Real Analysis
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Sup /sci/ I've finished my first Analysis course and now I learned the following:
>Basic set theory
>Axioms of the real numbers
>Topology of the real numbers (closure of a set, accumulation points, etc.)
>Compactness
>Sequences
>Continuity
>Differentation and Riemann Integration
>Series and Power Series
>Sequences and Series of Functions
And all of this with rigorous proof writing.
I think I'm ready for new material. The Real Analysis course I'm taking next year involves Hilbert Spaces, [math]l^p[/math] spaces, measure theory and Lebesgue integration among other things. How do I prepare for this? Any books to go from here?
Make sure you're familiar with linear algebra.
>>7759709
From linear algebra I know:
>diagonalizability
>orthogonal bases
>QR decomposition
>vector spaces
Is that enough?
>>7759712
yes. spectral theorem is basically generalized diagonalization for infinite dimensional linear spaces
>>7759714
So you got any books I can work through now?
>>7759706
>real analysis
>no such thing as fake analysis
Math is such cockamamie bullshit God damn
So glad I'm an engineer
>>7759732
>no such thing as fake analysis
Ever heard of calculus?
>>7759706
What book did you use, baby Rudin?
>>7759777
This one
>>7759706
Seriously? Is that all that real analysis is? So it's proving baby calc. I thought it involved more rigour in higher level calc at least.
>>7759799
>Hilbert spaces, measure theory and Lebesgue integration is baby calculus
Okay
>>7759803
Well the Hilbert spaces we pick it up in courses with only baby calc. and LA as prereqs.
Math majors when they talk about Analysis imply is this massive field completely inaccessible to us mortals.
>>7759778
top kek.
Prepare by reading baby Rudin and Stein's 4 analysis series books.
>>7759808
That's like saying solving classical mechanics problems is easy because you just apply F=ma.
