## Math 103: Applied Algebra, Fall 2009

under construction!

Office hours:MW1:30-2:20 and by appt (just talk to me after class, or call or email)

Office: APM 5256, tel. (858) 534-2734

Teaching assistant: Jaime Lust, APM 6341 email: jlust@math.ucsd.edu office hours: W 4-5pm, F 9-10am

Computation of grade: The grade is computed from your scores in the final (40%), two midterms (20% each) and homework (20%).

Dates of exams:

Midterms: Wednesday, October 28 and Friday, November 20

Final: Friday, December 11, 8am-11am

### Texts

• Joseph Gallian, Contemporary abstract algebra, seventh edition.

Tentative Syllabus We will primarily study groups in this quarter, roughly chapters 0-10 of the text book. A rough outline will be given below.

Week 1: Chap. 0, 2 examples of groups
Week 2: Chap. 1
Week 3: Chap. 3
Week 4: Chap. 4, 5
Week 5: Chap. 5
Week 6: Chap. 6, 7
Week 7: Chap. 7, 8
Week 8: Chap. 9, 10
Week 9:
Week 10:

Homework assignments

Homeworks need to be turned in on or before the stated date, usually a Friday. No homework needs to be turned in in weeks when a midterm is scheduled. However, some of the homework may also be part of the material being asked for the midterm. It is very important that you do the homework problems as most of the exam problems will be variations of homework problems.

Disclaimer: I will try to get the homework assignment on the net in time. Due to time and other limitations, this may not always be possible. The fact that there is no assignment posted for a particular date does therefore NOT necessarily mean that no homework is due.

for Oct 2: (preliminary, i.e. more problems will be added later): Chapter 0: #8, 10, 12, 16(only in 5th edition): Use Euclidean algorithm to calculate gcd(34, 126) and express it as a linear combination of 34 and 126; 18/20 (first number: fifth edition, second number: seventh edition), 19/21, 24/28, 32/36, 34/38, 48/54, 50/55

for Oct 9: Chapter 1: #4, 6, 8, 10. Chapter 2: #6, 11, 12, 14, 16, 20, 22, 24, 28, 33/35 (5th/7th edition; if there is no "/", it is the same number for both editions) Note: You may assume without proof in #11 that multiplication of matrices is associative.

for Oct 16:# Chapter 3: #2, 8/10, 10/12, 14/18, 16/20, 19/25, 22/28, 34/42, 36/44, 44/52, 51/59a,b, Chapter 4: #4, 8, 12, 18

Extra problems for practice (do not hand in): Chapter 3: #1, 7, 15, 23, 25, 33, 35, 39, 43 Chapter 4: #1, 3, 5, 9, 17

for Oct 23: Chapter 4: #14, 16, 22, 40, 46/45, 54, 56 Chapter 5: #4, 6, 8, 12, 18, 24, 28, 36, 46/48 (as usual, if there is a backslash, the numbers refer to 5th edition/7th edition)

Extra problems for practice (do not hand in): Chapter 4: #15, 19, 31, 47, 59 Chapter 5: #5, 7, 9, 11, 15, 37, 41

Midterm I: Material goes over chapters 0 until 5. You are allowed to use one hand-written cheat sheet, but no calculators or books. As to preparation, look at similar problems as homework problems (there are lots of them in the book). Make sure you understand the basic concepts.

for November 6 Chapter 6: #4, 10, 18, 20, 22/24, 24/26, 25/27 Chapter 7: #2, 6, 8, 10, 16, 20, 22/24, 24/26, 26/28

Extra problems for practice (do not hand in): Chapter 6: #1, 3, 5, 7, 19 Chapter 7: #3, 5, 7, 9, 15, 17, 19, 23/25, 25/27, 27/29

for November 13: Chapter 7: #30/34, 31/35, 42/46. Chapter 8: 4, 8/6, 10/8, 12/10, 26/28, 28/30

for November 20 (need not be turned in, but could be relevant for midterm; we will get the notion of "factor group" on Monday): Chapter 9: 4, 8, 10, 12, 16/18, 36/38, 66/74 additional: Chapter 9: 14, 22/24

IMPORTANT The midterm is moved to Monday, November 23. Material will go until the last homework assignment, with special emphasis on the material after the first midterm, Chapters 6-9. You need not worry about material we have not (yet) covered, such as e.g. inner direct sums.

for December 4 Chapter 10: #2, 10, 14, 20, 24/26, 32/34(hint: Use that U(40) is isomorphic to U(5) x U(8), see Theorem 8.3 - I'll say more about it in class on Wednesday), 50/52,

Here are solutions for the second midterm. Please study those problems again carefully on which you did not do well in the midterm. If some points are not clear to you, please ask the TA or me.

Final The final will be cumulative, with an emphasis on what we did in the second half (isomorphisms, homomorphisms, direct products, normal groups, factor groups, Lagrange Theorem). You are allowed to use a hand-written cheat sheet, normal size, can be written on both pages. No books or calculators.

Office hours in finals week:

Jaime: M12-1, Th 10-12(in calc lab)

my office hours: WTh 4-5. I will be around also on Tuesday afternoon from about 1:30 until 3pm. But email/call me before if you want to come, as I may not always be in my office.