# MA4J0 - Advanced Real Analysis

**Module code:**MA4J0**Module name:**Advanced Real Analysis**Department:**Mathematics Institute**Credit:**15

Content and teaching | Assessment | Availability

## Module content and teaching

###### Principal aims

The module build upon modules on the second and third year like Metric Spaces, Measure Theory and Functional Analysis I to present the fundamental tools in Harmonic Analysis and some applications, primarily in Partial Differential Equations. Some of the main aims include: Exploring the connections between singular integrals and the summation of Fourier series; Studying Connection between the boundedness of singular integrals and the existence of solutions for some partial differential equations; Understanding the scaling properties of inequalities; Defining Sobolev spaces using the Fourier Transform and the connections between the decay of the Fourier Transform and the regularity of functions.

###### Departmental link

http://go.warwick.ac.uk/MA4J0/

###### Other essential notes

Prerequisites: MA3G7 Functional Analysis I and MA359 Measure Theory. Desirable: MA3G8 Functional Analysis II.

## Module assessment

Assessment group | Assessment name | Percentage |
---|---|---|

15 CATS (Module code: MA4J0-15) | ||

B (Examination only) | 3 hour examination (Summer) | 100% |

## Module availability

This module is available on the following courses:

###### Core

N/A

###### Optional Core

N/A

###### Optional

- Undergraduate Mathematics (MMath) (G103) - Year 3
- Undergraduate Mathematics (MMath) (G103) - Year 4
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 3
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 4
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 5
- Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 4
- Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 3
- Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 4
- Postgraduate Taught Mathematics (G1P0) - Year 2
- Postgraduate Taught Mathematics (Diploma plus MSc) (G1PC) - Year 2
- Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc) (G1PD) - Year 2
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 5
- Undergraduate Discrete Mathematics (G4G3) - Year 4