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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 Term 15 credits (7.5 ECTS credits) Aberdeen No Dr Mark Grant

### Qualification Prerequisites

• Programme Level 2

None.

None.

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### 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.

### Contact Teaching Time

Information on contact teaching time is available from the course guide.

### Teaching Breakdown

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

### Summative Assessments

2x Assignments (30% each)

Test (30%)

10x Weekly Quiz (1% each, 10% total)

Alternative Resit Arrangements

Resubmission of failed elements (pass marks carried forward)

### Formative Assessment

There are no assessments for this course.

### Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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