Math 103A (Driver, Winter 2009) Applied Modern Algebra
(http://math.ucsd.edu/~bdriver/103A_W09/index.htm)
The Final
Exam is on Friday, March 20 from 3:00 - 6:00 PM in
HSS
1128A..
This final is cumulative.
Please bring a blue book!
You may bring one 8 1/2 X 11 sheet (front and back) of notes if you wish.
Finals Week Office Hours:
Tu -- Friday at 11:00 AM -- 12:00 Noon.
Math103A-Lecture-Notes.pdf
(3/13/2009)
Instructor: Bruce
Driver (bdriver@math.ucsd.edu),
APM 7414, 534-2648. Office Hours: Monday at
5:00PM - 6:00PM? and Friday at 10AM.
TA: Joseph Reed (j2reed@math.ucsd.edu),
APM 5801, 534-9054 . Office Hours: Monday at
3:00PM.
Meeting times: MWF 4:00p - 4:50p in
HSS 1128A. DI A01 Tu 4:00p - 4:50p
WLH 2112. (There will be section on Tuesday January 6, 2009.)
Textbook: Contemporary Abstract
Algebra by Gallian, 6th Edition. We will cover approximately Chapters 0-11
in Math 103A.
Prerequisites: The prerequisite is Math 109. Concurrent enrollment in
Math 109 is usually not recommended; please come talk to me if you want to take
this course and have not yet passed Math 109.
Homework: Homework will be assigned
weekly; the list of problems for the week will be posted on the class website.
Homework will be due in Discussion on Tuesday. Late homework will not be accepted, but
the lowest homework score will be dropped.
Exams: There will be 2 in-class midterms on
Wednesday January 28 and Wednesday February 25. The final exam is on
Friday March 20 from 3pm-6pm.
No books, notes, or calculators are allowed during exams. The Final Exam will be
cumulative and roughly the length of two midterms.
Grading:
Final Grade = homework
(25%) + 2 midterms (20% each) + final (35%).
Description: This is a first class in abstract algebra. The main
topic will be the theory of groups. Compared to Math 100A, this course goes more
slowly, is somewhat less proof-oriented, and spends more time on applications of
the theory. For most variations of the math major which require a course in
algebra, 103A suffices. If you are considering graduate study in mathematics,
however, you should take Math 100A instead.
Academic honesty: I expect you to abide by the university's policies.
Serious cases of dishonesty may be reported to the appropriate university
committee. The most straightforward kind of cheating which is obviously
disallowed is copying from a neighbor's exam, or consulting notes or the book
during an exam.
The honesty rules for homework are sometimes less obvious. So there is no
confusion, here are my particular rules.
- The homework you hand in should be your own written work, and your own
only. It is not acceptable to copy word for word, or paraphrase, the work of
another student in the class, or a solution found (say) on the internet or
in a solutions manual, and hand it in as your own work.
- You may work with others in the class (I am all for this), but be
careful not to violate rule 1 above. Certainly you can freely discuss
definitions, examples in the text, etc. with others to help you understand
them. For the homework problems, it is best to start by thinking about the
problems yourself, hard. You may see how to do some of them, but be stuck on
others. Wait a while, you will probably have additional insights the next
day (this is one reason it is important to start the homework early). You
can ask us or a friend for hints. Hopefully after more thought you will see
how to solve the ones you were stuck on. If not, and here and there a friend
tells you how to do a problem you were completely stuck on, and then you
write it up yourself using only your own understanding, that's OK. But this
should only be a problem here or there, not a significant fraction of them,
or else you won't learn how to work through these problems independently.
- Just to clarify further, reading through a friend's entire solution to a
problem which you did not think about yourself and then immediately writing
your own solution is not allowed. You are likely to end up writing a
paraphrase of the other solution and not really understand the proof, and
you won't gain the benefit that comes from thinking long and hard about the
problems.
Tentative Topics List: The following outline of what we will cover
and the order is subject to change.
 |
Chap 0: Equivalence relations and modular arithmetic. Check
digit schemes. |
|
Chap 2: Definition of a group. Examples. |
|
Chap 2: More examples of groups. Basic properties of groups.
|
|
Chap 1: Symmetry groups and Dihedral groups. Review of
functions. 1 |
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Chap 3: Subgroups. Examples. |
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Chap 3: Centers and centralizers. |
|
EXAM I |
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Chap 4: Cyclic groups. |
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Chap 4: More on cyclic groups. Euler Phi function.
|
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Chap 5: Permutation groups and Sn. Cycle notation and order
of a permutation. |
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Chap 5: Decomposition into 2-cycles. The alternating group
An. |
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Chap 5: Some applications of permutation groups. |
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Chap 6: Isomorphisms. |
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Chap 7: Cosets and Lagrange's Theorem |
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Chap 7: Fermat's Little Theorem. Applications to primality
tests. |
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Chap 7: The Orbit-Stabilizer Theorem and applications. 11/7
Chap 8: Direct Products |
|
EXAM II |
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Chap 8: Decomposing Zn and U(n).
|
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Chap 9: Normal subgroups and factor groups |
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Chap 9: More on factor groups and applications. |
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Chap 10: Homomorphisms 1. |
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Chap 10: More on Homomorphisms. First Isomorphism Theorem. |
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Chap 11: Fundamental Theorem of Abelian Groups |
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Chapter 29: Burnside's Theorem and group actions.
|
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Chapter 29: Applications of Burnside's Theorem. |
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FINAL EXAM |
