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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Real Analysis (MATH11136)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 5 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryNB. This course is delivered *biennially* with the next instance being in 2020-21. It is anticipated that it would then be delivered every other session thereafter.

This course introduces the essentials of modern real analysis which emerged from the work of Hardy and Littlewood in the 1930's and later from the work of Calderon and Zygmund in the 1950's. Many results and techniques from modern real analysis have become indispensable in many areas of analysis, including Fourier analysis and partial differential equations.
Course description - Covering lemmas, maximal functions and the Hilbert transform.
- The Fourier Transform, L1 and L2 theory.
- Weak type estimates and Interpolation.
- Introduction to singular integrals and Fourier multipliers.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Analysis (MATH10068) AND Linear Analysis (MATH10082) AND Essentials in Analysis and Probability (MATH10047)
Prohibited Combinations Other requirements In academic year 2022-23 and later, MATH10101 Metric Spaces is a prerequisite for this course.
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of any pre-requisite course listed above before enrolling
High Demand Course? Yes
Course Delivery Information
Academic year 2020/21, 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 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 20%, Examination 80%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)Real Analysis (MATH11136)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate facility with the maximal functions and simple singular integrals.
  2. Use interpolation to reduce the study of certain linear and sublinear operators to their endpoint bounds.
  3. Identify the essential features in methods and arguments introduced in the course and adapt them to other settings.
  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. Singular Integrals and Differentiability Properties of Functions, by E.M. Stein, Princeton University Press.

2. Fourier Analysis, by J. Duoandikoetxea, Graduate Studies in Mathematics, Amer. Math. Soc.

3. Classical Fourier Analysis, Loukas Grafakos, GTM, volume 249, Springer.
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Jonathan Hickman
Tel: (0131 6)50 5060
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
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