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MATH2581: ALGEBRA II

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Type	Open
Level	2
Credits	20
Availability	Available in 2024/2025
Module Cap
Location	Durham
Department	Mathematical Sciences

Prerequisites

Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061) and Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra I (MATH1071).

Corequisites

None.

Excluded Combinations of Modules

Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571)

Aims

To introduce further concepts in abstract algebra and develop their theory.

Content

Rings and fields.
Examples of groups.
Group actions.
Homomorphisms and quotient groups.
Finitely generated abelian groups.

Learning Outcomes

Subject-specific Knowledge:

By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Algebra.
have an awareness of the abstract concepts of theoretical mathematics in the field of Algebra.
have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: Rings and fields, example of groups, generators, homomorphisms.
Group actions, Equivalence relations.
Structure of finitely generated abelian groups.

Subject-specific Skills:

In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Abstract reasoning.

Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
Tutorials provide active engagement and feedback to the learning process.
The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total	Monitored
Lectures	42	2 per week	1 Hour	42
Tutorials	10	Fortnightly for 21 weeks	1 Hour	10	Yes
Problems Classes	9	Fortnightly for 20 weeks	1 Hour	9
Preparation and Reading				139
Total				200

Summative Assessment

Component: Examination		Component Weighting: 100%
Element	Length / Duration	Element Weighting	Resit Opportunity
Written examination	3 hours	100	Yes

Formative Assessment

Four written assignments to be handed per term. Normally each will consist of solving problems from a Problems Sheet and typically will be about 2-3 pages long. Students will have about one week to complete each assignment.

More information

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