MATH 230B LEC A: ALGEBRA (45580)
Lecture: MWF 11:00-11:50 RH306
Lecturer: Michiel F Kosters
Email: mkosters@uci.edu
Phone: (949) 824-0971
Office Location: 410X Rowland Hall
Office Hours: ?
Grader: Xiaowen Zhu
Email: xiaowz5@uci.edu
Office Location: 420 Rowland Hall
Schedule:
| Week | Monday | Tuesday | Wednesday | Thursday | Friday |
| Jan 8 | L: (7.1, 7.2, 7.3), 7.4 | L: 7.4, 7.5 | L: 7.6, 8.1 | ||
| Jan 15 | HOLIDAY | L: 8.1, 8.2 Homework: 7.3: 33* (challenge: find short proof, assume 1 in R), 34 7.4: 11, 23, 37 7.5: 2 (0 not in D), 6 7.6: 1, 5, 7 |
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L: 8.3 | |
| Jan 22 | L: 8.3, 9.1, 9.2 |
L: 9.3, 9.4 |
L: 9.4, 9.5 | ||
| Jan 29 | L: 10.1 |
L: 10.2 No 4-5 pm office hour |
L: 10.3 | ||
| Feb 5 | L: Office hour (in lecture hall) (NO OFFICE HOUR in afternoon) |
L: Go practice (office hour) Midterm, 4-6 pm, SH 174, Material: up to and including 10.3; exam will be 8 questions similar to a qual. |
L: talk about midterm, 10.5 (only exact sequences, up to page 385) | ||
| Feb 12 | L: 10.4 (see Chapter 4 of Link) |
L: 10.4 |
L: 12.1 | ||
| Feb 19 | HOLIDAY |
L: 12.1, 12.2 |
L: 12.3 | ||
| Feb 26 | L: 13.1 | L: 13.2 Homework: Homework_6.pdf |
L: 13.4 | ||
| March 5 | L: 13.5 | L: 13.6, in NS2 4201 | L: REVIEW Homework: Homework_7.pdf |
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| March 12 |
L: (linear) Math230b_Linear_Algebra_Exam_Problems.pdf 6, 9, 11 |
L: (linear) 4, 17, 20, (fields) 6, 7, 10 |
L: (linear) 19 (fields) 8, 13, 16, 17 |
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| March 19 |
EXAM 8:00-10:00am |
Website 230A, we start at page 246
Book: The primary textbook will be Abstract Algebra, Third Edition, by D. Dummit and R. Foote. Errata. We might use some other sources.
Grading policy: 20% homework, 25% midterm, 55% final.
Homework: You are encouraged to work together, but you should write down the solutions yourself. Also, acknowledge any sources, except Dummit and Foote. Write down names of collaborators.
Midterm: We will try to have a 2 hour midterm if possible.
* Short proof of 33a:
If $f=\sum_{i} a_i x^i$ such that $a_0 \in R^*$ and $a_i$ nilpotent for $i>0$, then $f$ is invertible with inverse $1/f=1/a_0 \sum_{i=0}^{\infty} (a_0-f)^i$, which is a polynomial since $a_0-f$ is nilpotent.
Conversely, if $f \in R[X]$ is a unit, then for any prime ideal $P \subset R$ the element $f \pmod{P}$ is a unit, that is, $f \mod{P}$ is a constant. Hence the constant term of $f$ does not lie in any prime ideal, that is, it is a unit, and the other terms lie in all prime ideals, and hence are nilpotent.
Course Summary:
| Date | Details | Due |
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