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### MTH 475: Abstract Algebra

Term:     Winter 2017
Room:   130 MSC
Times:   TR 3:30-5:17;   Final Exam: April 20, 12:00-3:00PM

#### Description of the course for both MTH 475-476:

Groups, Sylow theorems, quotient groups, permutation groups, solvable and simple groups, fundamental theorem of Abelian groups.  Introduction to rings,  commutative rings, Euclidean domains, PID's, UFD's, polynomial rings, irreducibility criteria for polynomials. Module theory and linear algebra.  Theory of fields, field extensions, geometric constructions, Galois theory, solvability by radicals, computing Galois groups of polynomials.

#### Prerequisites:

Abstract Algebra is the study of problems from number theory, polynomial equations, combinatorics, linear algebra, etc  from a more abstract point of view. Having knowledge of all of these areas is a must in order to get started in abstract algebra.  Most of the examples that we will provide in class will be from the above areas. Therefore the following classes are necessary in order to understand the basic concepts of algebra.
Notice that MTH 302 is an introduction to proofs. You are expected to know how to write basic proofs in this course, to know quantifiers, and be able to read formally written mathematics.

#### Textbooks:

• Lecture notes will be provided in class.  There is no textbook required for the course. Some recommended books are provided below:

• Abstract Algebra, Dummit & Foote
• Topics in Algebra, I. N. Hernstein
• Abstract Algebra, T. Hungerford

#### Attendance is mandatory. If you miss class, I expect you bring a doctor's note r a police report the next time you come to class.

There will be a homework set every Tuesday  due the following Tuesday.
• Homework                    70 %  (There will be 12 homework sets)
• Final                              30 %
The grade will be computed as follows:

Grade= (T-35)/15,  where T is your total score.

#### Homework  (due dates)

Each homework set will have 4-5 problems. You can work in groups, but you should write the problems by yourself and be prepared to come and explain your solutions on the blackboard before the class.  You will be able to drop the lowest score from the homework.  There will be no make up homework and no late homework will be accepted under any circumstances
1. Jan. 10: Homework # 1
2. Jan. 17: Homework # 2
3. Jan. 24: Homework # 3
4. Jan. 31: Homework # 4
5. Feb. 7:   Homework # 5
6. Feb. 14: Homework # 6
7. Feb. 28: Homework # 7
8. Mar. 7:   Homework # 8
9. Mar. 14: Homework # 9
10. Mar. 21: Homework # 10
11. Mar. 28: Homework # 11
12. April 4:   Homework # 12
13. April 11: Homework # 13
We will have projects focused on
• Solving the Rubik's cube
• Symmetries of the soccer ball
• Symmetries of the Klein's quartic

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