MAT2203: Abstract Algebra

This course is a foundation course that introduces learners to the basic mathematical concepts. It covers the following topics: Theory of Groups; Permutation Groups; Normal Sub-groups and Homomorphisms; and Quotient Groups and Fundamental Theorems. 

Course Objectives
By the end of the course the student should be able to: 

• Analyze the basic principles of sets and binary operations including closure, commutative, associative, identity and inverse and apply such to characterize some algebraic structures as monoids, semi-groups and groups. 
• Define the following: a group, a subgroup, a mapping, an equivalence relation, order of a group and order of an element and apply such to characterize different types of groups including dihedral groups and permutation groups and prove various theorems involving group properties. 
• Construct direct product of two groups and give analysis of the result under group properties 
• State and prove the famous Lagrange’s theorem and apply it in analysis of various problems involving group divisors and index of a group. 
• Define a cyclic group, use it identify an Abelian group and prove various theorems involving properties of cyclic and Abelian. vi. State and prove various theorems involving conjugacy, centralizer, the center, normalizers, and normal subgroups.   
• State the properties of Isomorphism and homomorphism prove the homomorphism theorems and work with them in quotient groups.  
• State and prove the fundamental theorem of finite Abelian groups, and Sylow’s theorems 

Define simple and soluble groups and solve various problem.  
 
Expected Learning Outcome
This course unit is meant: 

• To discuss the basic competence in the concepts, principle, and procedures necessary to develop the learners’ habit of critical thinking and logical reasoning in pure Mathematics.              
• To encourage orderliness, speed and accuracy in the presentation of mathematics. 
• To help learners acquire the skills of expression in proper mathematical language and using mathematical symbols correctly. 
• To provide instruction that contributes to the learners’ abilities to think critically and solve real life problems, to reason mathematically and apply computational skills. 
• To build a strong foundation in calculus as preparation for subsequent courses in mathematics and other sciences. 
• Lay a foundation for postgraduate study in pure Mathematics.