COURSE: MATH 5410-001, Call # 13370

TIME AND PLACE: 2:15-3:35, Online through Zoom

INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: 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 digital notes for the presentation of definitions, examples, and proofs of some theorems. Limited marginal notes, additional examples, and further explanations will be given using handwritten notes and a document camera. Copies of the Modern Algebra 1 group theory notes are online. 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.

VIDEOS: Each lecture will be recorded in Zoom and posted on D2L. The plan is to have videos prepared for each section covered (independent of the recorded lectures). Videos are accessible through my Online Modern Algebra: Groups webpage which includes links to ETSU's Panopto Host.

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.
Visual Group Theory by Nathan Carter, New York: Mathematical Association of America, 2009. I will use this resource for some motivational and geometric examples.
A History of Abstract Algebra, by Isreal Kleiner, Boston: Birkhauser, 2007. As time permits, I will insert some historical comments and this is a reliable source of such information.

PREREQUISITE: As the ETSU catalog states, the prerequisite for this class is Introduction to Modern Algebra (MATH 4127/5127).

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/ (last accessed 6/29/2019). 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. 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: Since this is an online class, your grade will be determined by the average on the assigned homework exercises. Grades will be assigned based on a 10 point scale with "plus" and "minus" grades being assigned on a 3 point subscale (for example, a 90, 91, 92 is an A-).

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.

NOTE: When we compare the undergraduate and graduate analysis sequences, we see that the material covered in the graduate class consists mostly of generalizations of the undergraduate material (for example, the undergraduate class covers Riemann integration and the graduate class covers Lebesgue measure and Lebesgue integration). This is not the case for the undergraduate and graduate algebra sequences, however. In Introduction to Modern Algebra 1 and 2 (MATH 4127/5127, MATH 4137/5137) you are introduced to the structures of modern algebra (groups, rings, fields, quotient groups, ideals, extension fields, algebraically closed fields, solvable polynomial equations). You elaborate on these structures with many examples and state numerous theorems which illustrate the properties and relations between them. However, there is only enough time to prove a limited number of the results. In this graduate sequence, we assume a familiarity with the structures discussed and go into more depth and many more proofs. In this class, we try to cover all of the material on group theory (sections I.1 through II.8 in the text).

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.; last accessed 1/5/2021).

IMPORTANT DATES: (see the official ETSU calendar for more details; accessed 1/5/2021):

• Tuesday, January 19 = First day of classes.
• Monday, January 25 = Last day to register or add without departmental permit.
• Monday, February 1 = Last day to drop without a grade of "W."
• Tuesday, February 2 = Begin late add with dean's permission.
• Thursday and Friday, February 18 and 19 = Break Day (no classes).
• Monday, March 1 = Last day for graduate students to apply for summer or fall 2021 graduation.
• Tuesday, March 9 = Last day to drop without dean's permission.
• Wedensday, March 10 = Last day to schedule oral defense of thesis for May 2021 graduation.
• Monday and Tuesday, March 15 and 16 = Break Day (no classes).
• Monday, March 29 = Last day to complete oral defense of thesis for May 2021 graduation.
• Friday, April 2 = University closed.
• Monday, April 5 = Deadline to upload approved thesis for May 2021 graduation.
• Wednesday, April 14 = Break Day (no classes).
• Wednesday, April 28 = Last day to withdraw from the university.
• Friday, April 30 = Last day of classes.

• A brief historical presentation on the relationship between classical algebra (polynomials, factoring, and so forth) and modern algebra (groups rings and fields) is given in A Student’s Question: Why The Hell Am I In This Class?. I use this as a supplement in Introduction to Modern Algebra (MATH 4127/5127) to motivate the study of group theory and to put it in a historical perspective.
• 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.
• 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.
• 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 6/29/2019.
• 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 6/29/2019).

Our tentative schedule for the year is as follows:

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Last updated: April 20, 2021.