Math 455: Abstract Algebra I - Fall 2012

Math 455: Abstract Algebra I - Fall 2012

 

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Important Notes

 

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Instructor Contact and General Information

 

Instructor: Luís Finotti

Office: Ayres Hall 243

Phone: 974-1321 (please do not ask me to call back -- leave your e-mail)

e-mail: lfinotti@utk.edu

Office Hours: M, W 11am-12pm or by appointment (subject to change!!)

 

Textbook: J. B. Fraleigh, ``A First Course in Abstract Algebra'', 7th Edition. Addison Wesley, 2002.

Prerequisite: Math 251 or 257 and Math 300 or 3007.

Class: M, W, F 10:10am to 11:00am at Ayres 114. (Section 001.)

Exams: Midterms: 10/05 (Fri) and 11/09 (Fri -- changed date!), in regular classroom and time; Final: 12/10 (Mon) from 8am to 10am also in our regular classroom.

Grade: 25% for quizzes/HW + 20% for each Midterm + 35% for the Final. Note the weight of the Quizzes/HWs!

 

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Course Information

Content

In this course (and in its sequel, Math 456) you will be introduced to algebraic structures such as groups, rings, and fields. It is very important that you already have some practice with writing proofs (which was covered in Math 300/307) and familiarity with matrices and linear algebra (which was covered in Math 251/257). You will have to write many proofs in this course, and some examples we will look into will be related to matrices. Therefore, I will assume you have the proper background from both Math 300/307 and Math 251/257. If you had difficulty in those courses, you might need to review the material. (I would gladly try to help you with that if you come to my office hours.)

Course Structure

An ambitious plan would be to cover Chapters I to IV (and perhaps some of VII), while skipping sections 17, 24, 25, 28 (and maybe some others), on 455 and to cover Chapters V, VI, IX, X on 456. We might not be able to cover all this, but I will try to do as much as possible, while keeping a reasonable pace.

Also, note that this outline is subject to change slightly without prior notice.

Homework and Quizzes

Homeworks will be assigned after every class and the selected problems and due dates will be posted at the section Homework of this page. No paper copy of the HW assignments will be distributed in class. It is your responsibility to check this page often! Besides HW assignments, other important information will be posted here. (Check the section Important Notes often!)

The HWs will be due on Wednesdays. Points will be taken from messy solutions in all assignments, and you need to show work in all questions (unless stated otherwise)! (This same applies to quizzes, HWs, exams and all graded work!)

I will do my best to post solutions to the most difficult problems. If I do, they will be posted in this page.

If you like to do your HW early, you can do problems in the list of Problems Likely To Be Assigned below, even before I assigned them. I might change a problem or two for the actual assignment, but that is not very likely. I hope to be able to keep this list ahead of the class, so that you can always start early. It will also be useful if I, for some reason, delay to post problems.

Also, some times I might get too ambitious in posting problems, i.e., I might think we will cover a section during the week, put exercises from it in the next assignment, and then end up not being able to finish it. In this case I might have to take a few problems off the assignment. The bottom line is the following: the assignment is not final until I remove the "More to come" from it. (If you've done problems which were removed, just saved them for the following week.)

Finally, if there is still a "More to come" in an assignment on a Friday, please write me right away so that I can update it. If I only realize on Tuesday (or Wednesday morning!) that an assignment was not complete (with the "More to come" still there) and nobody tried to contact me, I may add new problems just then, giving you little time to finish the assignment. (If I delay in replying, you can proceed with the Problems Likely To Be Assigned.)

In my opinion, doing the HW is one of the most important parts of the learning process, so the weight for them is greater than the weight of a single midterm, and I will assume that you will work very hard on them.

Also, you should try to come to my office hours if you are having difficulties with the course. I will do my best to help you. Please try to come during my scheduled office hours, but feel free to make an appointment if that would be impossible.

Finally, it is your responsibility to keep all your graded Quizzes, HW, and Midterms! It is very important to have them in case there is any problem with your grade. You can check all your scores at Blackboard. (Blackboard will be used only for scores. This is the official site for the course.)

Missed Work

There will be no make-up quizzes or exams. If you miss a quiz or exam and have a properly documented reason, your final will be used to make-up your score.

E-Mails

You will have to check your e-mail at least once a week, preferably daily. I will use your e-mail (given to me by the registrar's office) to make announcements. (If that is not your preferred address, please make sure to forward your university e-mail to it!) I will assume that any message that I sent via e-mail will be read in a week or less, and it will be considered an official communication.

Feedback

I have an On-line Feedback Form where you can anonymously send me your comments and suggestions. I will consider your comments and try to do whatever I can to resolve possible problems before it is too late. So, please, feel free to use it whenever you have any constructive comment or suggestion. (In fact, I would greatly appreciate it.) If you don't want you comments to be anonymous, just send me an e-mail or come by my office and we can discuss the problem.

 

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Legal Issues

Conduct

All students should be familiar and maintain their Academic Integrity: from
Hilltopics 2012/2013, pg. 46:

Academic Integrity

The university expects that all academic work will provide an honest reflection of the knowledge and abilities of both students and faculty. Cheating, plagiarism, fabrication of data, providing unauthorized help, and other acts of academic dishonesty are abhorrent to the purposes for which the university exists. In support of its commitment to academic integrity, the university has adopted an Honor Statement.

