This is a course in the basics of abstract algebra, with the goal of helping you prepare to take the graduate qualifying exam. This semester covers field theory, Galois theory, and some commutative algebra.
Prof. Paul Gunnells, LGRT 1115L, 545–6009, gunnells at math dot umass dot edu. The best way to contact me is by email. Please don’t leave a message on my office phone; I almost never listen to messages there.
Abstract Algebra, 3rd Edition by David S. Dummit and Richard M. Foote. Table of contents.
The textbook is very readable; the authors put a lot of work into their exposition, and there are many examples given in detail. It will be presumed that you are investing significant time with the textbook outside of class, since not every topic we need can be covered in class.
Other valuable references:
Introduction to Commutative Algebra, by Atiyah and Macdonald
Some free and excellent notes for group theory, field theory, and Galois theory are on James Milne’s webpage. He has also written a primer on commutative algebra. Unfortunately there is no full length graduate algebra textbook there.
The final will be cumulative, with some emphasis placed on topics covered after the midterm exam. The final will be given in person at the time assigned by the university later in the term. The final must be taken at this time.
The dates of the take-home midterm exam will be the following:
The exam will be emailed to you by noon on Wednesday and will be due on Moodle by 11:59pm Sunday. More instructions for the exam will be given later.
Problem sets will be assigned on the main course page. Submission instructions will come later; likely problem sets will be submitted through gradescope. Late problem sets will not be accepted for any reason. At the end of the term, a few problem set grades will be dropped, so missing one or two problem set submissions shouldn’t affect your grade. Only selected problems (randomly chosen by me) will be graded.
I encourage you to form study groups and to work on the problem sets together. In fact you will learn a lot more about the material through discussing it with your fellow students. However, there are a few guidelines to follow:
Remember that ultimately you’ll be taking exams by yourself, so if you choose to work with others, make sure that you’re understanding what’s going on.
If you do work with other students, you are responsible for writing up the problems yourself in your own words. In other words, your solution must be sunmitted separately; there are no group homework submissions allowed.
If you do work with your students on a problem set, you must indicate this on the first page of your HW submission. Please include the names of the students you worked with. This alerts the grader that some of your solutions may closely resemble other students and that there is nothing amiss.
Successful completion of the problem sets is essential to help you monitor your progress in the course. The homework problems will be very similar to problems that appear on exams. Please don’t postpone working on the problems; try to take a look at them shortly after the material is covered in class.
The grading for the course will be as follows. There will be a final exam worth 40%, and one take-home exam during the semester worth 30%. The remaining 30% will be based on homework exercises.
At the end of the term, some homework scores will be dropped (at least 1). This way, if you don’t do as well on an assignment because of extra work in another course or for any reason, it shouldn’t affect your final homework grade. Extensions for HW are not granted except for documented reasons.
I try to answer as many questions as possible during lecture. If you have a question, don’t be afraid to ask. Chances are other students also have the same question. I also usually stick around a few minutes after class to answer quick questions (such as questions about parts of the lecture, a homework problem you’ve tried, etc.). Most students find this to be a good way to clear up confusion.
Outside of class, the best way to get help is through my office hours. Sometimes only a little bit of consultation is all that’s needed to deal with difficulties. One thing to remember is that you will get much more out of office hours if you make a serious effort to do the problem on your own first.
Although I like to get a lot of questions from students, it is not possible to answer mathematical questions by email. Please don’t be offended if you ask me a mathematical question by email and I don’t respond. I’ve found in the past that trying to discuss mathematics by email rarely helps anyone, and usually only causes more confusion. It’s much more effective to ask me such questions during class or office hours.
The University of Massachusetts Amherst is committed to providing an equal educational opportunity for all students. If you have a documented physical, psychological, or learning disability on file with Disability Services (DS), you may be eligible for reasonable academic accommodations to help you succeed in this course. If you have a documented disability that requires an accommodation, please notify me within the first two weeks of the semester so that we may make appropriate arrangements.
Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst. Academic dishonesty is prohibited in all programs of the University. Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty. Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty. Instructors should take reasonable steps to address academic misconduct. Any person who has reason to believe that a student has committed academic dishonesty should bring such information to the attention of the appropriate course instructor as soon as possible. Instances of academic dishonesty not related to a specific course should be brought to the attention of the appropriate department Head or Chair. Since students are expected to be familiar with this policy and the commonly accepted standards of academic integrity, ignorance of such standards is not normally sufficient evidence of lack of intent. For more information see the website of Dean of Students Office.
Expectations for our course as as follows:
For homework, you will be allowed to work with other students collaboratively. In fact, I encourage you to form study groups to work together. However, it is your responsibility to make sure that you are learning the material. You also must submit your own work. Plagarism will be considered a violation of academic honesty and will be handled accordingly.
The in-person exam will be closed-book.
For the take-home exam, you will be allowed to use your textbook and your own course notes. You will not be allowed to discuss the exam with anyone else, except me (I can help with clarifying questions, just like a traditional exam; I can’t help with actual mathematical contributions, of course). I will closely watch my email during the exam to see if you have questions. You may not discuss the exam with any other students and may not use any resources other than those indicated above. Use of any unauthorized resources will be considered a violation of academic honesty and will be handled accordingly.