Courses / Module

RINGS & FIELDS 2

Module code: MT344P
Credits: 5
Semester: 2
Department: MATHEMATICS AND STATISTICS
International:

	Overview
	This module builds on previous knowledge and gives an in depth understanding of Rings and Fields, covering the following topics. Field Extensions. Fields as factor rings. Algebraic elements, minimal polynomials, existence of roots of polynomials. Existence and uniqueness of splitting fields. Finite Fields. Fields of rational functions. Theory of a single linear transformation. Jordan normal form. Cayley-Hamilton theorem.

Overview

This module builds on previous knowledge and gives an in depth understanding of Rings and Fields, covering the following topics. Field Extensions. Fields as factor rings. Algebraic elements, minimal polynomials, existence of roots of polynomials. Existence and uniqueness of splitting fields. Finite Fields. Fields of rational functions. Theory of a single linear transformation. Jordan normal form. Cayley-Hamilton theorem.

	Learning Outcomes
	On successful completion of the module, students should be able to: Determine the splitting field of a polynomial. Do calculations inside a finite field. State and prove the classical �impossibility proofs�. Compute the Jordan Normal form of a linear transformation. Use the methods from the course to solve problems. State definitions and theorems covered in the course. Prove simple algebraic results using rigorous arguments.

Learning Outcomes

Teaching & Learning methods

Assessment

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes Continuous assessment mark is carried forward to the Autumn. University scheduled written examination (Autumn): 120 minutes, On-campus

	Pre-Requisites
	MT242P and MT341P. Equivalent modules would also suffice.

Timetable

Search form

Courses / Module

RINGS & FIELDS 2

Semester 1

Semester 2