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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.
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