Math 367, 2012-2013 - Spring
Mathematics Department, Middle East Technical University, Ankara, Turkey
Instructor: Semra Öztürk Kaptanoğlu,
Office Hours: Thursday :13:00—15:30 (M 138)
Teaching Assistants :
Primarily: Onur Fen, Secondarily: S. Süleyman Kağan SAMURKAŞ
Office Hours will be announced.
Lectures : Monday: 8:40—10:30, Wednesday: 10:40—12:30
Recitation: Friday :11:40—13:30
All the lectures and recitations will be in Arf Lecture Hall. ( M-13 )
Text book: "Contemporary Abstract Algebra" by J. A. Gallian, D. C. Heath and
Company, 1994.
Supplementary book: Undergaraduate Algebra Problems and Solutions by
Mahmut Kuzucuoğlu,
Goals: The goal of the course is to introduce the fundamental concepts of
abstract algebra and thus to exhibit a typical model of mathematics as much as
possible.
Prerequisite: Math 116
Catalog Content: Groups, Lagrange's theorem. Factor groups,
homomorphisms. Isomorphism theorems, direct products. Groups acting on sets,
Cayley's theorem, Class equation. Statements of Sylow theorems and the
fundamental theorem on finite abelian groups. Rings, quotient rings,
homomorphisms, Isomorphisms theorems. Prime and maximal ideals. Integral
domains, field of fractions. Euclidean domains, PIDs, UFDs. Polynomials,
polynomials in several variables. Field extensions, algebraic and transcendental
elements. Finite extensions, algebraically closed fields. Impossibility of certain
geometric constructions. Finite fields.
If you miss any midterm exam you will not be allowed to take the final exam,
and also the “bütünleme sınavı”.
BE AWARE THAT : There are many examples of students failing the course who
are taking it to increase their grade. This assumption can be very wrong.
Grading will be based on exam grades, homeworks.
There will be three exams during the semester and a final exam, approximately one
each month.
Homeworks will be assigned regularly and at least one question of the exams will be
based on homework problems. Grading policy for the homeworks will be decided
later.
There will be suggested execises from the text book.
You should work on these
THIS IS CRUTIAL!!
before going to the recitation hours.
You are strongly advised to read the following as soon as possible.
Advice on studying by Peter J. Cameron and also
Reading and Writing in the Mathematics Classroom by Mark Freitag
Course outline:
(1 Week) Groups, subgroups, cosets, Lagrange's theorem.
(1 Week) Normal subgroups, Factor groups, homomorphisms.
(1 Week) Isomorphism, isomorphism theorems, direct products.
(1 Week) Groups acting on sets, Cayley's theorem, Class equation.
(1 Week) Statements of Sylow theorems and the fundamental theorem on finite
abelian groups.
(1 Week) Rings, ideals, quotient rings, homomorphisms.
(1 Week) Isomorphisms, isomorphism theorems, prime and maximal ideals.
(1 Week) Integral domains, field of fractions.
(1 Week) Euclidean domains, PIDs, UFDs.
(1 Week) Polynomials, polynomials in several variables.
(1 Week) Field extensions, algebraic and transcendental elements.
(1 Week) Finite extensions, algebraically closed fields.
(1 Week) Impossibility of certain geometric constructions.
(1 Week) Finite fields.