Global Opportunities

MAS3702 : Linear analysis

Semesters
Semester 1 Credit Value: 10
ECTS Credits: 5.0

Aims

To introduce students to the basic ideas of functional analysis, an important area of research developed to study integral and differential equations. To introduce students to the notion of convergence and continuous transformations on vector spaces.

Module Summary

At the end of the last century, mathematicians began to realise that the methods used to solve differential equations are quite like those involved in solving simultaneous equations and they began to investigate this similarity and make it rigorous. Thus, this topic grew out of an attempt to provide a framework to explain phenomena in applied mathematics. One needs linear algebra to explain the matrix behaviour, and analysis to explain the calculus. The result is the concept of a Banach space, a place where we have vectors and a notion of size, and operators, which are like matrices. The course develops the general theory, stressing the similarities between vectors and matrices and the new ideas.

Outline Of Syllabus

Norms. Cauchy sequences, completeness, Banach and Hilbert spaces. Examples: l^p spaces, spaces of continuous functions, matrices. Bounded operators on Banach spaces and Hilbert spaces: operator norm, adjoints, inverses, the spectrum.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture201:0020:0014 Formal Lectures – Present in Person; 6 Formal Lectures – Synchronous On-line.
Scheduled Learning And Teaching ActivitiesLecture21:002:002 Revision Lectures – Synchronous On-Line
Scheduled Learning And Teaching ActivitiesLecture51:005:005 Problem Classes – Synchronous On-Line
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Guided Independent StudyIndependent study581:0058:00Preparation time for lectures, background reading, coursework review
Total100:00
Jointly Taught With
Code Title
MAS8702Linear analysis
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A80N/A
Exam Pairings
Module Code Module Title Semester Comment
MAS8702Linear analysis1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10N/A
Prof skill assessmnt1M10N/A
Assessment Rationale And Relationship

AA substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.

Reading Lists

Timetable