COURSE: MATH 5420-001

TIME AND PLACE: 2:55-4:15, Gilbreath 104

INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: 4:15-5:00 TR

OFFICE: Room 308F of Gilbreath Hall

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

E-MAIL:gardnerr@etsu.edu
WEBPAGE: Dr. Bob's faculty webpage (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 in Beamer presentations and will be presented in class as time permits. Copies of the notes are online: Notes on Rings and Notes on Fields. You should read the online notes to be covered in class before each class (to, at least, familiarize yourself with the definitions; 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 may need to read the section of the book covered in that class for a complete, deep understanding of the material.

ADDITIONAL REFERENCES:
A First Course in Abstract Algebra, 7th Edition, John B. Fraleigh, NY: Addison-Wesley, 2003.
Introduction to Ring Theory, P.M. Cohn, Springer, 2000.
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. Homework will usually be due on Saturdays through DropBox in D2L. You will need to create PDFs of your homework to electronically submit it.

ACADEMIC MISCONDUCT: If you have any questions about the assigned homework problems, then I will try to address them in class. If you need additional information, then let me know. We can work it out through e-mail, Zoom, or in-person meetings in my office. You are not to collaborate with your classmates on homework! 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 (last accessed 1/9/2024). To avoid this, do not copy homework and turn it in as your own!!! If your homework is identical to one of your classmates, with the exception of using different symbols/variables and changing "hence" to "therefore," then we have a problem! If you copy a solution from a solution manual or from a website, then we have a problem! I will not hesitate to charge you with academic misconduct under these conditions. When such a charge is lodged, the dean of the School of Graduate Studies is contacted. Repeated or flagrant academic misconduct violations can lead to suspension and/or expulsion from the university (the final decision is made by the School of Graduate studies and the graduate dean, Dr. McGee).

GRADING: Homework will be assigned and collected regularly. 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. Remember that the lowest passing grade in a graduate course is a C, so you need an average of 73% on all assignments in order to pass this class.

DESIRE2LEARN: I will not rely on the Desire2Learn ("D2L") website for the posting of notes and supplements; all of this material is freely available on my faculty webpage and does not require a login. I will use D2L to collect homework (in DropBox) and to post your grades, homework solutions, and recordings of class lectures.

NOTE: The plan for Modern Algebra 2 is to cover the material on rings, modules, and fields. We'll put an emphasis on ring theory and modules, and to only touch lightly on field theory (though we will try to get to the Fundamental Theorem of Algebra in Section V.3).

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.; accessed 1/9/2024). There is also an online ETSU Divisive Concepts Syllabus Statement (accessed 1/9/2024).

ZOOM AND REMOTE ATTENDANCE: A ZOOM meeting is set up for each lecture through D2L. I encourage you to attend the in-person lectures if possible, but if you need to attend though ZOOM then that is fine. In particular, if you are not feeling well the please do not attend class in person. You can ask questions through D2L and I will respond, just like in class. These ZOOM meetings will be recorded and posted on D2L. We have new technology in the Gilbreath Hall classrooms and there may be unforeseen technical problems at the beginning of the semester.

COVID-19 POLICIES FOR THIS CLASS: Due to personal heath concerns and concerns over spreading COVID-19, I will likely wear a mask during each class. This may result in somewhat muffled lectures, but all classnotes are online and the lectures will closely adhere to the notes.

IMPORTANT DATES: See the official ETSU Academic Dates for possible updates (accessed 1/9/2024):

• Tuesday, January 16 = First day of classes.
• Monday, January 22 = Last day to change to/from audit grade.
• Monday, January 22 = Last day to register or add without departmental permit.
• Monday, January 29 = Last day to drop without a grade of "W," last day to add without Dean's permission.
• Tuesday, January 30 = Begin late add with dean's permission only.
• Friday, March 1 = Last day for Graduate Students to apply to graduate and submit committee forms for Summer 2024 or Fall 2024 graduation.
• Tuesday, March 5 = Last day to drop with a grade of "W" and without dean's permission.
• Monday, March 11 = Last day to submit Notification of Oral Defense form to the Graduate School for May 2024 graduation.
• Monday, March 11-Friday, March 17 = Spring Break (no class).
• Monday, March 25 = Last day to complete oral defense of thesis for May 2024 graduation.
• Friday, March 29 = University closed.
• Tuesday, April 2 = Deadline to upload committee-approved thesis for May 2024 graduation.
• Wednesday, April 24 = Last day to withdraw from the university.
• Friday, April 26 = Last day of classes.

• 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 on the seminar and details on the presentation itself are online. A YouTube video of the presentation is also available. (accessed 1/9/2024)
• I have information on the Nova episode The Mathematical Mystery Tour from 1985 on my webpage. The webpage includes a link to the YouTube site which contains the show (last accessed 10/25/2016).
• 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 10/25/2016.
• 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 the TopDocumentaryFilms website (last accessed 10/25/2016).
• A more recent math documentary is Zero to Infinity (accessed 4/2/2023), an episode of the PBS series NOVA. It is hosted by Talithia Williams and premiered November 16, 2022.

Our tentative schedule for the course is as follows:

Return to Bob Gardner's home page
Last updated: April 2, 2024.