[Math] Modern Analysis and Abstract Analysis?


Mostly I encounter textbooks named Analysis, Mathematical Analysis,… But recently, i encountered a book named A Course In Modern Analysis.

Please explain the difference between Modern Analysis and "Classical" Analysis. Also, please give some information about what Abstract Analysis means.

It's quite weird to me that the number of Modern Analysis textbooks is very small.

Best Answer

It depends on the age of the book.

"A Course of Modern Analysis" by E. Whittaker, first published in 1902, covers analytic functions, infinite series, Fourier series, Riemann integration etc. - all topics that today we would just call "analysis".

On the other hand "Introduction to Modern Analysis" by S. Kantorowitz, published in 2003, covers measure theory, functional analysis, Banach algebras, spectral theory etc. i.e. a more abstract and generalised treatment of analysis.