THE UNIVERSITY of EDINBURGH

DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Linear Analysis (MATH10082)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryIn this course, we will introduce students to techniques and tools in modern analysis which have important uses in a variety of areas of analysis, including the study of partial differential equations and Fourier analysis.

We will achieve this in the context of linear analysis, introducing normed linear, inner product spaces and their completions, Banach and Hilbert spaces. The structure and geometry of these spaces will be studied as well as continuous linear operators acting on them. Many examples will be studied as well as connections to other fields.
Course description - Inner product spaces and normed spaces.
- Completeness and completions of spaces with concrete realisations of standard examples. Lp spaces, Holder and Minkowski inequalities.
- Geometric and metric properties of Hilbert spaces, including orthonormal bases and generalised Fourier series.
- Bounded linear functionals, operators and duality,
- Test functions and distributions.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Analysis (MATH10068)
Students MUST have passed: Honours Algebra (MATH10069)
Co-requisites
Prohibited Combinations Students MUST NOT also be taking Linear and Fourier Analysis (MATH10081)
Other requirements Students will find it useful to have taken, or be taking, MATH10047 Essentials in Analysis and Probability and MATH10082 Linear Analysis.

Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.

High Demand Course? Yes
Course Delivery Information
Academic year 2019/20, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 95 %, Coursework 5 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 5%, Examination 95%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)MATH10082 Linear Analysis2:00
Academic year 2019/20, Part-year visiting students only (VV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 95 %, Coursework 5 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 5%, Examination 95%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate facility with the interplay between analysis, geometry and algebra in the setting of Banach and Hilbert spaces, both abstractly and in specific examples.
  2. Use orthogonality arguments in a variety of theoretical and concrete situations.
  3. Work with the classes of normed linear spaces appearing in the course, particularly specific calculations around Hilbert spaces and operators acting on them.
  4. Produce examples and counterexamples illustrating the mathematical concepts presented in the course.
  5. Understand the statements and proofs of important theorems and be able to explain the key steps in proofs, sometimes with variation.
Reading List
1. An Introduction of Hilbert Space, by N. Young, Cambridge Mathematical Textbooks.
2. Introduction to Hilbert Space, by S. Berberian, Oxford University Press.
Additional Information
Graduate Attributes and Skills Not entered
KeywordsLAn
Contacts
Course organiserProf Jim Wright
Tel: (0131 6)50 8570
Email: J.R.Wright@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
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