## Real analysis

Real analysis is a branch  of mathematics, which analyse the real numbers and real valued functions.  It is traditionally deals with the theory of functions of real valued variables. It may look abstract, but it gives the solid foundation to the understanding of real numbers and how real numbers are working.  By this understanding we know from where the results which we are using, coming from.   This understanding gives us a mentality, which is very important in any kind of science, to search for the roots.

Some Famous mathematicians who are dealing with real analysis:

Henri Lebesgue:

Henri Lebesgue was a famous French mathematician, who is famous for his theory of integration.

Riemann Lebesgue lemma, Lebesgue dominant convergence theorem, Lebesgue constant and so many more theorems and integrals are coming under his name.

Pierre Fatou

Pierre Joseph Louis Fatou (1878-1929) was another French mathematician and an astronomer. He is famous for his major contribution in Analysis. Fatou conjecture, Fatou's theorem,Fatou-Bieberbach domain, Fatou lemma and Fatou sets are some of  his findings.

John Edensor Littlewood:

John Edensor Littlewood(1885-1977) was a famous British mathematician, known for his achievements analysis, differential equations and number theory.

Littlewood conjecture, Littlewood polynomial, Littlewood's three principles of real analysis, Littlewood's Tauberian theorem are some of his findings.

### Topics under real analysis

1. General topics under analysis
• Limits
• Sequences and series
• Convergence
• Functions
• Derivatives
• Integrals

2.   Fundamental theorems in analysis

3.   Fundamental topics in analysis

•      Numbers
•      Sets
•      Maps

4.     Applied maths

5.     Related fields of analysis.

Students can get a basic knowledge about analysis by going through the topics listed above.  They can practice the problems given, and they can verify their solutions with the solutions given. If you are having any doubt you can contact us through mail, we will help you to clear your doubts.