MT2002 Algebra 2007-8

Edmund F Robertson

• Contents
• About the course
• Introduction
• Groups - definition and basic properties
• Modular arithmetic
• Permutations
• Symmetries
• Order of an element
• Subgroups
• Cyclic groups
• Alternating groups
• Cosets and Lagrange's Theorem
• Homomorphisms of groups
• Isomorphisms
• Normal subgroups
• Quotient groups
• The first isomorphism theorem
• Rings: definition and basic properties
• Examples of rings
• Special types of rings
• Subrings, ideals and quotients
• Homomorphisms, isomorphisms and the first isomorphism theorem for rings
• Conclusion
• About this document ...