Undergraduate Course: Real Analysis (MATH11136)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Year 5 Undergraduate)
||Availability||Available to all students
|Summary||NB. This course is delivered *biennially* with the next instance being in 2022-23. 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.
In academic year 2022-23 and later, MATH10101 Metric Spaces is a prerequisite for this course.
- 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.
Information for Visiting Students
|Pre-requisites||Visiting 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?
Course Delivery Information
|Not being delivered|
On completion of this course, the student will be able to:
- Demonstrate facility with the maximal functions and simple singular integrals.
- Use interpolation to reduce the study of certain linear and sublinear operators to their endpoint bounds.
- Identify the essential features in methods and arguments introduced in the course and adapt them to other settings.
- Produce examples and counterexamples illustrating the mathematical concepts presented in the course.
- Understand the statements and proofs of important theorems and be able to explain the key steps in proofs, sometimes with variation.
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.
|Graduate Attributes and Skills
|Course organiser||Dr Jonathan Hickman
Tel: (0131 6)50 5060
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427