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Meeting Time: | MWF 9 - 9:50 |
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Location: | Morton 203 |

Instructor: | Ryan Vinroot Office: Jones 130 Office Hours: M 3-4, W 3-4, Th 3-4:30 (and Th 10-11:30 AM), or by appointment/walk-in. |

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

Grade Breakdown: | 2 Tests - 20% each, Homework/Quizzes - 30%, Final Exam - 30%. The grading scale will be the standard 10 percentage point scale, so that a final score of 93 or higher is an A, 90-92 is an A-, 87-89 is a B+, 83-86 is a B, 80-82 is a B-, 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 Chapters 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 | Tues, Feb 28/Wed, Feb 29 | 7:30-9 pm | Morton 203 |

Test 2 | Due Mon, Apr 9 | Take-home | Take-home |

Final Exam | Fri, May 4 | 9-12 | TBA |

- All relevant announcements will be listed here. Check back frequently (don't forget to refresh your browser) for updates.
- Important Dates and Class Holidays:
- Fri, Jan 27: ADD/DROP DEADLINE
- Sat, Mar 3 - Sun, Mar 11: NO CLASS (Spring Break)
- Fri, Mar 16: WITHDRAW DEADLINE
- Fri, May 4, 9:00 - 12:00 - FINAL EXAM

- (1/18) The first homework, listed below, is due at the beginning of class on Mon, Jan 23. 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).
- (1/18) 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, Jan 18) 2:30-5, on Thurs, Jan 19, 9-11:30, or on Fri, Jan 20, 2-3:30.
- (1/27) Here is the handout on properties of powers in groups which I gave to you in class: pdf.
- (2/3) Here are some notes on the group
*U(n)*, including a full solution to Problem 13 from Chapter 0, as well as a proof of closure of the operation in*U(n)*, which I left as an exercise for you in class: pdf. - (2/3) I originally made a small typo in HW 4 below, which I have now fixed. You should do Problem 36 in Chapter 3, not Problem 37.
- (2/6) Quiz 1 will be on Mon, Feb 13, at the end of class. It will cover any material in the book or from lecture from Chapters 1, 2, and through page 60 of Chapter 3.
- (2/8) On Thurs, Feb 9, my office hours will be shifted to 3:30-5 (instead of 3-4:30, as I have to sub for a class 2-3:20).
- (2/20) Here are some problems from the Supplementary Exercises in the book
which you can work on to prepare for the exam. Many of these are closer to
more challenging homework problems, but nonetheless will help you become more
comfortable with the material. The first list of problems require a good
working knowledge of the material covered, while the second list of problems
are more challenging (but still good problems to work on). Make sure you
can do all of the problems in the first list before working on the problems
in the second list:

pgs. 91-94 #1, 2, 5, 11, 12, 16, 18, 27, 30, 31, 33, 44, 47

pgs. 91-94 #6, 9, 13, 17, 20, 23, 34 - (2/24) I will have the following extra/extended office hours next Monday and Tuesday, before the midterm: Mon, Feb 27, 2:30-4:30, and Tues, Feb 28, 2:30-4:30.
- (2/29) I will have extended office hours today, Wed, Feb 29, 2:30-4:30.
- (3/26) My regular office hours 3-4 pm today are canceled.
- (3/28) My morning office hours on Thurs, Mar 29, will be 9:30-11 AM rather than 10-11:30 AM.
- (4/18) Here is an optional homework assignment, related to the rationalizer of a group element, and when it is a subgroup. There is no penalty for not doing this assignment, but you may turn it in any time before the final exam, for extra points towards your HW/quiz score for the course: Extra HW.
- (4/23) I will have additional office hours on Tues, Apr 24, 2:30-4 pm, to answer questions about the last homework, due on Wed, Apr 25.
- (4/25) 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. - (4/26) I will have office hours during the first week of Final Exams on the
following days and times:

Mon, Apr 30, 12-2,

Tues, May 1, 12-2, 4-5,

Wed, May 2, 12-2, 3-4:30,

Thurs, May 3, 12-2, 3-4:30.

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 also be 2 quizzes (15 min during class) during the semester, the first of which will be before the first midterm. Your homewok and quizzes will count for a total of 30% of your final grade.

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. |
Mon, Jan 23 |

2 | pg. 52 #1, 4, 8, 11, 12 | Fri, Jan 27 |

3 | pgs. 53-54 #19, 28, 29, 34, 35, 36 pg. 36 #10, 11 |
Fri, Feb 3 |

4 | pgs. 65-69 #8, 18, 20, 36, 51, 52, 56, 59 | Fri, Feb 10 |

5 | pg. 68 #42, pgs. 83-85 #4, 21, 22, 28, 37, 54, 64 | Fri, Feb 17 |

6 | pgs. 167-169 #4, 10, 36 | Fri, Mar 2 |

7 | pgs. 243-244 #9, 12, 22, 42, pgs. 255-257 #8, 20, 26, 45 | Fri, Mar 16 |

8 | pgs. 114-117 #17, 28, 33, 36, 40, 15, 18, 53 | Fri, Mar 23 |

9 | pgs. 133-135 #1, 4, 6, 15, 22, 29, 32, 35 | Fri, Mar 30 |

10 | pgs. 149-151 #8, 16, 20, 34, 43 | Fri, Apr 13 |

11 | pg. 212 #8, 9, pgs. 193-196 #7, 8, 14, 40, 47, 53 | Fri, Apr 20 |

12 | pgs. 212-215 #11, 13, 21, 56, pgs. 269-270 #4, 10 | Wed, Apr 25 |

- 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.