In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real functions. By definition, real analysis focuses on the real numbers, often including positive and negative infinity to form the extended real line.
This subject is generally considered as being one of the hardest undergraduate math classes. This is mainly because it is a proof heavy class and the proofs are not always obvious.
Where is Real Analysis used ?
It has applications to any setting where one integrates functions, ranging from harmonic analysis on Euclidean space to partial differential equations on manifolds, from representation theory to number theory, from probability theory to integral geometry, from ergodic theory to quantum mechanics.
Is the Subject easy or tough ?
While the concepts can be difficult to understand at first, since they based on what you did in calculus, it should still be apparent that they are useful concepts to know
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