Math 522: Algebra II

Fall 2016


Instructor: Prof. Dr. Kazım İlhan İkeda
Classroom: B0522 (Engineering Building)
Book: Abstract Algebra, Dummit and Foote, John Wiley & Sons, Inc., 3rd Edition

Week Topic Lecturer* Day Note
1

7.1. (Ring Theory:) Basic Definitions and Examples (pg. 223)

7.2. Examples: Polynomial Rings, Matrix Rings, and Group Rings (pg. 233)

Sevan Kazazyan September 19, 2016
2

7.3. Ring Homomorphisms an Quotient Rings (pg. 239)

7.4. Properties of Ideals (pg. 251)

Sevan Kazazyan September 26, 2016
3

7.5. Rings of Fractions (pg. 260)

7.6. The Chinese Remainder Theorem (pg. 265)

Serdar Nair October 3, 2016
4

8.1. Euclidean Domains (pg. 270)

8.2. Principal Ideal Domains (P.I.D.'s) (pg. 279)

Serdar Nair October 10, 2016
5

8.3. Unique Factorization Domains (U.F.D.'s) (pg. 283)

9.1. (Polynomial Rings:) Definitions and Basic Properties (pg. 295)

Başak Hanedar October 17, 2016
6

9.2. Polynomial Rings over Fields I (pg. 299)

9.3. Polynomial Rings that are Unique Factorization Domains (pg. 303)

Başak Hanedar October 24, 2016
7

9.4 Irreducibility Criteria (pg. 307)

9.5 Polynomial Rings over Fields II (pg. 313)

Faruk Badak October 31, 2016
8

9.6 Polynomials in Several Variables over a Field and Gröbner Bases (pg. 315)

13.1. (Field Theory:) Basic Theory of Field Extensions (pg. 510)

Faruk Badak November 7, 2016
9

13.2. Algebraic Extensions (pg. 520)

13.3. Classical Straightedge and Compass Constructions (pg. 531)

Barış Akalın November 21, 2016
10

13.4. Splitting Fields and Algebraic Closures (pg. 536)

13.5. Separable and Inseparable Extensions (pg. 545)

Barış Akalın November 28, 2016
11

13.6. Cyclotomic Polynomials and Extensions (pg. 552)

14.1. (Galois Theory:) Basic Definitions (pg. 558)

Devrim Çatak December 5, 2016
12

14.2. The Fundamental Theorem of Galois Theory (pg. 567)

14.3. Finite Fields (pg. 585)

Devrim Çatak December 12, 2016
13

14.4. Composite Extensions and Simple Extensions (pg. 591)

14.5. Cyclotomic Extensions and Abelian Extensions over \(\mathbb{Q}\) (pg. 596)

Ahmet Coşar December 19, 2016
14

14.6. Galois Groups of Polynomials (pg. 606)

14.7. Solvable and Radical Extensions: Insolvability of the Quintic (pg. 625)

Ahmet Coşar December 26, 2016
15

14.8. Computation of Galois Groups over \(\mathbb{Q}\) (pg. 640)

14.9. Transcendental Extensions, Inseparable Extensions, Infinite Galois Groups (pg. 645)

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*: The following presenter must be ready due to the possible absence of the actual presenter.

Important Dates
September 5-9, 2016 Course Registration
September 26-28, 2016 Course Add/Drop
October 18, 2016 Withdraw from the Course
October 28, 2016 Half day (Republic's Day)
November 14-18, 2016 Publicity Week (Holiday)
January 6, 2017 Last Day of the Course
January 12, 2017 Last Day for Entering Grades