The course splits into two distinct but related parts: group theory and ring theory. In the first part we introduce the idea of a group, i.e., a set with one binary operation (usually written as multiplication) defined on it and satisfying certain axioms. After giving the basics of group theory we study some deep results on finite groups, culminating in the Sylow theorems. In the second part we introduce the idea of a ring, i.e., a set with two binary operations (addition and multiplication) defined on it, satisfying most of the well-known axioms of arithmetic. Here our main focus is on integral domains, and the factorization of their elements into primes.
A knowledge of group theory and ring theory is important for an understanding of many areas of mathematics including: advanced number theory; cryptography; coding theory; differential, finite and algebraic geometry; algebraic topology; representation theory and harmonic analysis including Fourier series. It is also has many practical applications including to the structure of molecules, crystallography and elementary particle physics. In fact anywhere you have symmetry you will find groups and also often rings.
Pre-requisites
Prerequisite is MATHS 1007A/B Mathematics I (Pass Div I) or both MATHS 1007A/B Mathematics I (Pass Div II) and MATHS 2004 Mathematics IIM (Pass Div I). PURE MTH 2002 Algebra II is assumed knowledge but the necessary material is revised at the start of the course.
Recommended Text
A First Course in Abstract Algebra , J.B. Fraleigh.
Supplementary Examinations
Information about supplementary examinations is
here on the University's website.
Consulting time
I will be in my office available for consulting on Groups and Rings
between 10.30 and 11.30 on Tuesdays. My office is room 4.19, 10 Pulteney Street.
For consulting at other times ring me on 8303 4174 or
email me.
Handouts
Assignments
Last changed Thursday, 18 February, 2010.
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