Math 100A  Abstract Algebra I (Fall 2017)
The course meets MWF 11:50 in Peterson 104.
For the course syllabus and policies, see the bottom of this page.
Here is a picture of my dodecahedronicosahedron model
(click here for a closer look):
Announcements (most recent first)

This concludes the announcements for Math 100A.
The web page for Math 100B is here.

Course grades have been submitted.
The passing score for the final exam is 41 (out of 90).
The final grade cutoffs are as follows:
Percentage 
92 
88 
85 
81 
77 
73 
67 
62 
55 
46 
Minimum grade 
A+ 
A 
A 
B+ 
B 
B 
C+ 
C 
C 
D 

I have posted sample questions and sample answers for the final exam.

In advance of the final exam, I'll be having extra office hours Friday, 46pm in the usual place (APM 7202). Zonglin will have extra office hours Saturday 10am12pm
in APM 7421 (not his office). Remember, you need your ID to enter APM over the weekend; please use the doors on the north side of the building, as the card reader on the south side is broken.

Some corrections have been made to HW 7; see the latest version online. Also, HW 8 has been posted.

Zonglin has rescheduled his office hours on Tuesday, November 21: they will now be held 12pm and 56pm.

Some corrections have been made to HW 6; see the latest version online. Also, HW 7 has been posted.

By popular demand, the due date for HW 6 has been pushed back to Wednesday, November 22 at 5pm (i.e., the usual weekly time). However, my office hours for that day are rescheduled to Monday, November 20, 46 pm.

The Putnam competition will be held Friday, December 2. Any UCSD student may participate (you do not have to be enrolled in Math 96). To sign up, contact Prof. Kane.

I have posted sample questions for the second midterm; see the homework section.

Due to the midterm on Wednesday, November 15, my office hours that day will instead be held Tuesday, November 14, 24pm. (As usual, I may leave anytime after 3:30 if there is no one present.)

For those planning ahead, the meeting time for Math 100B will be MWF 1212:50.

HW 5 is now posted.

HW 4 is now posted. Remember, no homework due October 25 due to the midterm on the 23rd.

I have posted sample questions for the first midterm; see the homework section.
Note: despite the fact that HW 3 included a question about normal subgroups,
they will not be on the midterm.

Zonglin has rescheduled his office hours from Thursday, October 19 to Friday, October 20, 10:00am12:00pm.

In advance of the first midterm on October 23,
I will have extra office hours on Friday, October 20, immediately after class (24pm; arrive by 3:30). In exchange, my office hours on Wednesday, October 25 are cancelled. (Similar adjustments will happen for the second midterm and the final.)

I have updated the grading policy to include minimum grade cutoffs (with no other changes). See below.

At this point, I am able to enroll all waitlisted and concurrent enrollment students. See the math front office if you need help with this process.

HW 3 is now posted. The syllabus for the first midterm will be the same as for HW 13 combined.
 HW 1 is now posted. In general, problem sets will be posted after Monday's lecture, to be due on Wednesday of the following week.
Homework assignments

HW 1, due Wednesday, October 4: pdf.

HW 2, due Wednesday, October 11: pdf.

HW 3, due Wednesday, October 18: pdf.

No homework due Wednesday, October 25 due to midterm 1
(see midterm sample questions
and sample answers).

HW 4, due Wednesday, November 1: pdf.

HW 5, due Wednesday, November 8: pdf.

No homework due Wednesday, November 15 due to midterm 2
(see midterm sample questions
and sample answers).

HW 6, due Wednesday, November 22: pdf.

HW 7, due Wednesday, November 29: pdf.

HW 8, due Wednesday, December 6: 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.

Friday, September 29: overview of the syllabus; laws of composition (2.1).

Monday, October 2: definition of groups, examples (2.2).

Wednesday, October 4: subgroups of the additive group of integers (2.3, up to 2.3.7).

Friday, October 6: cyclic groups (Artin 2.3.72.4.2).

Monday, October 9: Klein four group, quaternion group, permutations (2.4.3; 1.5).

Wednesday, October 11: isomorphisms (2.6); permutations (1.5).

Friday, October 13: homomorphisms (examples, kernel, image) (2.5); conjugation (2.6).

Monday, October 16: equivalence relations (2.7).

Wednesday, October 18: cosets, Lagrange's theorem (2.8).

Friday, October 20: normal subgroups (2.5, 2.8); quotient groups (2.12).

Monday, October 23: first midterm.

Wednesday, October 25: quotient groups (2.12).

Friday, October 27: correspondence theorem (2.10); more on quotient groups (2.12).

Monday, October 30: first isomorphism theorem (2.12); product groups (2.11);
more examples of quotient groups.

Wednesday, November 1: isometries of Euclidean spaces (6.2, 6.3).

