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Meeting Time: | MWF, 10:00 - 10:50 |
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Location: | Jones 306 |

Instructor: | Ryan Vinroot Office: Jones 130 Office Hours: Mon, Wed 3:30-4:30, Th 9-10:30, or by appointment/walk-in. |

Textbook: | Contemporary Abstract Algebra, Seventh Edition, by Joseph A. Gallian |

Grade Breakdown: | 2 Tests - 100 points each, Homework - 100 points, Final Exam - 200 points, for a total of 500 points. The grading scale will roughly be a 10 percentage point scale, so that a final score of 450 (90%) is in the A range, a score of 400 (80%) is in the B range, etc. |

Attendance Policy: | You are expected to attend all lectures. Attendance is crucial in order to succeed in the course. Any legitimate absence for a test must be discussed with me prior to the test date. |

Prerequisites: | Math 214 - Foundations of Mathematics, and Math 211 - Linear Algebra. |

Test 1 | Mon, Oct 5 | In class | Jones 306 |

Test 2 | Fri, Nov 13 | Take home | Take home |

Final Exam | Wed, Dec 16 | 2-5 | Jones 306 |

- Important Dates and Class Holidays:
- Sat, Oct 10 - Tues, Oct 13: NO CLASS (Fall Break)
- Wed, Nov 25 - Sun, Nov 29: NO CLASS (Thanksgiving Break)
- Wed, Dec 16: FINAL EXAM

- The first homework, listed below, is due at the beginning of class on Monday, Aug 31.
- I wrote up some notes (pdf) regarding the
group
*U(n)*. These notes have a solution to Problem 13 on page 22 of the text (a homework problem), which guarantees the existence of inverses in*U(n)*. Also, I explain in the notes why the product modulo*n*of two elements in*U(n)*remains in*U(n)*, which was left as an exercise for you to think about. - The following are a selection of review problems from the book to prepare
for the Final Exam:

pgs. 91-94 #1, 21, 39, 44

pgs. 176-177 #24, 33, 35, 44, 45, 47

pgs. 230-233 #1, 3, 7, 15, 28, 39

pgs. 276-278 #7, 14, 19, 29.

For each homework problem assigned, a complete solution with each step explained should be written up. Be sure to explain your steps and reasoning for calculations as well as for proofs. Homework is due at the beginning of class on the due date of the assignment. Late homework will be marked off 20% for every day late. Homework turned in after class on the due date is considered one day late, and the day after 2 days late, and so on. Everything is easier, of course, if you turn in the homework on time!

There will be several "Group Assignments" during the semester, other than the individual assignments. Group assignments will be completed by a group of 3 or 4 students in a collaborative effort, but only one write-up of the problems will be required. All students in the group receive the same score for the homework. The responsibility of writing up solutions should be shared. I suggest rotating this responsibility among the group members.

Assignment |
Problems |
Due Date |

1 | pgs. 22-24 #11, 13, 26, 30, 32, 54 | Mon, Aug. 31 |

2 | pgs. 52-54 #11, 24, 28, 36 pg. 36 #11, 12 |
Wed, Sept. 9 |

3 | pgs. 53-54 #14, 35 pgs. 65-69 #18, 26, 31, 56 |
Wed, Sept. 16 |

Group 1 | pgs. 23-24 #27, 44, pg. 36 #16 pgs. 53-55 #23, 39, pg. 67 #38 |
Mon, Sept. 21 |

4 | pg. 66 #20, pgs. 83-85 #21, 22, 24, 64 | Fri, Sept. 25 |

5 | pgs. 83-85 #28, 33, 37, 56, 62 Optional: pg. 83 #36 |
Wed, Sept. 30 |

6 | pgs. 243-245 #22, 40, 46 pgs. 256-257 #26, 42, 45 |
Mon, Oct. 19 |

7 | pgs. 115-117 #18, 28, 36, 40, 53, 56 Optional: pg. 116 #48 |
Mon, Oct. 26 |

8 | pgs. 134-135 #15, 24, 26, 29, 32, 35 | Mon, Nov. 2 |

9 | pgs. 150-151 #16, 24, 34 | Fri, Nov. 6 |

10 | pgs. 193-196 #7, 8, 14, 53, 54 | Mon, Nov. 23 |

11 | pgs. 194-196 #22, 52, pgs. 212-215 #13, 50, pg. 269 #7 | Wed, Dec. 2 |

- There are some very useful links related to abstract algebra on the homepage of Professor Joseph Gallian, the author of the text, which is here.
- There are several opportunities for undergraduates through the William & Mary mathematics department, including research in mathematics. If you are interested, feel free to ask me or someone else in the Mathematics department about these opportunities. Information is available here.