Math 100B - Abstract Algebra II (Winter 2018)
The course meets MWF 12-12:50 in Center 113.
For the course syllabus and policies, see the bottom of this page; however, note that this material is
subject to revision until the first lecture.
Announcements (most recent first)
I have posted a sample final exam
and sample answers.
Reminder: Zonglin will have extra office hours Monday, March 19, 4-6pm in APM 5748; I will have extra office hours Tuesday, March 20, 3-5pm in APM 7202.
Due to schedule conflicts, Zonglin and I have rescheduled some of our office hours for Weeks 9-10.
No office hours Tuesday, March 6 (although sections will meet as scheduled).
To replace this, Zonglin will have extra office hours Friday, March 2, 3-5pm in APM 5728.
On Tuesday, March 13, Zonglin's office hour 11am-12pm is cancelled (his earlier office hour and sections will meet as scheduled). To replace this, Zonglin will have an extra office hour
Monday, March 12, 2-3pm in APM 5748.
My office hours Wednesday, March 14 are cancelled. Instead, I have reserved room APM 6402 for a study session; and I will be available to answer questions by videoconference (email me if you want to set this up).
No office hours Thursday, March 15.
Zonglin will have extra office hours Monday, March 19, 4-6pm in APM 5748.
I will have extra office hours Tuesday, March 20, 3-5pm in APM 7202.
I have posted sample questions and sample answers for the midterm.
On account of the midterm on Wednesday, February 21, my office hours for that week are rescheduled to Tuesday,
February 20, at the same time (3-5pm).
Due to a schedule conflict, my office hours on Wednesday, February 14 will start at approximately 3:30pm.
Due to a schedule conflict, my office hours on Wednesday, February 7 will end at 4:30pm.
On Monday, February 5, the math department is co-presenting a documentary about the work of research mathematicians, followed by a Q&A with Prof. Zelmanov. See the flyer.
For the problem on HW 3 about generalized eigenspaces, the definition of a generalized eigenspace is at the beginning of section 4.7 (which we did not cover in class). You shouldn't need any of the results about Jordan decompositions (which we will treat in another fashion later).
My office hours on Wednesday, January 10 will run 3-4pm, rather than 3-5pm as usual.
HW 1 is now posted.
HW 1, due Wednesday, January 17: pdf.
HW 2, due Wednesday, January 24: pdf.
HW 3, due Wednesday, January 31: pdf.
HW 4, due Wednesday, February 7: pdf.
HW 5, due Wednesday, February 14: pdf.
No homework on Wednesday, February 21 due to the midterm scheduled that day
(see midterm sample questions
and sample answers).
HW 6, due Wednesday, February 28: pdf.
HW 7, due Wednesday, March 7: pdf.
HW 8, due Wednesday, March 14: pdf.
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, January 8: overview of the syllabus; fields; examples (3.2).
Wednesday, January 10: vector spaces over an arbitrary field (3.3).
Friday, January 12: spans, linear independence, bases (3.4, 3.5).
Monday, January 15: NO LECTURE (holiday).
Wednesday, January 17: dimension of a vector space (3.5).
Friday, January 19: matrices and linear transformations (4.2); direct sums (3.6).
Monday, January 22: infinite-dimensional vector spaces (3.7); the dimension formula for a linear
Wednesday, January 24: linear operators (4.3); eigenvectors (4.4).
Friday, January 26: characteristic polynomial (4.5).
Monday, January 29: definition of a ring, examples (11.1).
Wednesday, January 31: polynomial rings (11.2).
Friday, February 2: homomorphisms and ideals (11.3).
Monday, February 5: quotient rings (11.4).
Wednesday, February 7: adjoining elements (11.5).
Friday, February 9: product rings (11.6).
Monday, February 12: fractions (11.7).
Wednesday, February 14: maximal ideals (11.8).
Friday, February 16: unique factorization domains (12.2).
