Unit Code: MTH814

Unit Name: General Lattice Theory

Description: This course is designed to prepare students for an important foundation of advanced mathematics. This course includes: Two definitions of Lattices, How to Describe Lattices, polynomials Identities and Inequalities, Free Lattices and Special Elements, Distributive Lattices, Boolean Algebras, Topological Representation, Pseudo Complementation, Weak Projectivity and Congruences, Distributive, Standard, and Neutral Elements, Structure Theorems, Modular Lattices, Semimodular Lattices, Complemented Modular Lattices, Characterizations of Equational Classes, The Lattice of Equational Classes of Lattices, Free products of Lattices, The structure of Free Lattices, Reduced Free Products and Hopfain Lattices.

Learning Target Outcomes: As a result of successfully completing this course, the student will be able to: 1. Distinguish between the two definitions of Lattices. 2. Demonstrate accurate and efficient use of lattice techniques; 3. Develop capacity for mathematical reasoning through analyzing, proving and explaining concepts from lattice. 4. Apply lattice theory techniques to solve diverse situations in mathematics, engineering and other sciences. 5. Explain the concepts of Distributive Lattices and Free products of Lattices and Hopfain Lattices.. 6. Explain the concepts of Congruences and Ideals, Modular and Semimodular Lattices.

Prerequisite: Minimum Entry Requirements of the programme

Prerequisite Sentence: N/A

Credit Point: 30

Offered In: Semester 1,2