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

Instructor: | Ryan Vinroot Office: Jones 130 Office Hours: W 3 - 4:30 and Th 2:30 - 4:30, or by appointment/walk-in. |

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

Grade Breakdown: | 2 Tests - 20% each, Homework - 25%, Final Exam - 35%. The grading scale will roughly be a 10 percentage point scale, so that a final score of 90% is in the A range, a score of 80% is in the B range, etc. |

Attendance & Lecture 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. Please do not email or text during lecture, and keep all cell phones/hand held devices/laptops put away during lecture (especially during exams). |

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

After the quick review in the first week, we will jump right into the first main topic of the course: groups. Chapters 1-11 of the book cover topics on groups, but we will not go through this material linearly. We will first cover Chatpers 1-4 (and a touch of 8), which give an introduction to groups. The other main topic of the course is that of rings, and the next topic we will cover is the introduction to rings in Chapters 12-13. We will then go back to groups, and cover topics on permutation groups, cosets, and group isomorphisms in Chapters 5-7. Finally, we will learn about group and ring homomorphisms, along with factor groups and factor rings, in parallel in Chapter 9-10 and 14-15. By the end of the semester, we will have covered topics in Chapters 1-15 (although not every topic in every chapter).

Test 1 | Thurs, Oct. 6 | 6-7:30/8-9:30 pm | Jones 306 |

Test 2 | Due Nov. 21 | 10:00 AM, Take-home | Jones 306 |

Final Exam | Wed, Dec 7 | 2-5 | Jones 306 |

- All relevant announcements will be listed here. Check back frequently (don't forget to refresh your browser) for updates.
- Important Dates and Class Holidays:
- Wed, Sept 7: ADD/DROP DEADLINE
- Sat, Oct 8 - Tues, Oct 11: NO CLASS (Fall Break)
- Fri, Oct 21: WITHDRAW DEADLINE
- Thurs, Nov 24 - Sun, Nov 27: NO CLASS (Thanksgiving Break)
- Wed, Dec 7, 2:00-5:00 - FINAL EXAM

- (8/24) The first homework, listed below, is due at the beginning of class on Mon, Aug 29. The purpose of the first homework is to review crucial concepts from Math 214. I will grade this homework very carefully, and it should be completed as if it is a Math 214 take-home exam (although using any class material is fine).
- (8/24) I will determine my regular weekly office hours as we all settle in to our semester schedule, but during this first short week, I will be available in my office for questions as often as possible. Please feel free to drop by today (Wed, Aug 24) 11-12 and/or 3-5, on Thurs, Aug 25, 2:30-5, or on Fri, Aug 26 (times TBD).
- (9/7) The math server is back up! I will now use this course homepage for all announcements, handouts, and assignments, as originally planned. Note that the College shifted the add/drop deadline to TODAY, Sept. 7.
- (9/7) By next week, I will have a set schedule for office hours. Today (9/7) I will have office hours 11-12 and 1:30-2:30. Tomorrow (9/8), I will have office hours 2:30-4:30.
- (9/21) I made a typo on the assigned problems for HW#4. On p. 85, you should do problem #64, not #65.
- (9/29) To review for the first midterm, which is now scheduled for next
Thursday, Oct 6, 6-7:30 pm or 8-9:30 pm, you should do as many problems as
you can from
Chapters 1-4, or from the Supplementary Exercises on pgs. 91-94. While any
problems you haven't yet done will help you prepare for the midterm, here is
a list of twenty to get you started:

pg. 35 #1, 2, pgs. 52-53 #10, 15, pgs. 66-67 #26, 34, pgs. 83-84 #21, 43, pgs. 91-94 #1, 5, 6, 12, 16, 26, 27, 30, 33, 34, 44, 47. - (10/3) I will have extra and extended office hours this week to help you prepare for the first midterm exam. My office hours this week will be as follows: Mon 3-4:30, Wed 2-5, Thurs 2-5.
- (11/28) I will have extra office hours today, Mon, Nov. 28, 2-3, and tomorrow, Tues, Nov. 29, 2:30-4:30. I will have my regular office hours on Wed and Thurs this week as well.
- (11/30) The following are a collection of problems which would be good to
do in preparation for the final. Some of these problems are more involved
than those you might be expected to do on the Final Exam, but are good
problems for review anyway:

pgs. 91-94 #2, 11, 28, 35, 40

pgs. 176-177 #24, 33, 35, 44, 45, 51

pgs. 230-233 #1, 3, 7, 10, 12, 15, 28, 39

pgs. 276-278 #7, 14, 15, 19, 29.

You should also work on any problems from the second take-home midterms which you did not turn in for that. - The following are the times I will be in my office on the Monday and Tuesday before the final exam: Mon 12/5 and Tues 12/6, 8:30-10:30, 12-2, and 3-5.

For each homework problem assigned, a complete solution with each step explained should be written up clearly and neatly. Be sure to completely 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 next weekday after that 2 days late, and so on. Everything is easier, of course, if you turn in the homework on time!

There will be a few "Group Assignments" during the semester, other than the individual assignments. Group assignments will be completed by a group of approximately 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 in some way.

Assignment |
Problems |
Due Date |

1 | pgs. 22-24 #11, 13, 18, 22, 26, 51, 54, 55 Please also read the following regarding #11, 13, 18: pdf. |
Fri, Sep 2 |

2 | pgs. 52-54 #11, 17, 18, 24, 28, 35, 36 | Fri, Sep 9 |

3 | pg. 36 #10, 12, pg. 54 #34, pgs. 65-68 #4, 7, 18, 36, 52 | Fri, Sep 16 |

4 | pgs. 66-69 #19, 20, 42, 55, 56 pgs. 83-85 #22, 24, 64 |
Fri, Sep 23 |

Group 1 | pg. 24 #44, 45, pg. 36 #16 pgs. 53-55 #23, 39, pg. 67 #38 |
Mon, Sep 26 |

5 | pgs. 83-85 #26, 28, 33, 37, 54, 60 Extra (not required): pgs. 83-85 #36, 56 |
Fri, Sep 30 |

6 | pgs. 167-169 #1, 53, pg. 177 #53 pgs. 243-245 #22, 42, 46 |
Fri, Oct 14 |

7 | pgs. 255-257 #13. 20, 26, 45 pgs. 113-115 #2, 17, 30 |
Fri, Oct 21 |

8 | pgs. 113-117 #3, 18, 28, 32, 36, 53, 56 Extra: pg. 116 #48 |
Fri, Oct 28 |

Group 2 | pg. 116-117 #50, 52 pg. 243 #24, pgs. 257-258 #40, 52 |
Mon, Nov 7 |

9 | pgs. 133-135 #1, 6, 19, 24, 27, 29, 38 Extra: Give a complete proof of Theorem 8.3 on pg. 159 |
Fri, Nov 4 |

10 | pgs. 133-135 #15, 17, 35 pgs. 149-150 #9, 15, 16, 20, 34 |
Fri, Nov 11 |

11 | pgs. 193-196 #7, 14, 47, 53 pgs. 211-215 #5, 9, 54, pg. 288 #16 |
Wed, Nov 30 |

- 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.