 Niels Henrik Abel, 1802-1829 |
 Evariste Galois, 1811-1832 |
 Peter Ludwig Sylow, 1832-1918 |
 Emmy Noether, 1882-1935 |
Niels Henrik Abel, 1802-1829 |
Evariste Galois, 1811-1832 |
Peter Ludwig Sylow, 1832-1918 |
Emmy Noether, 1882-1935 |
COURSE: MATH 5410-001, Call # 84711
TIME AND PLACE: 2:55-4:15 TR, Gilbreath Hall room 314
INSTRUCTOR: Dr. Robert Gardner OFFICE HOURS: TR 4:15-5:00
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 theorems. 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 (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.
VIDEOS: Videos are available for each section covered. Videos are accessible through my Online Modern Algebra: Groups webpage, which includes links to videos on ETSU's Panopto Host and on YouTube. No login is required to see the videos.
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. 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 8/22/2023). 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). During tests, I will "patrol" the room to make sure everyone is doing their own work and that phones are securely put away. Once you start a test, you must stay in the room until you complete it or until the class time is over. If you provide have a documented medical need to leave class during the test then this will, of course, be honored (provided you give me the documentation before hand).
GRADING: Homework (H) to be turned in will be assigned regularly. We will have two tests (T1 and T2) and your average will be computed as follows:
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: 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.; accessed 8/22/2023). There is also an online ETSU Divisive Concepts Syllabus Statement (accessed 8/30/2023).
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 calendar and calendar with School of Graduate Studies deadlines for more details; accessed 8/22/2023):
The ETSU Abstract Algebra Club: As a student in this class, you will be enrolled in the ETSU Abstract Algebra Club. A description of the club is online here. We should have at least one formal meeting per semester.
Other Supplemental Material: The following may be of interest:
Our tentative schedule for the year is as follows:
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I.5. Normality, Quotient Groups, and Homomorphisms |
I.5.2 |
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Return to Bob Gardner's home page
Last updated: December 2, 2023.