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Faculty Handbook 2019-2020

# Module Description

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

## Department: Mathematical Sciences

### MATH1071: Linear Algebra I

Type Level Credits Availability Module Cap Open 1 20 Available in 2019/20 Durham

#### Prerequisites

• Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.

#### Corequisites

• Calculus and Probability I (MATH1061)

#### Excluded Combination of Modules

• 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 problems 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.

#### Teaching Methods and Contact Hours

 Activity Number Frequency Duration Total/Hours Lectures 58 3 per week in terms 1, 2 or 3 per week in term 2 (alternating fortnightly with Problems Classes), 2 revision lectures in term 3. 1 Hour 58 Tutorials 14 Weekly in weeks 2-10, fortnightly in weeks 14-20, and one in week 21. 1 Hour 14 ■ Problems Classes 4 Fortnightly in weeks 13-19 1 Hour 4 Support classes 18 Weekly in weeks 2-10 and 12-20 1 Hour 18 Preparation and Reading 106 Total 200

#### Summative Assessment

Component: Examination Component Weighting: 100%
Element Length / duration Element Weighting Resit Opportunity
Written examination 3 hours 100% Yes

#### Formative Assessment:

Weekly written assignments during the first 2 terms. Normally, each will consist of solving problems and will typically be one to two pages long. Students will have about one week to complete each assignment. 45 minute collection paper in the beginning of Epiphany term.

Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University