Courses @ NUIM.ie :: Module, ALGEBRA (E)

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ALGEBRA (E)

Module code: MT615
Credits: 7.5
Semester: 1
Department: MATHEMATICS AND STATISTICS
International:

	Overview
	Module Objective: To give an introduction to modern Algebra. Linear Algebra: vector spaces; linear dependence and independence; basis and dimension; linear maps and connections with matrix algebra. Group Theory: notion of a group; examples of groups including permutation groups, symmetry groups, matrix groups, cyclic groups; subgroups; orders of groups and elements; Lagrange's Theorem; homomorphisms and isomorphisms. Parallels between group theory and linear algebra. Consideration of how algebra could be taught in a second level classroom.

Overview

Module Objective: To give an introduction to modern Algebra.
Linear Algebra: vector spaces; linear dependence and independence; basis and dimension; linear maps and connections with matrix algebra.
Group Theory: notion of a group; examples of groups including permutation groups, symmetry groups, matrix groups, cyclic groups; subgroups; orders of groups and elements; Lagrange's Theorem; homomorphisms and isomorphisms. Parallels between group theory and linear algebra. Consideration of how algebra could be taught in a second level classroom.

	Learning Outcomes
	On successful completion of the module, students should be able to: State the axioms defining groups and vector spaces. State any definitions or theorems given in the course. Deduce simple properties from these. Determine whether a given set is a group or vector space. Give examples of groups, vector spaces. Give examples of group homomorphisms and linear maps. Demonstrate how this subject could be taught in a second level classroom.

Learning Outcomes

Teaching & Learning methods

Assessment

	Repeat options
	1.5 hour 'in-house' written examination. Continuous assessment is carried forward to the autumn.

	Timetable
	This timetable is not currently available, please contact the Mathematics And Statistics Department.

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ALGEBRA (E)