Algebra 2 Durham University

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Algebra 2 Durham University

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

Department: Mathematical Sciences

MATH2581: ALGEBRA II

TypeOpenLevel2Credits20AvailabilityAvailable in 2017/18Module CapLocationDurham

Prerequisites

  • Calculus and Probability 1 (MATH1061) and Linear Algebra 1 (MATH1071).

Corequisites

  • None.

Excluded Combination 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.
  • Vector spaces over arbitrary fields.
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 Contact Hours

ActivityNumberFrequencyDurationTotal/Hours
Lectures422 per week1 Hour42
Tutorials11Fortnightly for 20 weels1 Hour11
Problems Classes9Fortnightly for 20 weeks1 Hour9
Preparation and Reading138
Total200

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / durationElement WeightingResit Opportunity
Written examination3 hours100%Yes

Formative Assessment:

One written assignment to be handed in every third lecture in the first 2 terms. Normally each will consist of solving problems from a Problems Sheet and typically will be about 2 pages long. Students will have about one week to complete each assignment.