Math.412.001& Math.612.001 Modern Algebra Fall 2016
Assigned Problems

The table below shows the assigned problems for each section of the text we will cover.  Please note:

  • Polished work problems are indicated with a *. 
  • Format and content guidelines for regular problem sets and polished work are in the homework information page and the math writing page.  
  • Problems marked with ** are optional for undergrads, required for masters students; these are not polished work problems. 
  • An x preceding a number indicates an extra problem not from our textbook.  These are presented in a separate sheet of extra problems.
  • (PIP) on the due date means "put in portfolio."  This assignment will not be collected and graded, but should be put into the portfolio for review at the next exam.

Section

Problems

Due Date

1.1

2,4,5,7*,8,9, x1.1.1, x1.1.2

9/6

1.2

3,4,5*,7,8,11,12,16,19,21,25,28*, 34**, x1.2.1, x1.2.2

9/9

1.3

2, 6, 9, 10, 15, 17*, 19, 24, 25*, 28**

9/13

2.1

1, 3, 11ac, 12ab, 16, 17, 19, 20*, 21, 25, 31*, 33**

9/16

2.2

1bc, 2c, 6*, 7, 8

9/20
2.3
1, 3, 4*, 6, 7a, 13*
9/20

3.1

1,3,4,9,13,17,21,29*,31,34*,35 9/23

3.2

2, 5, 6, 9, 11, 13, 15, 23, 28, 29, 37**(This one seems to be extra tricky!  Not everyone will find a solution.)
9/30 (PIP)

3.3

3, 4, 8, 9, 10 , 13, 17, 23, 25, 26, 28, 29, 33, 38

9/30 (PIP)
Exam 1  9/30/2016
1.1 - 3.1
First Polished Work Compilation: Second drafts of * problems from 1.1 thru 3.1.  See detailed instructions here.
10/7
1.1 - 3.3 Exam Solutions
10/11

7.1

1, 3ad, 4ad, 6(just U6 and U30; see Corollary 2.10), 9, 11b, 14, 19*, 20, 21,24*, 25, 29*, 31**, 33**

10/18

7.2

1, 4, 5, 7ac, 11 (see a comment here), 13, 14, 18 (hint), 22*, 25**, 28* (hint), 30**,
33( try to solve this without using the solution in the back of the book)

10/21
7.3
This assignment looks too long.  I suggest you work first on the highlighted items, and if have the time and inclination you can then go back to some of the other items..
1, 2, 3a, 4, 5, 8, 11a, 13, 14, 19, 21, 22, 23, 27, 30 (hint) , 31, 38*, 40*, 44, 45 (hint), 47, 49.   Grad students: consider 4b to be **.
10/25

7.4

Start with highlighted problems.  1, 2, 3, 4, 5, 6,  10, 11, 14, 18, 19, 23, 27, 28ac, 29a, 35, 37, 44 (possibly tricky)

11/1

7.5

1, 2cd, 3be, 4, 5, 8, 9, 10, 11, 12, 14, 19, 24,
18 (Note: do not assume that H, K, or G, is finite),  22

11/4 (PIP)
7.6
1, 3a, 4, 5, 6, 7, 14, 15, 16, 17, 18, 19, 20, 21, 24, 28, 32
11/8 (PIP)
7.7
1, 2, 5, 7, 9, 14, 15, 17, 21, 23, 26
11/8 (PIP)
Exam 2  11/11/2016
7.1 - 7.3
Second Polished Work Compilation: Second drafts of * problems from 7.1 thru 7.3.  See detailed instructions here.
11/18
7.1 - 7.7
Exam Solutions
11/22
7.8
1abd, 2, 3, 6a, 7, 10*, 11 (ℝ** defined on page 181 in the first example), 18, 22*, 24**
12/2
8.1
1bc, 4,  5 (hint: consider examples of the form G x G ), 6a, 7, 9, 11, 14*, 20, 22*
12/6
8.2
1, 3abc, 5ab,  6ab, 7b, 11 (note p is prime, pG = 0 means that for every x in G, adding copies of x produces the addititive identity element 0), 12*, 16*
PIP
6.1
tbd PIP
6.2
tbd PIP