MATH 230C LEC A: ALGEBRA (45540)
Lecture: MWF 11:00-11:50 RH 440R
Lecturer: Michiel F Kosters
Email: mkosters@uci.edu
Phone: (949) 824-0971
Office Location: 410X Rowland Hall
Office Hours: MO 1-2 pm, 4-5 pm, WE 3-4 pm (please come, also outside of this hours)
Grader: Xiaowen Xhu
Schedule:
| Week | Monday | Tuesday | Wednesday | Thursday | Friday |
| April 2 | L: Exam 230B | L: Separable (13.5) | L: Primitive element, normal (13.4 14.4) | ||
| April 9 | L: Artin-Dedekind, def Galois ext. (14.1, 14.2) |
L: Main th. Galois theory (14.1, 14.2) HW: 230C_HW_1.pdf |
L: Galois theory of poly (14.2) | ||
| April 16 | L: Galois theory of poly 2 (discrimiant compu and 14.6) |
L: Finite fields, Galois groups over Q (14.3, 14.8) HW: 230C_HW_2.pdf |
L: Cyclic extensions (14.5) | ||
| April 23 |
L: L: C allg. closed, Equations and radicals (14.6, 14.7) |
L: Equations and radicals (14.7) |
L: Transcendence bases, inf. Galois theory (14.9) |
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| April 30 | L: Representation theory 1: 1.1, 1.2, 1.3, 1.4 |
L: Representation theory 2: 1.5, 2,1, 2.2, 2.3 HW: 230C_HW_4.pdf |
L: Representation theory 3: 2.4, 2.5, 3.2 | ||
| May 7 | L: Representation theory 4: 3.1, 5.1, 5.3, 5.7, 5.8 |
L: Solutions requested problems hw 1,2,3,4 (HW 1.1, 2.3, 2.9, 2.10, ...) |
L: Solutions requested problems hw 1,2,3,4 HW: 230C_HW_5.pdf |
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| May 14 |
Problem session 1: Gal 1,5,11,12,14 |
Problem session 2: Gal 15,16,19,20,22 | Problem session 3: Gal 24, 25,32,33,34 | ||
| May 21 |
Problem session 4: Gal 35, 36, 37 |
Problem session 5 Rep 4,6,7 |
L: Solutions of last hw, questions | ||
| May 28 | HOLIDAY |
L: No lecture, office hour FINAL RH440R, 4-6.30 pm, just about fields + representations; 8 problems, most questions will be similar to questions from 230_C_Galois.pdf and 230_C_Rep.pdf |
L: Discussion final | ||
| June 4 | L: Problem session 6: Fall 2016, 1,2,4,5,7,10 | L: Problem session 7: Spring 2016, 1,2,3,4,7,8 | L: Problem session 8: Fall 2015, 1,2,3,4,7,8,10 | ||
| June 11 | NO FINAL |
Book: The primary textbook will be Abstract Algebra, Third Edition, by D. Dummit and R. Foote - we will cover Chapter 14 (but in a different order). Errata. We might use some other sources, such as http://www.jmilne.org/math/CourseNotes/FT.pdf (Notes by Milne on field theory). For the part on representation theory, we will use Serre, Linear Representations of Finite Groups . We will cover sections
1.1, 1.2, 1.3, 1.4, 1.5
2.1, 2.2, 2.3, 2.4, 2.5
3.1, 3.2
5.1, 5.3, 5.7, 5.8
Grading policy: 20% homework, 20% participation second half (showing solutions to problems, being present, commenting on solutions), 60% 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.
Note:
Exercises Galois theory from sheet for HW: 2,3,4,6,7,8,9,10,13,17,18,21,23,26,27,28,29,30,31
Exercises representation theory from sheet for HW: 2,5,8,9,10,11,12,13,14
Course Summary:
| Date | Details | Due |
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