COURSE: MATH 4127-001, Call # 83926

TIME AND PLACE: 12:45-2:05 TR in Warf-Pickel Hall room 308

INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: 2:05-3:00 TR

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: A First Course in Abstract Algebra, 7th edition, by John B. Fraleigh (2002).

CLASS NOTES: We will use overheads for component of the lecture consisting of definitions, statements of theorems, and some examples. I will use the white board for additional examples and proofs of theorems. Copies of the notes are online at: http://faculty.etsu.edu/gardnerr/4127/notes.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:
Groups and Their Graphs by Israel Grossman and Wilhelm Magnus, New York: Yale University Press, 1964. Our text does not give many details or examples of Cayley digraphs (in Section 7), but this book goes into a reasonable amount of detail and includes many more examples.
Visual Group Theory by Nathan Carter, New York: Mathematical Association of America, 2009. I will use this resource for some motivational and geometric examples.
Algebra by Thomas W. Hungerford, New York: Springer-Verlag, 1974. This is a standard graduate level algebra textbook. I will lightly rely on it for deeper results and proofs (some of which are omitted from our text).
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.

PREREQUISITES: As the ETSU catalog states, the prerequisites for this class are Linear Algebra (MATH 2010) and Mathematical Reasoning (MATH 3000). We will depend heavily on both of these prerequisites, especially Mathematical Reasoning. Several examples will require knowledge of matrices. We will also have examples related to modular arithmetic and complex numbers, but this material will be reviewed in the class.

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 7/12/2014). 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: Your grade will be determined by the average on three tests (T₁-T₃), and homework (HW). Your average is determined by

THE FINAL: We will use the time for the final to take a third (noncomprehensive) test on Thursday, December 11 from 1:20 p.m. to 3:20 p.m.

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

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_Attachment.pdf (last accessed 7/12/2014).

PRE-FINALS WEEK POLICY: The week before finals week is called "Pre-Finals Week" (the week of December 1 this semester). ETSU has a policy which is explained both in the ETSU Faculty Handbook and the ETSU Student Handbook stating that instructors cannot administer finals during Pre-Finals Week (the primary exception being lab classes). You can access the Student Handbook and Pre-Finals Week policy online at: http://catalog.etsu.edu/content.php?catoid=7&navoid=295 (last accessed 7/12/2014). KNOW YOUR RIGHTS! You have the right to take your finals during finals week and you should be provided the proper amount of time to prepare for your finals. The specific policy from the Student Handbook is (emphasis added by me):

NOTE: This class is probably the most abstract math class you will take in your undergraduate curriculum! It covers material from the area of mathematics known both as "abstract algebra" and "modern algebra." Both terms are accurate; the second deserves some explanation. This class does not deal with "classical algebra" in the sense of dealing with polynomials, quadratic equations, and "solving for x." However, the topics of this class are inspired by these classical problems and ultimately our topics do deal with these topics (as well as many others). Primarily, this class deals with groups and rings. An additional topic is fields, and this area is dealt with mostly in the second course in the introductory algebra sequence (namely, Introduction to Modern Algebra 2, MATH 4137/5137). This class is a prerequisite for the graduate level Modern Algebra 1 (MATH 5410).

The rule of thumb is that you should allot an appropriate amount of time for your studies, at the freshman and sophomore level, at least 2 hours outside of class for each hour spent in class. This is a minimum for a class of this level!

IMPORTANT DATES (see http://www.etsu.edu/etsu/academicdates.aspx for the official ETSU calendar; last accessed 7/12/2014):
Monday, September 1 = Labor Day Holiday.
Sunday, September 7 = Last day to drop without a grade of "W."
Tuesday, September 30 = Test 1 (0, I.1-I.7).
Monday and Tuesday, October 13 and 14 = Fall Break Holiday.
Monday, October 13 = Last day to drop without dean's permission.
Thursday, November 6 = Test 2 (II.8-II.11, III.13-III.15).
Thursday and Friday, November 27 and 28 = Thanksgiving Holiday.
Tuesday, December 2 = Last day to withdraw from the university.
Thursday, December 4 = Last day of class.
Thursday, December 11 = Final (Test 3, IV.18-IV.23), 1:20 p.m. to 3:20 p.m. (the final exam schedule is online at http://www.etsu.edu/reg/registration/finalexam.aspx; last accessed 7/12/2014).

• "Groups: A Geometric Introduction," is an introduction to frieze and wallpaper groups. There are some undefined terms in the presentation (such as "subgroup," "isomorphism", and "coset") which are meant as an introduction to these new ideas. This is also a supplement to Section II.12 of Fraliegh's text. There is a PowerPoint presentation (prepared in Microsoft PowerPoint 2010) with embedded audio, a transcript in PDF, and a Windows Media Video: PowerPoint, transcript, video. The video is also on YouTube here (last accessed 8/11/2014).
• 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.
• "Permutation Groups: Cycles, Transpositions, and Futurama," presented at special Kappa Mu Epsilon, TN Beta meetings: PowerPoint.
• 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 7/12/2014).
• 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 7/12/2014.
• 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 7/12/2014).
• The syllabus for Introduction to Modern Algebra 2 (MATH 4137) is posted here.

Our tentative schedule is as follows:

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. Partial answers to some of the odd numbered problems are given in the back of the book. However, these answers are not explained in any level of detail, so you are expected to provide the details.

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. If I get homework from two (or more) of you that is virtually identical, then neither of you will get any credit. Some of the homework problems are fairly standard for this class, and you may find proofs online. However, 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. You are expected to give all details and document all claims on the homework!!!

Return to Bob Gardner's home page
Last updated: December 14, 2014.