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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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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
SummaryThis 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 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 connections with partial differential equations.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Analysis (MATH10068) AND ( Linear Analysis (MATH10082) OR Linear and Fourier Analysis (MATH10081)) AND Essentials in Analysis and Probability (MATH10047)
Co-requisites
Prohibited Combinations Students MUST NOT also be taking Functional and Real Analysis (MATH11134)
Other requirements Students wishing to take both MATH11135 Functional Analysis and MATH11136 Real Analysis in the same academic session should register for the 20 credit course MATH11134 Functional and Real Analysis.
Information for Visiting Students
Pre-requisitesNone
Course Delivery Information
Not being delivered
Learning Outcomes
1. Facility with the maximal functions and simple singular integrals.
2. Ability to use interpolation to reduce the study of certain linear and sublinear operators to their endpoint bounds.
3. Capacity to identify the essential features in methods and arguments introduced in the course and adapt them to other settings.
4. Be able to 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
Recommended:

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.
Additional Information
Graduate Attributes and Skills Not entered
KeywordsRAna
Contacts
Course organiserDr Thomas Leinster
Tel: (0131 6)50 5057
Email:
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email:
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