MATH 321

Course Code & Number

MATH 321

Course Title

Abstract Algebra I

Level

BS

Credit Hours/ ECTS Credits

(3+1+0) 3 TEDU Credits, 7 ECTS Credits

Year of Study:

Junior

Semester:

Fall

Type of Course:

Compulsory

Mode of Delivery:

Face-to-face

Language of Instruction:

English

Pre-requisite / Co-requisite:

Catalog Description

Arithmetic in the integers. Congruence in the integers and modular arithmetic. Binary operations. Groups. Subgroups. Cyclic groups. Permutation groups. Isomorphisms and homomorphisms. Cosets. Normal subgroups. Quotient groups. Direct products. The classification of finite abelian groups.

Course Objectives

The main objective of this course is to provide a solid foundation in the fundamental structures of group theory, enabling students to construct a cohesive understanding of algebraic systems and equipping them with the mathematical rigor required to analyze the relationships, symmetries, and internal logical connections inherent in these structures. 

Course Learning Outcomes

Upon completion of this course, students will be able to: 

1. Solve algebraic problems by applying properties of integers, congruence relations, modular arithmetic, and binary operations, 
2. Investigate algebraic structures using the properties of groups, subgroups, cyclic groups, and permutation groups (including symmetric and alternating groups), as well as Cayley’s Theorem, 
3. Analyze group homomorphisms, isomorphisms, cosets, normal subgroups, and quotient groups using their structural properties, Lagrange’s Theorem, and the Isomorphism Theorems, 
4. Analyze the structure of groups through internal and external direct products, including the classification and decomposition of finite abelian groups in terms of their invariants, 
5. Construct rigorous mathematical proofs of algebraic statements and results in group theory.

Course Coordinator:

Dr. Fuat Erdem