Math 100C - Abstract Algebra III (Spring 2018)
The course meets MWF 12-12:50 in APM B402A.
For the course syllabus and policies, see the bottom of this page.
Announcements (most recent first)
No office hours on Wednesday, May 16 since there is no homework due that day. However, if you wish to reach me by videoconference, let me know and I will set that up.
I have posted sample questions and
sample answers for the midterm.
I will hold extra office hours Friday, May 11, 4-6pm.
For those who may be interested in variations of the straightedge-and-compass construction, this Wikipedia page
references some examples. For example, the rules of Japanese origami (paper-folding)
are axiomatized by the Huzita-Hatori axioms; in the corresponding algebraic setup, one can compute not only square roots but also cube roots.
On Wednesday, May 2, my office hours will be held 3-5pm instead of 2-4pm. The problem set will correspondingly be due an hour later (at 6pm rather than 5pm).
TritonEd is now available; sorry for the delay. As usual, on TritonEd regularly enrolled students are added to the course automatically, but concurrent enrollment students must add themselves in order to receive grade data there.
No office hours on Wednesday, April 18. Instead, I'll hold office hours Tuesday (April 17) 9-11pm by videoconference; click here to participate.
You will be prompted to download the Zoom client, which is available as a free download for MacOS, Windows, Linux, or through the appropriate app stores for iOS, Android, and Windows Phone. You can also start the client and input the meeting code directly: 314-677-8110.
Zonglin's Thursday office hours will be held in APM 7421.
No office hours on Wednesday, April 4. For any urgent concerns, email me or see Zonglin.
Due to speaking engagements at research conferences, I will have more absences than
usual this quarter; however, this will not lead to any cancellation or rescheduling of lectures.
I will need to reschedule office hours and/or conduct some by videoconference; watch these announcements for updates.
HW 1, due Wednesday, April 11: pdf.
HW 2, due Wednesday, April 18 in class: pdf. On this day, there will be an in-class quiz based on the homework; see below.
HW 3, due Wednesday, April 25: pdf.
HW 4, due Wednesday, May 2: pdf.
HW 5, due Wednesday, May 9: pdf.
No homework due Wednesday, May 16 due to the midterm scheduled for May 14.
HW 6, due Wednesday, May 23: pdf.
No homework due Wednesday, May 30. However, I am planning to provide an optional problem set which is not to be turned in
(and will not be used on the final exam).
HW 7, due Wednesday, June 6.
Topics by date
All numbering refers to Artin. Listings for future dates are subject to adjustment based on how far we get in class.
Monday, April 2: overview of the syllabus; overview of group representations (10.1).
Wednesday, April 4: irreducible representations (10.2).
Friday, April 6: unitary representations (10.3).
Monday, April 9: Maschke's theorem (10.3).
Wednesday, April 11: characters and character tables (10.4).
Friday, April 13: more on character tables (10.4); one-dimensional characters (10.5).
Monday, April 16: regular representations (10.6); Schur's lemma (10.7).
Wednesday, April 18: quiz.
Friday, April 20: proof of the orthogonality relations (10.8).
Monday, April 23: algebraic integers (13.1).
Wednesday, April 25: algebraic and transcendental elements (15.2).
Friday, April 27: the degree of a field extension (15.3).
Monday, April 30: finding minimal polynomials (15.4).
Wednesday, May 2: straightedge-and-compass constructions (15.5).
Friday, May 4: adjoining roots (15.6). We'll skip over finite fields (15.7) because we covered these in 100B.
Monday, May 7: splitting fields (16.3). We also started isomorphisms of field extensions (16.4).
Wednesday, May 9: primitive element theorem (15.8).
Friday, May 11: isomorphisms of field extensions (16.4).
Monday, May 14: midterm.
Wednesday, May 16: fixed field theorem (16.5).
Friday, May 18: Galois extensions (16.6).
Monday, May 21: the main theorem of Galois theory (16.7).
Math 100A/B/C is a rigorous three-quarter introduction to the methods and basic structures of higher algebra. Topics include: representation theory of finite groups; Galois theory of fields; applications to constructions in Euclidean geometry; solvability of polynomial equations.
Instructor: Kiran Kedlaya,
kedlaya [at] ucsd [etcetera].
TA: Zonglin Jiang, zojiang [at] ucsd [etcetera].
Lectures: MWF 12:00-12:50pm in APM B402A. No lectures on the following university holidays: Monday, May 28 (Memorial Day).
Sections: Tuesday 11:00-11:50am in APM B412.
Instructor (Kedlaya): typically Wed 2-4 in APM 7202, but watch the announcements for weekly adjustments.
TA (Jiang): Tue 12-1pm in APM 5728 and Thu 3-4pm in APM 7421.
