, 28, 32, 33, 39*.
3. Probably more to be added later in the week.


Week 10 (Mar 15 - Mar 21)

1. Read Section 3.2 thoroughly. This is terribly important!!!
2. Section 3.2: 1, 2, 4, 5, 6, 8, 10, 11, 12, 14, 15, 16, 17, 19, 23, 28, 29, 30, 37, 38. ( We will do some of these problems in class.)


Week 9 (Mar 8 - Mar 14)

ENJOY SPRING BREAK! Good luck for the second class test!


Week 8 (Mar 1 - Mar 7)

1. Section 3.1: 1, 2, 4, 5, 6, 7, 8, 9, 12, 13 (a), 16, 17, 26, 29, 30.
2. Section 3.2: 1, 2, 4, 5, plus more later.


Week 7 (Feb 22 - Feb 28)

Read Chapter 12: Public Key Crypography. Skip the proofs of the two lemmas (I will do these in class) and read the rest. This is a beautiful application of elementry number theory. I think you will enjoy reading this stuff. Otherwise, there is no homework for this week. Complete all the assigned problems in Chapter 2 from the previous weeks.


Week 6 (Feb 16 - Feb 21)

1. Section 2.3: Do all problems in this section. Most of these are straightforward. A few require some thought. So, if you are stuck, ask for help! I will do some of these problems in the class.


Week 5 (Feb 9 - Feb 15)

1. Section 2.1: Do all problems 1 - 18, 22, 24.
2. Section 2.2: Do 1 (a), 1(b), 2(a), 2(c), 3(a), 5, 6, 7, 8, 9(b), 10 (a).


Weeks 3 and 4 (Jan 26 - Feb 8)

1. Page 18-20: Do problems 1, 2, 3, 6, 8, 9, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 23, 27(a), 28.
2. If p is a prime bigger than 5, then show that p^2 + 2 is composite. (Hint: what are the remainders obtained when p is divided by 6?)
3. If p not equal to 5 is an odd prime, then show that either p^2+1 or p^2 -1 is divisible by 10.

NOTE: This is the homework for the next two weeks. I will work out some of these problems in class if time permits.


Week 2 (Jan 19 - 25)

1. Section 1.2: Do problems 1, 2, 3, 4, 5, 6, 7, 10, 11, 14, 18, 19, 20, and 26.
2. Show that (2a+1, 9a+4) = 1 and (5a+2, 7a+3) = 1 for any integer a.
3. Prove that the product of any 4 consecutive integers is divisible by 24.
4. Please please please read Section 1.4 (This would be an excellent bed-time reading! It tells you some of the fascinating history of prime numbers.)


Week 1 (Jan 12 - 18)

1. Show that if an integer a is not a perfect cube, then a^{1/3} is irrational.
2. Use division algorithm to show that every fourth power is of the form 5k or 5k+1.
3. Do exercises 1, 2 (a), and 2(b) from page 6.