production
Skip to Content

MA2008: LINEAR ALGEBRA I (2017-2018)

Last modified: 23 Aug 2017 15:27


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 Undergraduate Level 2
Session First Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Old Aberdeen Sustained Study No
Co-ordinators
  • Dr Ellen Henke

Qualification Prerequisites

  • Programme Level 2

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

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

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.

Further Information & Notes

Course Aims
There are three main aims of the course. These are (1) to give an introduction to basic mathematical
and algebraic concepts like sets, relations, functions, groups, rings, fields, (2) to give a solid introduction to commonly used methods and results from linear algebra, and (3) to give the students an impression of how a mathematical theory is build up through definitions, lemmas/propositions/theorems and proofs.
 
Learning Objectives
By the completion of the course a student should be able to
  • work with sets, relations, functions from the viewpoint of naive set theory;
  • define the basic concepts of Linear algebra, such as a vector space over a field, a linear transformation etc., and understand the connections among linear transformations, matrices and systems of linear equations;
  • define linear independence, span and related notions and learn how to determine independence;
  • prove simple results about matrices;
  • systematically solve a system of linear equations;
  • describe row reduction in terms of elementary matrices, and prove simple results in terms of elementary matrices;
  • find the inverse of a given matrix, if it exists, and know how to determine whether or not it does;
  • define vector subspaces of a vector space, know how to determine if a given subset is a vector subspace, and apply to certain vector subspaces associated with a matrix and/or a linear transformation;
  • prove elementary results about vector spaces and the connection with matrices and systems of linear equations;
  • define a basis of a finite dimensional vector space, find a basis for a given vector space, define dimension, and know how to calculate it;
  • prove elementary results about bases and dimension;
  • define rank and nullity and know how to calculate them;
  • define and calculate the determinant of a matrix;

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.

Teaching Breakdown


Assessment

1st Attempt

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

Formative Assessment

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.

Compatibility Mode

We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.