Real Analysis

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Anonymous

Real Analysis 2016-01-03 12:09:09 Post No. 7759706

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Real Analysis 2016-01-03 12:09:09 Post No. 7759706

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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?

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Make sure you're familiar with linear algebra.

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>>7759709

From linear algebra I know:

>diagonalizability

>orthogonal bases

>QR decomposition

>vector spaces

Is that enough?

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>>7759712

yes. spectral theorem is basically generalized diagonalization for infinite dimensional linear spaces

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>>7759714

So you got any books I can work through now?

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>>7759706

>real analysis

>no such thing as fake analysis

Math is such cockamamie bullshit God damn

So glad I'm an engineer

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>>7759732

>no such thing as fake analysis

Ever heard of calculus?

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>>7759706

What book did you use, baby Rudin?

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>>7759777

This one

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>>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.

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>>7759799

>Hilbert spaces, measure theory and Lebesgue integration is baby calculus

Okay

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>>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.

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>>7759778

top kek.

Prepare by reading baby Rudin and Stein's 4 analysis series books.

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>>7759808

That's like saying solving classical mechanics problems is easy because you just apply F=ma.

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