2022-23 Spring Semester (REVISED SYLLABUS)


 Ahmet Beyaz (beyaz at metu.edu.tr)

Gülin Ercan (ercan at metu.edu.tr)

Burak Kaya (burakk at metu.edu.tr)

Gökhan Benli (benli at metu.edu.tr) (Course Coordinator)


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  ODTÜClass for information about office hours. Note that the times of office hours may change.


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:  Online  Midterm Exam: 15 %

                In Class Final Exam:  85%


Exam Dates:   Online Midterm Exam:   Saturday , May 20, 13:00

                       In Class Final Exam:                     TBA


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

One inclass 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 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)