#### Prerequisites
* Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.
#### Corequisites
* Calculus I (MATH1061)
#### Excluded Combination of Modules
* Calculus I (Maths Hons) (MATH1081), Linear Algebra I (Maths Hons) (MATH1091), Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.
#### Aims
* This module is designed to follow on from, and reinforce, A level mathematics.
* It will present students with a wide range of mathematics ideas in preparation for more demanding material later.
* Aim: to give a utilitarian treatment of some important mathematical techniques in linear algebra.
* Aim: to develop geometric awareness and familiarity with vector methods.
#### Content
* A range of topics are treated each at an elementary level to give a foundation of basic definitions, theorems and computational techniques.
* A rigorous approach is expected.
* Linear Algebra in n dimensions with concrete illustrations in 2 and 3 dimensions.
* Vectors, matrices and determinants.
* Vector spaces and linear mappings.
* Diagonalisation, inner-product spaces and special polynomials.
* Introduction to group theory.
#### Learning Outcomes
Subject-specific Knowledge:
* By the end of the module students will: be able to solve a range of predictable or less predictable problems in Linear Algebra.
* have an awareness of the basic concepts of theoretical mathematics in Linear Algebra.
* have a broad knowledge and basic understanding of these subjects demonstrated through one of the following topic areas:
* Vectors in Rn, matrices and determinants.
* Vector spaces over R and linear mappings.
* Diagonalisation and Jordan normal form.
* Inner product spaces.
* Introduction to groups.
* Special polynomials.
Subject-specific Skills:
* Students will have basic mathematical skills in the following areas: Modelling, Spatial awareness, Abstract reasoning, Numeracy.
Key Skills:
#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
* Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
* Tutorials provide active engagement and feedback to the learning process.
* Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills. They are also an aid in developing students' awareness of standards required.
* Initial diagnostic testing and associated supplementary support classes fill in gaps related to the wide variety of syllabuses available at Mathematics A-level.
* The examination provides a final assessment of the achievement of the student.
More details at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/MATH1071
