COURSE: MATH 5420-001, Call # 14360

TIME AND PLACE: 12:45-2:05 TR in Lamb Hall, Room 231

INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: 3:35-4:00 TR and by appointment

OFFICE: Room 308F of Gilbreath Hall

PHONE: 439-6979 (308F Gilbreath), Math Department Office 439-4349

E-MAIL:gardnerr@etsu.edu
WEBPAGE: http://faculty.etsu.edu/gardnerr/gardner.htm (see my webpage for a copy of this course syllabus, copies of the classnotes in PDF, and updates for the course).

TEXT: Algebra, by Thomas W. Hungerford (1974).

CLASS NOTES: We will use projected digital notes for the component of the lecture consisting of definitions, statements of theorems, and some examples. Proofs of the vast majority of theorems, propositions, lemmas, and corollaries are available and in Beamer presentations and will be presented in class as time permits. The white board for marginal notes and additional examples and explanation. Copies of the notes are online at: http://faculty.etsu.edu/gardnerr/5410/notes-rings.htm and http://faculty.etsu.edu/gardnerr/5410/notes-fields.htm It is strongly recommended that you get printed copies of the overheads before the material is covered in class. This will save you from writing down most notes in class and you can concentrate on listening and supplementing the notes with comments which you find relevant. You should read the online notes to be covered in class before each class (we may not have class time to cover every little detail in the online notes). Try to understand the definitions, the examples, and the meanings of the theorems. After each class, you should read the section of the book covered in that class, paying particular attention to examples and proofs.

ADDITIONAL REFERENCES:
A First Course in Abstract Algebra, 7th Edition, John B. Fraleigh, NY: Addison-Wesley, 2003.
Abstract Algebra, 3rd Edition, David S. Dummit and Richard M. Foote, Hoboken, NJ: John Wiley and Sons, 2004.
A History of Abstract Algebra, by Isreal Kleiner, Boston: Birkhauser, 2007. As time permits, I will insert some historical comments and this is be a reliable source of such information.

PREREQUISITE: The prerequisite for this class is Modern Algebra 1 (MATH 5410).

HOMEWORK: YOU MUST SHOW ALL DETAILS ON THE HOMEWORK PROBLEMS!!! Justify every step and claim you make - this is how you convince me that you know what you are doing. You may find some answers online, but these rarely sufficiently justify all steps and are unacceptable as homework solutions.

ACADEMIC MISCONDUCT: While I suspect that you may work with each other on the homework problems (in fact, I encourage you to), I expect that the work you turn in is your own and that you understand it. Some of the homework problems are fairly standard for this class, and you may find proofs online or in an online version of the solutions manual. The online proofs may not be done with the notation, definitions, and specific methods which we are developing and, therefore, are not acceptable for this class. If I get homework from two (or more) of you that is virtually identical, then neither of you will get any credit. If you copy homework solutions from an online source, then you will get no credit. These are examples of plagiarism and I will have to act on this as spelled out on ETSU's "Academic Integrity @ ETSU" webpage: http://www.etsu.edu/academicintegrity/faculty.aspx (last accessed 7/21/2013). To avoid this, do not copy homework and turn it in as your own!!! Even if you collaborate with someone, if you write the homework problems out in such a way that you understand all of the little steps and details, then it will be unique and your own work.

GRADING: Homework (H) to be turned in will be assigned regularly. Your grade will be determined from your performance on the homework. Grades will be assigned based on a 10 point scale with "plus" and "minus" grades being assigned as appropriate. Based on the assignment of grad points by ETSU, the plus and minus grades should be given on a 3 point subscale. For example, a B+ corresponds to an average of 87, 88, or 89; an A- corresponds to an average of 90, 91, or 92; an A corresponds to an average of 93 to 100 (ETSU does not grant A+ grades, nor passing graduate grades lower than C), etc.

DESIRE2LEARN: I will not rely on the Desire2Learn ("elearn") website. Instead, I will simply post all material directly on the internet. However, I will post your homework grades on D2L.

SYLLABUS ATTACHMENT: You can find an on-line version of the university's syllabus attachment (which contains general information concerning advisement, honor codes, dropping, etc.) at: http://www.etsu.edu/reg/documents/PDF/Syllabus%20Attachment.pdf (last accessed 8/25/2015).

NOTE: The plan for Modern Algebra 2 is to cover the material on rings and fields. We will only touch on modules very lightly and comment on the material necessary for our work on fields. We will give a thorough survey of Galois theory. In the opinion of your humble instructor, the two main goals of the Modern Algebra sequence are to give a proof (which is as "algebraic" as possible) of the Fundamental Theorem of Algebra (we do this in Section V.3) and to prove the insolvability of the quintic (we do this in Section V.9).

IMPORTANT DATES: (see http://www.etsu.edu/etsu/academicdates.aspx for the official ETSU calendar; accessed 2/8/2015):

• Tuesday, January 19 = First day of classes.
• Monday, January 25 = Last day to change to/from audit grade.
• Monday, January 25 = Last day to register or add without departmental permit.
• Monday, February 1 = Last day to add with departmental permit.
• Monday, February 1 = Last day to drop without a grade of "W."
• Tuesday, March 8 = Last day to drop without dean's permission.
• Monday, March 14 = Last day to schedule thesis defense for spring graduation.
• Monday, March 28 = Last day to defend thesis for spring graduation.
• Tuesday, April 26 = Last day to withdraw from the university.
• Thursday, April 28 = Last day of classes.

• Compass and straight edge constructions are touched on in the appendix to Section V.1. There is a PowerPoint presentation (prepared in Microsoft PowerPoint 2010) with embedded audio, a transcript in PDF, and a Windows Media Video on this material, based on the material from Fraleigh's Section 32: PowerPoint, transcript, video. The video is also on YouTube here (last accessed 1/22/2014).
• October 2011 marked the bicentennial of the birth of Evariste Galois, one of the giant figures in modern algebra. To celebrate this anniversary, I prepared a seminar presentation. Details can be found on the seminar and the presentation itself online. A YouTube video of the presentation is here. (accessed 1/2/2105)
• Information on the Nova episode The Mathematical Mystery Tour from 1985 can be found on my webpage http://faculty.etsu.edu/gardnerr/Math-Mystery-Tour/mathematical-Mystery-Tour.htm. The webpage includes a link to the YouTube site which contains the show (last accessed 4/11/2013).
• A more contemporary documentary is The Story of Maths, a BBC production from 2008. This is a four part series and all of this series is available online: The Story of Maths. (In fact, this is posted on an excellent website which includes a number of documentaries and is a "must visit": Top Documentary Films!) Also of interest is the Wikipedia page for The Story of Maths. The series is available from a number of online streaming video sources, as revealed by a Google search. This websites were all active as of 4/12/2013.
• A lighter documentary on the history of math is The Story of One, narrated by Monty Python-er Terry Jones. It is also a BBC production and dates from 2005. If you are involved in teaching, this is a nice documentary which should be accessible by highs schoolers and middle schoolers. It is on TopDocumentaryFilms at: http://topdocumentaryfilms.com/story-of-one/ (last accessed 4/12/2013).

Our tentative schedule for the year is as follows:

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Last updated: April 27, 2016.