Welcome to Abstract Algebra
F20O5..(3)..MAS4301 4864 MWF7..LIT.205
Prof. Jonathan King squash@math.ufl.edu
Dept. of Mathematics http://www.math.ufl.edu/~squash/
402 Little Hall (Top floor, NE corner) 392-0281 x270
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The theory of Groups arose from the idea of composing "actions". (E.g, on a
Rubic's Cube, the turning of one face by a quarter-turn.)
The notions of Groups, Rings, and Fields are omnipresent in branches of
mathematics, and bring together what superficially appear to be different
ideas in disparate realms of mathematics.
Examples: In the 15-puzzle (the little plastic squares that slide in a 4x4
frame), how many of the patterns are obtainable without prying the pieces
out and putting them back in? How can one quickly tell whether a pattern
is legal?
What peg-jump patterns reduce to a single peg?
How big is the group of spins of a basketball? --is every composition of
simple-spins simply another simple-spin? What is the "dimension" of the
group?
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Our textbook is
Contemporary Abstract Algebra 6-th edition (sixth edition),
by Joseph A. Gallian, [Houghton Mifflin Publishing, ISBN:0618514716]
which is in the UF bookstore, and perhaps some other local bookstores. As
the semester progresses, you will also need to print-out a few pages of
handouts that I have prepared for you,
We will cover some material that is not in our text; in particular,
applications of group-theory for solving certain games and puzzles.
REQUIREMENT: You will need to be able to print out POSTSCRIPT (.ps) files,
and PDF files. Please install (free) postscript-printing software ASAP.
We will cover all of chapters 1-11, plus an in-depth introduction to
fields, to finite fields, and a sampling of Ring theory. well as some
additional topics on games that I have prepared. Along the way, we'll
introduce complex numbers, and the notion of a field being "algebraically
closed".
Teaching Page: http://www.math.ufl.edu/~squash/teaching.html
Course Page: http://www.math.ufl.edu/~squash/course.linalg.html
There will be three exams, Z, Y and X. Exam Z will have a take-home part
(Z-home) and an in-class part (Z-class). For the take-home you will work
in TEAMS of (usually) 3 students. The take-home must be carefully typed
and proofread. You will have about 1 week for the take-home part.
Each student needs to be in Gainesville during all the week of the exam,
as you are responsible to your teammates.
Take-home exams are open notes/library and you may use calculators
or computers.
Each student takes the in-class part individually; his score on Z is that
of Z-home plus Z-class. Exams Y and X run similarly, but X (the last
exam) will have no in-class component. X-home will be due around the last
week of class.
There will be NO final exam. The in-class exams are open-brain, closed
book/notes/calculators. Dates of exams are to be determined.
There will also be a small number of "miniscores"; quizzes, graded-hw,
in-class presentations...
HOMEWORK: For Friday, 26Aug2005: Please read all of Chapter 0.
Please hand in: P.23: 1-4, 5(Florida DL), 14.
For Monday, 29Aug: Read chapter 1 through P.53.
Please hand in: P.23: 18,19. P.53: 1,2,3,5.
We will have an "How to use the Mailing List & Archive",
in the Little Hall Atrium (3rd floor, center) from
==== 5:10-5:40PM on 24Aug2005. ================