Monday, February 19: NO LECTURE (Presidents Day).
Wednesday, February 21: midterm.
Friday, February 23: overview of finite fields (15.7).
Monday, February 26: Gauss's lemma (12.3).
Wednesday, February 28: Eisenstein criterion (12.4).
Friday, March 2: Gauss primes (12.5).
Monday, March 5: Modules (14.1).
Wednesday, March 7: Free modules (14.2).
Friday, March 9: Diagonalizing integer matrices (14.4).
Monday, March 12: Generators and relations (14.5).
Wednesday, March 14: Finitely generated abelian groups (14.7).
Friday, March 16: Structure of linear transformations (14.8).
Math 100A/B/C is a rigorous three-quarter introduction to the methods and basic structures of higher algebra. 100B will focus on rings and fields.
Topics include: linear algebra over fields; rings; polynomial rings; ideals and quotients; unique factorization; quadratic number fields; linear algebra over rings.
UCSD also offers a two-quarter algebra sequence, Math 103A/B
(offered both fall/winter and winter/spring).
Between the two, Math 100 offers a greater emphasis on concepts and mathematical rigor, as well as some advanced topics not covered in Math 103 (e.g., Galois theory). Math 100 is recommended for students planning further study in pure mathematics, while Math 103 is recommended for most other students.
Students may not receive credit for both Math 100B and Math 103B. (Note that 100A is a valid prerequisite for 103B, but 103A is not a valid prerequisite for 100B.)
Instructor: Kiran Kedlaya,
kedlaya [at] ucsd [etcetera].
TA: Zonglin Jiang,
zojiang [at] ucsd [etcetera].
Lectures: MWF 12:00-12:50pm in Center 113. No lectures on the following university holidays: Monday, January 15 (Martin Luther King Day); Monday, February 19 (Presidents Day).
Sections: Tue 8:00-8:50am, 10:00-10:50am in APM 5402. (The 9:00am section has been cancelled and replaced with office hours; see below.)
Instructor (Kedlaya): Wed 3-5pm, APM 7202; I reserve the right to leave after 4:30 if no one is present or has warned me in advance that they plan to come late. Exceptions (including adjustments for the midterm and final) will be noted in the course announcements.
TA (Jiang): Tue 9-10am, APM 5402 (between the two sections); Tue 11am-12pm, APM 5748;
Thu 10am-12pm, APM 5748.
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 in the fall (which might make it easier to find a used copy). The material for 100B will be drawn primarily from chapters 3-4 and 11-14.
Math 100A or consent of instructor.
Any flavor of Math 100A is accepted, including
my fall 2017 lecture,
David Stapleton's fall 2017 lecture, or any previous year's edition. However, Math 103A is not accepted as a prerequisite.
Homework: Weekly assignments. In general, problem sets will be posted after Monday's lecture, to be due on Wednesday of the following week.
To receive credit, homework must be submitted in the dropbox in the basement of APM no later than 6pm on the due date. No extensions will be granted; see below for grading policies.
Midterm exam: in class on Wednesday, February 21.
No makeup exam will be given; see below for exam policies.
Final exam: Wednesday, March 21, 11:30am-2:30pm, in the lecture room (Center 113). No makeup exam will be given. See UCSD exam policies as well as course-specific policies below.
Grading: 30% homework, 30% midterm,
40% final exam; or 45% homework, 55% final exam (whichever is higher).
In both formulas, the lowest homework assignment will be dropped.
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-, while any score in the 70th percentile or higher is guaranteed at least a B-.
| 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 accomodation; 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, but the lowest homework assignment will be dropped.
This applies even if you add the course late (as of the first day of classes, there was no waitlist).
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).
All exams 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. 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 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 exams will be given. A missed 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 and midterm results (using the 30/30/40 option).
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 or exam affected by a violation.
If you suspect a violation, please bring it to the attention of the instructor and/or TA immediately.