Syllabus Application
Algebra I
MATH 511
Faculty:
Faculty of Engineering and Natural Sciences
Semester:
Fall 2025-2026
Course:
Algebra I - MATH 511
Classroom:
FENS-L058,FENS-L065
Level of course:
Masters
Course Credits:
SU Credit:3.000, ECTS:10
Prerequisites:
-
Corequisites:
-
Course Type:
Lecture
Instructor(s) Information
Mohammad Sadek
- Email: mmsadek@sabanciuniv.edu
Course Information
Catalog Course Description
Introduction to group theory. Isomorphism theorems. Permutation groups and Cayley's theorem. Conjugacy classes. Lagrange's theorem and the Sylow theorems. principle ideal domains. Polynomial ring.
Course Learning Outcomes:
| 1. | Define and use Subgroups, Ideals, Homomorphisms and other basic concepts about Groups and Rings, |
|---|---|
| 2. | Analyze and produce proofs of statements involving Groups and Rings, |
| 3. | Use some fundamental examples such as the Symmetric Group and its Subgroups, Cyclic Groups, Matrix Groups, and Polynomial Rings, |
| 4. | Distinguish basic Algebraic structures from each other up to Isomorphism, |
| 5. | Use the three Isomorphism theorems for Groups and Rings, |
| 6. | Use Direct and Semi-direct Product Constructions, |
| 7. | Use Group Actions to study structures of Groups and to do effective counting in Groups, |
| 8. | Apply Sylow Theorem and the Structure Theorem on Finitely Generated Abelian Groups, |
| 9. | State basic Ring types such as Local Rings, Principal Ideal Domains, Unique Factorization Domains. |
Course Objective
-
Course Materials
Resources:
-
Technology Requirements:
-