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MATH1071: Linear Algebra I

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 1
Credits 20
Availability Available in 2024/2025
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • Normally, A level Mathematics at grade A or better and ASlevel Further Mathematics at grade A or better, orequivalent.

Corequisites

  • Calculus I (MATH1061)

Excluded Combinations of Modules

  • Calculus I (Maths Hons) (MATH1081), Linear Algebra I (Maths Hons) (MATH1091), Mathematics for Engineers and Scientists (MATH1551), SingleMathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after thismodule.

Aims

  • This module is designed to follow on from, and reinforce, A levelmathematics.
  • It will present students with a wide range of mathematics ideas inpreparation for more demanding material later.
  • Aim: to give a utilitarian treatment of some important mathematicaltechniques in linear algebra.
  • Aim: to develop geometric awareness and familiarity with vectormethods.

Content

  • A range of topics are treated each at an elementary levelto give a foundation of basic definitions, theorems and computationaltechniques.
  • A rigorous approach is expected.
  • Linear Algebra in n dimensions with concrete illustrationsin 2 and 3 dimensions.
  • Vectors, matrices and determinants.
  • Vector spaces and linear mappings.
  • Diagonalisation, inner-product spaces and specialpolynomials.
  • Introduction to group theory.

Learning Outcomes

Subject-specific Knowledge:

  • By the end of the module students will: be able to solve arange of predictable or less predictable problems in LinearAlgebra.
  • have an awareness of the basic concepts of theoreticalmathematics in Linear Algebra.
  • have a broad knowledge and basic understanding of thesesubjects 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 followingareas: 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 theapplication of the theory to practical examples.
  • Tutorials provide active engagement and feedback to the learning process.
  • Weekly homework problems provide formative assessment to guidestudents in the correct development of their knowledge and skills. Theyare also an aid in developing students' awareness of standardsrequired.
  • Initial diagnostic testing and associated supplementarysupport classes fill in gaps related to the wide variety of syllabusesavailable at Mathematics A-level.
  • The examination provides a final assessment of the achievementof the student.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures583 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 Hour58 
Tutorials9Weeks 4, 6, 8, 10 (Term 1) and 14, 16, 18, 20 (Term 2), plus 1 revision tutorial in Easter term. 1 Hour9Yes
Problems Classes4Fortnightly in weeks 13-191 Hour4 
Support classes18Weekly in weeks 2-10 and 12-201 Hour18 
Preparation and Reading111 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 90%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 hours100Yes
Component: Continuous AssessmentComponent Weighting: 10%
ElementLength / DurationElement WeightingResit Opportunity
Fortnightly assessments during the first 2 terms. Normally, each will consist of solving problems. Students will have about one week to complete each assignment.  100 

Formative Assessment

40 minute collection paper in the beginning of Epiphany term. Fortnightly formative assessment.

More information

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