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### Course Overview

Linear algebra is the study of vector spaces and linear maps between them and it is a central subject within mathematics.

It provides foundations for almost all branches of mathematics and sciences in general. The techniques are used in engineering, physics, computer science, economics and others. For example, special relativity and quantum mechanics are formulated within the framework of linear algebra.

The two courses Linear Algebra I and II aim at providing a solid foundation of the subject.

### Course Details

Study Type Level Undergraduate 2 First Sub Session 15 credits (7.5 ECTS credits) Old Aberdeen No Dr Ellen Henke

### Qualification Prerequisites

• Programme Level 2

### What courses & programmes must have been taken before this course?

• MA1006 Algebra (Passed)

None.

None.

No

### Course Description

This is the first part of the two parts course on linear algebra. The whole course contains the following topics:

* Fields
* Vector spaces
* Linear maps
* Matrices
* Linear equations
* Eigenvalues and eigenvectors

Syllabus

• Basic set theory: Naive understanding of a set and of relations, in particular equivalence relations. Maps (injective/surjective/bijective). The principal of induction.
• Definitions, examples and elementary properties of groups, rings and fields. In particular integers mod n and fields of prime order.
• Solving a linear system over a field. Elementary row operations, row echelon form, Gaussian algorithm for solving a linear system over a field.
• Vector spaces and K-algebras. Definition of a vector space over a field. Examples.
• Subspaces of a vector space, intersection and sum of subspaces.
• Span, spanning sets. Linear independence. Basis, dimension. Elementary results about bases and dimension.
• Linear transformations. Definition, kernel, image, the matrix of a linear transformation with respect to bases. The rank of a matrix and the rank-nullity theorem.
• Invertible matrices and the Gauss-Jacobi method for finding the inverse of a matrix.
• A brief introduction to determinants of matrices with entries in arbitrary fields.

### Degree Programmes for which this Course is Prescribed

• BSc Applied Mathematics
• BSc Computing Science-Mathematics
• BSc Mathematics
• BSc Mathematics with French
• BSc Mathematics with Gaelic
• BSc Physics with Geology
• MA Business Management - Mathematics
• MA Mathematics
• MA Mathematics with Gaelic
• Mathematics Joint
• Mathematics Major
• Mathematics Minor

### Contact Teaching Time

43 hours

This is the total time spent in lectures, tutorials and other class teaching.

### Assessment

1st Attempt

1 two-hour written examination (80%); in-course assessment (20%).

None.

### Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinator for feedback on the final examination.

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