Course Code : PMAT 31312
Title : Abstract Algebra
Pre-requisites : PMAT 21263
Learning Outcomes:
At the end of this course, the student should be able to
- demonstrate factual knowledge including mathematical notation and terminology used in this course
- analyze and use basic definitions in Abstract algebra including binary operations, groups, subgroups, homomorphism, rings and ideals
- examine the fundamental principles including the laws and theorems arising from the concepts covered in this course
- develop and apply the fundamental properties of abstract algebraic structures, the substructures, their quotient structures and their mappings
- build experience and confidence in proving theorems about the structure size and nature of groups, subgroups, rings, subrings ideals and the associated mappings
- apply course materials along with techniques and procedures covered in this course to solve problems
- develop specific skills, competencies and thought processes sufficient to support further studies or work in this or related fields.
Course Contents:
Binary Operations: Definition and properties
Groups: Definition and Examples, Basic properties, Subgroups, Cyclic Groups, Abelian Groups, Finite & Infinite Groups, order of a group, order of an element
Normal subgroups: Definition and examples, Quotient groups, Cosets, Lagrange theorem
Group isomorphism: Definition of Group Homomorphism, Kernel of a homomorphism, Image of a homomorphism, Group Isomorphism
Rings: Definition and examples, Basic properties, Subrings, Characteristic of a ring, Ideals, Integral domains; Fields.
Method of Teaching and Learning: A combination of lectures and tutorial discussions.
Assessment: Based on tutorials, tests and end of course examination.
Recommended Reading:
1. Fraleigh, J.B. (8th Ed., 2020). First Course in Abstract Algebra, Pearson.
2. Dummit, D.S. & Foote, R.M. (3rd Ed., 2011). Abstract Algebra, Wiley.
3. Pinter, C.C. (2nd Ed., 2010). A Book of Abstract Algebra, Dover.