2021-22 Spring Semester

Instructors:

 Mohan Bhupal (bhupal@metu.edu.tr)

Gülin Ercan (ercan@metu.edu.tr)

Ebru Solak (esolak@metu.edu.tr)

 

Course description:

Binary operations. Groups. The symmetric group. Subgroups. The order of an element. Cyclic groups. Rings. Integral domains. Subrings. Ideals. Fields: Q, R, C, Z_p. The concept of an isomorphism. The ring of integers and the ring of polynomials over a field: Division and Euclidean algorithms. GCD and LCM. Prime factorization. Quotient structures.

 

Objectives: This course aims to introduce students to algebraic concepts, such as groups, rings and fields. These concepts constitute an essential part of mathematical culture.

 

Office Hours: See the office hours section of the web page for the office hours of your instructors and also see ODTÜClass. Note that the times of office hours may change. The office hours will be conducted online over Zoom.

 

Textbook: Elements of Modern Algebra, J. Gilbert, L. Gilbert. Seventh edition. There are several copies available in the reserve section of library.

 

Supplementary Textbooks:

A first course in Abstract Algebra, John B. Fraleigh

 

Grading: First Midterm Exam: 30%

                Second Midterm Exam: 30%

                Final Exam: 40%

 

Exam Dates: First Midterm Exam: 17:40, 12 April 2022.

                      Second Midterm Exam: 17:40, 17 May 2022.

                      Final Exam: TBA.

 

Please follow the announcements on the page of the course in ODTÜClass.

One make-up exam will be offered after the final exam for those who have (for a valid reason) missed a previous exam. If you miss more than one exam, you may compensate for only one of them with a make-up exam.  If you get less than 15 (out of 100) in the Midterm exams, you will NOT be allowed to take the final exam and you will get NA. If you miss two exams you will get NA.

 

Tentative course outline:

Below is the tentative course plan. Keep in mind that this tentative course plan is subject to change depending on our progress each week.

 

Week 1: Divisibility, prime factors and GCD (Sec. 2.3, 2.4)

Week 2: Congruence of integers, binary operations (Sec. 2.5, 1.4)

Week 3: Binary operations, matrices, classes (Sec. 1.4, 1.6, 2.6)

Week 4: Groups (Sec. 3.1, 3.2)

Week 5: Subgroups, cyclic groups (Sec. 3.3, 3.4)

Week 6: Isomorphisms, homomorphisms (Sec. 3.5, 3.6)

Week 7: Permutation groups, cosets (Sec. 4.1, 4.4)

Week 8: Normal subgroups, quotient groups (Sec. 4.5, 4.6)

Week 9: Rings, subrings, integral domains (Sec. 5.1, 5.2)

Week 10: Fields, ideals (Sec. 5.2, 6.1)

Week 11: Quotient rings, homomorphisms (Sec. 6.1, 6.2)

Week 12: Real and complex numbers (Sec. 7.1, 7.2)

Week 13: Polynomials, divisibility, factorization in F[x] (Sec. 8.1,8.2, 8.3)

Week 14: Zeros of a polynomial (Sec. 8.4)