All students should follow the Honor Statement: from Hilltopics 2012/2013, pg. 16:

Honor Statement

``An essential feature of The University of Tennessee is a commitment to maintaining an atmosphere of intellectual integrity and academic honesty. As a student of the University, I pledge that I will neither knowingly give nor receive any inappropriate assistance in academic work, thus affirming my own personal commitment to honor and integrity.''

You should also be familiar with the Classroom Behavior Expectations.

Disabilities

Students with disabilities that need special accommodations should contact the Office of Disability Services and bring me the appropriate letter/forms.

Sexual Harassment and Discrimination

For Sexual Harassment and Discrimination information, please visit the Office of Equity and Diversity.

Campus Syllabus

Please, see also the Campus Syllabus.

 

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Important dates:

 

Wednesday, August 22 - Classes begin.

Friday, August 31 - Last day to add, change grade options, or drop a full semester course without a "W".

Monday, September 03 - Labor Day Holiday. (No class.)

Friday, October 05 - Midterm I.

Thursday-Friday, October 11-12 - Fall Break. (No class.)

Friday, November 09 - Midterm II. (Note change in date!)

Tuesday, November 13 - Last day to drop a full term course with a "W".

Thursday-Friday, November 22-23 - Thanksgiving. (No class.)

Tuesday, December 04 - Last Class Day.

Tuesday, December 11 - Final.

 

More dates.

 

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Links

   

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Handouts

   

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Problems Likely To Be Assigned

This list is subject to change without prior notice. The official assignments will be posted below.

 

Section I.1: 4, 6, 9, 10, 14, 18, 19, 24, 26, 31, 36, 38.

Section I.2: 2, 4, 6, 8, 10, 23, 24, 27.

Section I.3: 2 to 8, 11, 12, 15.

Section I.4: 3 to 7, 10, 12, 14, 28.

Section I.5: 2, 4, 6, 7 (for 2, 4 and 6 only), 8, 9, 13, 14, 17, 18, 22, 23, 26 (G_2, G_3 and G_4 only), 27, 31, 42, 54.

Section I.6: 2, 6, 10, 16, 18, 22, 46.

Section I.7: 1, 2, 5.

Section II.8: 1, 3, 4, 6, 8, 12, 16, 18, 40, 42, 46.

Section II.9: 2, 3, 4, 8, 12, 13, 16, 18, 34.

Section II.10: 4, 6, 12, 14, 16, 30, 31.

Section II.11: 1, 6, 8, 11, 14, 16, 22, 46, 47, 49.

Section III.13: 2, 3, 8, 18, 19, 25, 29, 37, 38, 42, 47, 49.

Section III.14: 6, 7, 13, 14, 30, 31, 34.

Section III.15: 5, 11, 14, 28, 29, 40.

Section IV.18: 3, 5, 8, 11, 13, 15, 16, 18, 23, 27, 50, 52.

Section IV.19: 7, 9, 14, 23, 27.

 

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Homework

 

HW1 - Due on Wednesday 09/05:

Section I.1: 4, 6, 9, 10, 14, 18, 19, 24, 26, 31, 36, 38.

Section I.2: 2, 4, 6, 8, 10, 23, 24, 27.

Section I.3: 2 to 8, 11, 12, 15.

 

HW2 - Due on Wednesday 09/19:

Section I.4: 3 to 7, 10, 12, 14, 28.

Section I.5: 2, 4, 6, 7 (for 2, 4 and 6 only), 8, 9, 13, 14, 17, 18, 22, 23, 26 (G_2, G_3 and G_4 only), 27, 31, 42, 54.

 

HW3 - Due on MONDAY 10/01 (if you want it graded by Wednesday, otherwise you don't have to turn it in (no penalty)):

Section I.6: 2, 6, 10, 16, 18, 22, 46.

Section I.7: 1, 2, 5.

 

HW4 - Due on Wednesday 10/10:

Section II.8: 1, 3, 4, 6, 8, 12, 16, 18, 40, 42, 46.

 

HW5 - Due on Wednesday 10/24:

Section II.9: 2, 3, 4, 8, 12, 13, 16, 18, 34.

Section II.10: 4, 6, 12, 14, 16, 30, 31.

 

HW6 - Due on Wednesday 10/31:

Section II.11: 1, 6, 8, 11, 14, 16, 22, 46, 47, 49.

 

HW7 - not to be turned in (just practice for the exam):

Section III.13: 2, 3, 8, 18, 19, 25, 29, 37, 38, 42, 47, 49.

 

HW8 - Due on Wednesday 11/21:

Section III.14: 6, 7, 13, 14, 30, 31, 34.

 

HW9 - Due on Wednesday 11/28:

Section III.15: 5, 11, 14, 28, 29, 40.

 

HW10 - not to be turned in (just practice for the final):

Section IV.18: 3, 5, 8, 11, 13, 15, 16, 18, 23, 27, 50, 52.

Section IV.19: 7, 9, 14, 23, 27.

And that's all!

 

PLEASE, HIT ``REFRESH'' (OR ``RELOAD'') IN YOUR BROWSER WHEN VISITING THIS PAGE!!!!!!! I usually get messages asking for the update in the HW when it has already been updated. Since I change this page often, some times the browser don't see the changes. But, if you hit refresh and there is still problems missing, feel free to write me.

 

If it is already Friday afternoon and there still is a ``More to come'' after the HW assignment due on the coming Wednesday, write me an e-mail at lfinotti@utk.edu, and I'll update it and let you know.

 

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