School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2022/23 Last Updated: 14 February 2023

MAT-30045 - Linear Algebra and Rings

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MAT-20025 Abstract Algebra

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This module will introduce students to more advanced ideas in vector spaces and rings, building on the introduction to these mathematical structures at level 5. The module aims to broaden the scope of these ideas and to prepare students for more advanced study of these topics at Level 7.

recall the definition of a linear transformation and be able to prove and apply associated results, including the use of linear transformations to change between bases in a vector space: 1,3

recall the definitions of eigenvalue and eigenvector of a linear transformation and apply these concepts to, inter alia, the diagonalisation of square matrices: 1,3

2,3

2,3

define different types of ring, and state and prove associated results: 2,3

recognise and define ideals and Euclidean domains, prove associated results and/or solve associated problems: define polynomial rings and solve associated problems:

recall the definitions of eigenvalue and eigenvector of a linear transformation and apply these concepts to, inter alia, the diagonalisation of square matrices: 1,3

2,3

2,3

define different types of ring, and state and prove associated results: 2,3

recognise and define ideals and Euclidean domains, prove associated results and/or solve associated problems: define polynomial rings and solve associated problems:

Learning/teaching comprises 30 hours video lectures, and 5 hours flipped examples classes.

Independent study comprises 30 hours examples class preparation, 10 hours for completion of assignment, 20 hours preparation for examination, 53 hours consolidation of lecture material, and 2 hours final exam.

Independent study comprises 30 hours examples class preparation, 10 hours for completion of assignment, 20 hours preparation for examination, 53 hours consolidation of lecture material, and 2 hours final exam.

None

Linear Algebra assignment

Take-home, written assignment. This consists of a set of questions with pre-allocated space for written solutions. Students should expect to spend 5 hours on the assessment.

Ring Theory Coursework

Take-home written coursework covering the Ring Theory part of the module. Students should expect to spend 5 hours on the assessment.

Closed-book examination

The examination paper will consist of no less than five and not more than eight questions all of which are compulsory. The examination will be closed book.