MATH 100A - Abstract Algebra

Fall 2012

Instructor: Professor Mark Gross; AP&M 7444; phone 534-2652; email: mgross@math.ucsd.edu

Office hours: 1-2, Mondays, 2-3, Wednesdays and Fridays.

Teaching Assistant: Michael Kasa; AP&M 6452; e-mail mkasa@math.ucsd.edu

Office hours: 2-3 pm Monday, 10 am -12 Thursday, 11 am -12 Friday.

Special announcement: Michael Kasa will hold special office hours 10-12 Wednesday and Thursday during exam week in place of the regularly scheduled office hours.

Time and place: Lectures are MWF 10:00-10:50 WLH 2111

Sections are Thursday 8:00 - 8:50 and 9:00-9:50 am in APM B412

Final exam is Friday, December 14, 8:00a - 11:00a.

Text: "Abstract Algebra" by John Beachy and William Blair, Third Edition

Syllabus: Math 100A is the first quarter of a rigorous introduction to abstract algebra. While the long-term goal, to be achieved in the third quarter, is to understand Galois theory, the topic covered in this quarter will be group theory. We will cover chapters 1, 2, 3 and as much of 7 as time permits.

Important: Should you take this course? Math 100ABC is a rigorous introduction to abstract algebra in which concepts and proofs are emphasized more than techniques. Math majors may choose to take either Math 100ABC or Math 104AB (Modern Algebra), which is less theoretical. However, students who are contemplating graduate study in mathematics are advised to take Math100 rather than Math 104. The prerequisite for this course is either Math 31CH or 109, and I strongly recommend that students who got less than a B+ in 109 take 104 instead.

Homework, grading, etc. There will be weekly problem sets, which will be graded and returned. You are encouraged to work on these problem sets with a small group of other students in the class, but every student should write up his or her own solutions. The in class exams will consist of one quiz (50 minutes), one midterm (50 minutes) and a final. Your grade will be based on the following:

Problem sets 25%
Quiz 10% (Monday, October 22)
Midterm 20% (Friday, November 9)
Final 45%

Class notes, first installment. Class notes, second installment.

Problem set #1 Due in class on 10/8. Beachy and Blair, Section 1.1, 3, 12, 14, 16, Section 1.2, 1, 8, 10, 11, 16, 17.

Problem set #2 Due in class on 10/15. Beachy and Blair, Section 1.3, 4, 12, 14, 18, Section 1.4, 5, 8, Section 2.1, 9, Section 2.2, 5, 10.

Problem set #3 Due in class on 10/22. Beachy and Blair, Section 3.1, 2, (b), (d), (f), 9, 10, 23, Section 3.2, 8, 11, 15, 17, Section 3.3, 2, 6, 8.

The quiz on 10/22 will cover the material of the first three homeworks.

Problem set #4 Due in class on 10/29. Beachy and Blair, Section 3.3, 9, 11, Section 3.7, 3, 4, 7 (b), (d), (f), Section 3.4, 2, 4, 6, 16.

Quiz solutions.

Problem set #5 Due in class on 11/5. Beachy and Blair, Section 3.4, 21, Section 3.5, 3, 11, 12, 20, Section 2.3, 3, 4, (b), (d), 11.

Note: For more on the Futurama theorem, there is a relevant Youtube clip . Furthermore, Ron Evans will be giving a talk on the subject on Tuesday, 11/27: see Student Colloquium

The midterm will cover material up to and including the material on Problem Set 5.

Problem set #6 Due in class on 11/19. Beachy and Blair, Section 3.6, 4, 5, 6, 10, 11, Section 3.7, 15, Section 3.8, 2, 4, 6, 13.

Exam solutions.

Problem set #7 Due in class on 12/3. Beachy and Blair, Section 3.8, 18, 20, 21, 23, 28, Section 7.1, 4, 9, 12, 13, Section 7.2, 1, 2, 4, 9.

Extra Problems These are not to be handed in, but I strongly recommend working on these before the final exam! Beachy and Blair, Section 7.2, 11, 13, 15, Section 7.3, 1, 2, 5, 7.

Practice exams You can find plenty of practice exams on websites for previous incarnations of this class: see Ron Evan's Fall 2011 Math 100A, Mia Minnes' Fall 2010 Math 100A.