310Fall13
Math 310  Fall 2013 Section 2
Instructor: Petronela Radu, 239 Avery
Hall, pradu@math.unl.edu, 4729130, www.math.unl.edu/~pradu3/
Office hours: Tuesday 9:30 11:00, Wednesday 10:30  12:00 or by appointment
Text: A Concrete Introduction to Higher Algebra, Third Edition, by Lindsay Childs (2009 hardcover)
Homework Policy: The schedule below (which
will be adjusted as the course proceeds), indicates the chapters/sections that will be discussed each week and the assigned problems. Homework will be collected in class on the Thursday following the week in which it was assigned (unless other due date is announced). Homework should be done in groups of three or four people (unless otherwise specified). Each group should
turn in only one homework set. Your name on the homework set is your
confirmation that you have made a substantial and meaningful contribution. For
each problem, indicate who did the writeup. Be sure that everyone in your
group does more or less the same amount of writing over the entire semester.
Quizzes: There will be twelve 10point quizzes (usually on Tuesdays; beginning 10/20 they will be on Thursdays) that will be announced in advance. The problem(s) on the quiz will be very similar (possibly identical) to one or more of those on the homework collected that week. No makeup quizzes will be given, but only your top 10 quiz scores will be counted.
Exams: There will be two onehour exams and a two hour final exam. The final exam is scheduled for Monday, December 16, 3:30 p.m.  5:30 pm, Avery 112.
Calculators: Calculators will not be allowed on quizzes or exams (although they may be useful on the homework).
Scores: Your scores for homework, quizzes, hour exams and the final will be posted on Blackboard. Homework scores will eventually be normalized so that the total contribution of homework is 100 points.
Course Grade: Your final course grade will be based on a total of
100 points: 15 (homework) + 15
(quizzes) + 40 (hour exams) + 30 (final exam).
The final letter grade will be computed based on the
following table:
Final average

97100

9297

8892

8588

8185

7781

7477

7174

6771

6467

6064

5560

<55

Letter grade

A+

A

A

B+

B

B

C+

C

C

D+

D

D

F

Schedule (subject to change!)
 Week 1 (August 26  August 30): 1 (pg. 7): 2; 2A (pg. 1315): 2, 8, 13, 20; 2B (pg. 1819): 27, 30; 2C.
 Week 2 (September 3  September 6): 2D (pg. 24): 36; 3A (pg. 28): 3, 5; 3B (pg. 34): 19, 25, 30; 3C (pg. 36): 35 (iii), 35 (iv), 37.
 Week 3 (September 9  September 13): 3D (pg. 43): 41, 43, 44, 46; 3E (pg. 47): 57, 58, 60 (iii), 64, 65.
 Week 4 (September 16  September 20): 4A (pg. 5657): 1, 4, 5; 4B (pg. 58): 10, 14; (pg. 59) 19, 21; (pg. 6263) 32, 38.
 Week 5 (September 23  September 27): 4C (pg. 67): 43, 45; 5A (pg. 7374): 1, 5; 5B (pg. 7778): 12, 16, 20; 5E (pg. 85): 41; 5F (pg. 8889): 44.
 Week 6 (September 30  October 4): 6C (pg. 105): 8, 10; 6D (pg. 108110): 17, 22, 27, 30; 6E (pg. 112113): 43, 52; 6F (pg. 116117): 62.
Exam 1  Thursday, October 10, in class. The review session is scheduled for Wednesday, October 9, in Avery Hall 111. Review problems for Exam 1 (pdf)
 Week 8 (October 14  October 18): 7A (pg. 130131): 1, 4, 10, 13, 16; 7C (pg. 138139): 21, 24, 26, 33. (due on Thursday, Oct. 24)
 Week 9 (October 21  October 25): 9A (pg. 174175): 3, 4, 7, 8, 14, 15; 9B (pg. 177179): 17, 20, 21, 26, 27, 35. (due on Thursday, Oct. 31)
 Week 10 (October 28  November 1): 9C (pg. 174175): 40, 42, 44, 45, 51, 53, 54; 12A (pg. 261264): 1, 3, 5, 7, 12. (due on Thursday, Nov. 7)
 Week 11 (November 4  November 8): 12A (pg. 261264): 15, 16; 12 B (pg. 270271): 34; The problem ``Five pirates and a monkey" from https://www.math.okstate.edu/~wrightd/crypt/lecnotes/node24.html
Five pirates and a monkey are shipwrecked on an island. The pirates have collected a pile of coconuts which they plan to divide equally among themselves the next morning. Not trusting the others, one pirate wakes up during the night and divides the coconuts into five equal parts with one left over, which he gives to the monkey. The pirate then hides his portion of the pile. During the night, each of the other pirates does exactly the same thing by dividing the pile he finds into five equal parts leaving one coconut for the monkey and hiding his portion. In the morning, the pirates gather and split the remaining pile of coconuts into five equal parts and again one is left over for the monkey. What is the smallest number of coconuts the pirates could have collected for their original pile?
Square roots modulo m and factoring large numbers:
1. Find all integers between 100 and 300 that are square roots of 1 mod 21.
2. Assume that you know that $64^2=1 (mod 91). Use this information to factor 91.
(Homework due on Thursday, Nov. 14)
 Week 12 (November 11  November 15): 13 A (pg. 287): 1; 13B (pg. 289): 6; 14 A (pg. 297299): 1, 4, 10; 14 B (pg. 301302): 15, 20, 21, 25, 31. (due on Thursday, Nov. 21)
Exam 2  Thursday, November 21, in class. The review session is scheduled for Monday, November 18, in Avery Hall 111, from 5:00 to 7:00 pm. Review problems for Exam 2 (pdf)
 Week 14 (November 25  November 29): 14 C (pg. 305306): 37, 39, 40, 41, 42, 43, 46, 47; 15 A (pg. 308): 1, 2. (due Friday, Dec. 6 at 11:00 am)
 Week 15 (December 2  December 6): 15 B: 4, 5, 6, 7;
Primitive Element Theorem:
1. In F= Z_31, let U be the set of units of F. Then: i) find the order of 2; ii)find the order of 5; iii) find an element of order 15; iv) Find an element of order 2; e) find a primitive element for F.
2. In F=Z_73, let U be the set of units of F. i) Show that 2 has order 9. ii) Show that 21 has order 24.;iii) Find a power of 21 whose order is 8; iv) Use i) and iii) to find a primitive element for F. (due on Thursday, Dec. 12)
 Week 16 (December 9  December 13): Final Review.
Departmental grading appeals policy: Students who believe that their academic evaluation has been prejudiced or capricious have recourse for appeals to (in order) the instructor, the Department Chair, the Department Grading Appeals Committee, and the College Appeals Committee.