Friday, November 3: dihedral groups; classification of finite groups of orthogonal matrices (6.4).

Monday, November 6: discrete groups of isometries; translation and point groups (6.5).

Wednesday, November 8: interaction between translation and point groups (6.5).

Friday, November 10: no lecture (holiday: Veterans Day).

Monday, November 13: plane crystallographic groups (6.6).

Wednesday, November 15: second midterm.

Friday, November 17: abstract symmetry groups (6.7).

Monday, November 20: the operation on cosets, counting formula (6.8, 6.9).

Wednesday, November 22: operations on subsets, finite subgroups of the rotation group (6.10, 6.12).

Friday, November 24: no lecture (holiday: Thanksgiving).

Monday, November 27: finite subgroups of the rotation group continued (6.12).

Wednesday, November 29: Cayley's theorem, the class equation (7.1, 7.2).

Friday, December 1: pgroups, class equation of the icosahedral group (7.3, 7.4).

Monday, December 4: comparison of the icosahedral group to A_5, simplicity of A_5 and of A_n for n >= 5,
statement of the first Sylow theorem (7.4, 7.5, 7.7).

Wednesday, December 6: statements of the Sylow theorems, some applications, proof of the first Sylow theorem (7.7).

Friday, December 8: Sylow subgroups of symmetric and matrix groups, application to classification of groups of order 12 (7.8).
Course syllabus
Math 100A/B/C is a rigorous threequarter introduction to the methods and basic structures of higher algebra. 100A will focus on group theory.
Topics include: groups, subgroups and factor (quotient) groups, homomorphisms, permutation groups, matrix groups, and some advanced topics as time permits (e.g., the Sylow theorems).
UCSD also offers a twoquarter 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 100A and Math 103A; however, 100A is a valid prerequisite for 103B. On the other hand, 103A is not a valid prerequisite for 100B without permission of the instructor.
I will be teaching the entire 100 sequence this year. This fall, there is also a second lecture of 100A available; both 100A lectures are equally valid prerequisites for 100B.
Instructor: Kiran Kedlaya,
kedlaya [at] ucsd [etcetera].
TA: Zonglin Jiang, zojiang [at] ucsd [etcetera].
Lectures: MWF 1:00p1:50p in Peterson 104. No lectures on the following university holidays: Friday, November 10 (Veterans Day); Friday, November 24 (day after Thanksgiving).
Sections: Tue 2:00p2:50p, 3:00p3:50p in APM 5402. Please attend your assigned section, or see the math front office to switch.
Office hours:

Instructor (Kedlaya): Wed 2:00p4:00p, APM 7202; I reserve the right to leave anytime after 3:30 if no one is present. Exceptions to be noted in the course announcements (see above).

TA (Jiang): Tue 4:00p6:00p and Thurs 9:00a11:00a, APM 5748.
Text:
Algebra by Michael Artin, second edition (required). The hardcover, softcover, and eBook versions of the text are all interchangeable. For 100A, only chapters 17 will be used; the same text will be used for 100B and 100C.
Prerequisites:
Math 31CH or Math 109 or consent of instructor.
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 5pm on the due date. No extensions will be granted; see below for grading policies.
Midterm exams: in class on Monday, October 23 and Wednesday, November 15.
No makeup exams will be given; see below for exam policies.
Final exam: Monday, December 11, 2017, 11:30am2:30pm, in the lecture room (Peterson 104). No makeup exam will be given. See UCSD exam policies as well as coursespecific policies below.
Grading: 30% homework; 20% first midterm; 20% second midterm;
30% final exam. The lowest homework assignment will be dropped.
The lowest midterm score will be replaced with the final exam score if this is to your benefit.
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:
Percentage 
97 
93 
90 
87 
83 
80 
77 
73 
70 
Minimum grade 
A+ 
A 
A 
B+ 
B 
B 
C+ 
C 
C 
Additionally, any score in at least the 90th percentile or higher is guaranteed an A grade, while any score in the 70th percentile or higher is guaranteed a B 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 scores, exam scores,
and final grades. (No other material will be posted there.)
Policies
No extensions will be given for homework assignments, but the lowest homework assignment will be dropped. This applies even to students who get in off the waitlist; such students should submit homework while still on the waitlist, which will be graded and returned on schedule. (Exception: students who transfer from the other 100A lecture will receive credit for homework submitted to that course.)
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 other source is a violation of academic integrity (see below).
All exams will be closedbook: 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;

assign seating before or during the exam;

make video recordings for the purposes of monitoring academic integrity.
Exam accommodations will be made only in cases mandated by university policies:

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.
All accommodation requests must be made with sufficient advance notice, preferably by the end of week 1. No accommodations are available for homework assignments.
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 (without the final exam substitution).
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.