I'm confused about a course named "Topics in Modern Analysis" in a master program. I need to know the prerequisites for this course in some details.
About my skills: (1)I'm self-studying (2) I'm reading "Principle of Analysis by Rudin" (just finished the first 5 chapters) and "Linear algebra done right by Axler". Also, I exercise writing proofs.
The course is described as follows:
Topics:
1- Basics of functional analysis: metric, norm, scalar product,
Banach space, Hilbert space, orthonormal basis, orthogonal complement,
separable Hilbert space, formal Fourier series, operators, properties
of operators, application of the basic concepts to integral
transforms, to dierential and nonlinear equations2- Application to the Wavelet Transform: numerical approximation of
functions, advantages and disadvantages of individual methods, Haar
transformation, continuous wavelet transformation, discrete wavelet
transformation – multiscale analysis.
Best Answer
You'll need to continue Principles of Mathematical Analysis to about Chapter 9 and then, I would assume, read either the real analysis half of Real and Complex Analysis by Rudin or some other source for Lebesgue integration. However, it would be best to ask your future instructor this question, because it's not clear how much background you'd need in Lebesgue integration or at what level of difficulty. The wording "proving (at a higher level of abstraction)" suggests to me that the course may not be at a very high level.