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Modern Algebra Spring 2006 |
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Modern Algebra Spring 2006 |
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| Lecture: | MWF 9:10-10:00, HSS 213 |
| Prerequisites: | MATH 301 (Exploration & Proof) and MATH 325 (Linear Algebra) with a grade of 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 ideas in the concept of groups, rings, fields, modules, and their quotient structures and homomorphisms--the topics of MATH 335 & 435. Our main goal in MATH 335 is the study of groups and rings. We will not strive for the maximal possible generality but rather work out as many concrete examples/incarnations of theoretical concepts as possible. Another goal of this course is to make the students immerse in communicating mathematical thoughts (proofs, examples, counterexamples) in a written form.
We will cover groups for about 2/3 of the semester (definition and basic properties, examples, symmetric groups, subgroups, cyclic groups, homomorphisms, isomorphisms, normal subgroups, left and right cosets, Lagrange's theorem, factor/quotient groups, isomorphism theorems, fundamental theorem of finitely generated abelian groups) and rings for about 1/3 of the semester (definition of rings, unit, zero-divisor, division ring, integral domain, and field, basic properties, examples, ring homomophisms and isomorphisms, subrings, images and kernels, definition of ideals and quotient rings, one- and two-sided ideals, isomorphism theorems, properties of ideals, PIDs, greatest common divisor, UFDs, division algorithm, irreducibility of polynomials).
Text book:
Joseph A. Gallian, Contemporary Abstract Algebra, Houghton Mifflin
We will cover most of Chapters 1-16.
Gallian's website has some some additional recourses, e.g., true-or-false quizlets.
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.
Quizzes: I will frequently check your progress through unannounced quizzes given at the beginning of class. A quiz will typically test your concept of a certain definition or statement. There will be no make-up quizzes. At the end of the semester, I will drop the lowest of your quiz grades.
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
Tutoring
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)