Algebra by Michael Artin, second edition (required). The hardcover, softcover, and eBook versions of the text are all interchangeable. This is the same text that was used for my 100A lecture last fall, and for 100B this winter (which might make it easier to find a used copy). The material for 100C will be drawn primarily from chapters 10, 13, 15, and 16.
Math 100B or consent of instructor.
Students wishing to proceed from 103B to 100C should contact the instructor.
Homework: Weekly assignments. In general, problem sets will be posted after Monday's lecture, to be due on Wednesday of the following week. In most cases, homework must be submitted in the dropbox in the basement of APM no later than 5pm on the due date. (Exception: homework 2 is due in class in connection with the quiz; see below.)
No extensions will be granted; see below for grading policies.
Quiz: in class on Wednesday, April 18. For the quiz only, you will be allowed to bring your solutions for Homework 2 to use as notes; you will turn these in together with the quiz.
No makeup quiz will be given; see below for exam policies.
Midterm exam: in class on Monday, May 14.
No makeup exam will be given; see below for exam policies.
Final exam: Wednesday, June 13, 11:30am-2:30pm, room TBA. No makeup exam will be given. See UCSD exam policies as well as course-specific policies below.
Grading: 30% homework, 10% quiz, 20% midterm, 40% final.
The lowest homework assignment will be dropped. In addition, you will have the option to drop either the quiz or the midterm (but not both), replacing that score (by percentage) with the final exam score (by percentage). I will do this computation at the end of the term so as to maximize your raw score.
The conversion of raw percentages into letter grades will be made in order to maintain a grade distribution comparable with historical averages for this course.
However, the following minima are guaranteed:
Additionally, any score in at least the 85th percentile or higher is guaranteed at least an A-; any score in the 65th percentile or higher is guaranteed at least a B-; any score in the 45th percentile or higher is guaranteed at least a C-. (You may wish to consult my Math 100A and Math 100B home pages to see some examples of my grade cutoffs.)
| Minimum grade
Notwithstanding the above, to receive a passing grade, you must fulfill the following conditions.
You must take the final exam, at the scheduled time and place (unless granted a mandated accommodation; see policies), and receive a passing grade.
You must not be found in violation of UCSD's academic integrity or harassment policies.
Please access TritonEd for homework and exam scores. No other material will be posted there.
No extensions will be given for homework assignments (nor adjustments for adding the course late), but the lowest homework assignment will be dropped.
At the top of each homework assignment, you must specify all outside resources that you consulted, or write "None" if none were used. You do not need to report use of the main textbook, any additional notes distributed via this web site, your own notes from lecture, or consultations with the professor or TA (including discussions during sections or office hours). You do need to report use of any other textbooks, any materials found online (in a precise fashion; e.g., for Wikipedia you must specify particular articles), and any consultation with anyone other than the professor or TA (including study group partners). If you collaborate with other students in the class, you must write up your solutions in your own words; copying solutions verbatim from another student, or quoting another source without attribution, will be treated as a violation of academic integrity (see below).
The midterm and final exam will be closed-book: no outside materials may be consulted.
This includes the textbook, lecture notes, the Internet, and anyone other than the exam proctor(s).
For the quiz, you will be allowed to consult your solutions to homework 2, which you will submit together with the quiz; no other materials may be used. We reserve the right to:
require students to produce their UCSD student ID cards for admission to the exam room
and/or submission of completed exams;
assign seating before or during the exam;
make video recordings for the purposes of monitoring academic integrity.
Exam accommodations (for the quiz, midterm, and final) will be made only in the following cases mandated by university policies.
(Other circumstances, such as a family/medical emergency during finals week, may be covered by the incomplete policy; see below.)
All accommodation requests must be made with sufficient advance notice, preferably by the end of week 1. No accommodations are available for homework assignments.
For disability accommodations, please follow
Department of Mathematics procedures. Having documentation on file with OSD is not sufficient.
For athletic accommodations, please have a cognizant representative of the Department of Athletics contact the instructor.
For religious accommodations consistent with UCSD policy, please contact the instructor.
No makeup quizzes or exams will be given. A missed quiz or exam will be scored 0 and handled in accordance with the course grading scheme (see above).
A request for an Incomplete grade will only be granted in accordance with UCSD policies. In particular, you must be on track to receive a passing grade based on your submitted homework, quiz, and midterm results without dropping any results.
To convert an incomplete into a final grade, you must provide to the instructor proper documentation of the circumstances leading to the Incomplete, and arrange with the instructor to complete all outstanding course requirements no later than the end of the subsequent quarter.
Violations of UCSD's academic integrity policies (cheating, plagiarism, etc.) will be handled by the instructor using
UCSD administrative measures.
In addition, the instructor reserves the right to assign a 0 score to any homework, quiz, or exam affected by a violation.
If you suspect a violation, please bring it to the attention of the instructor and/or TA immediately.