Syllabus Application
MATH 511
Algebra I
Faculty
Faculty of Engineering and Natural Sciences
Semester
Fall 2025-2026
Course
MATH 511 -
Algebra I
Time/Place
Time
Week Day
Place
Date
08:40-10:30
Wed
FENS-L065
Sep 29, 2025-Jan 3, 2026
08:40-09:30
Thu
FENS-L058
Sep 29, 2025-Jan 3, 2026
Level of course
Masters
Course Credits
SU Credit:3, ECTS:10
Prerequisites
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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
This is the first part of the two-semester basic algebra course for graduate students. The aim is to strengthen students' familiarity with basic algebraic structures which are commonly used in all parts of mathematics. These structures include groups, rings, vector spaces, modules and fields.
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