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Modern Algebra II Fall 2006 |
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Modern Algebra II Fall 2006 |
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| Lecture: | MWF 10:10-11:00, TH 425 |
| Prerequisites: | MATH 335 (Modern Algebra) with grade C or better, or consent of the instructor |
| Instructor: | Dr. Matthias Beck | ||||
| Office: | Thornton Hall 933 | ||||
| Office hours: |
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& by appointment | |||
| Phone: | +1 415 405 3473 | ||||
| Email: |
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Algebra studies the structure of sets with operations, such as integers with addition and multiplication, or vector spaces with linear maps. The abstract point of view, based on an axiomatic approach, reveals many deep ideas behind seemingly innocent structures--such as the arithmetic of counting numbers--and serves as an elegant organizing tool for the vast universe of modern algebra. Generations of brilliant minds have crystallized these ideas in the concepts of groups, rings, fields, modules, and their quotient structures and homomorphisms--the topics of MATH 335 & 435. Our main goal in MATH 435 is the study group actions, rings, and modules, with applications in computational algebra through Gröbner bases.
Syllabus: Review of basic properties of groups and rings and their quotient structures and homomorphisms, group actions, Sylow's theorems, principal ideal domains, unique factorization, Euclidean domains, polynomial rings, cyclotomic polynomials, primitive roots, ideals in polynomial rings, finite fields, Berlekamp's algorithm, term orderings, Gröbner bases, Buchberger's algorithm. If time permits, we will also cover basic concepts of modules.
Text books:
(1) Niels Lauritzen, Concrete Abstract Algebra, Cambridge University Press, 2003.
(2) Robert B. Ash, Abstract Algebra: The Basic Graduate Year.
(3) Edwin H. Connell, Elements of Abstract and Linear Algebra.
We will cover Lauritzen's Sections 2.10, 3.5, 4.1-4.6, 4.8, 4.9, 5.1-5.9 and Ash's Chapter 4 (as far as we'll get...).
Grading system & exam dates:
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I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me.
Homework: I will assign homework problems as we go through the material. We can discuss the homework problems at any time during class. All homework assignments of a given week have to be handed in by the start of the Wednesday class of the following week. You may hand in some of your problems early to be able to correct your mistakes. Although you may (and should) work together with your class mates, the solutions you hand in have to be your own.
The way to learn math is through doing math. It is vital and expected that you attend every lecture. You will get a good feel for the math from there, but it is even more crucial that you do the homework. Working in groups is not only allowed but strongly recommended. The Blackboard system allows you to send emails to anybody in your class. Blackboard also features an online discussion board. Contact each other and work together.
Some more general fine print:
SFSU academic calender
Math typesetting programs
Academic Integrity and Plagiarism
CR/NCR grading
Incomplete grades
Late and retroactive withdrawals
Students with disabilities
Religious holidays
This syllabus is subject to change. All assignments, as well as other announcements on tests, policies, etc., are given in class. If you miss a class, it is your responsibility to find out what's going on. I will try to keep this course web page as updated as possible, however, the most recent information will always be given in class. Always ask lots of questions in class; my courses are interactive. You are always encouraged to see me in my office.
"If you don't like your analyst, see your local algebraist!"
Gert Almkvist (founder and director of The Institute for Algebraic Meditation)
