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/sci/ - Science & Math

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6297089 No.6297089 [Reply] [Original]

Are there any direct applications of these analysis classes? While I understand their importance to mathematics, I haven't heard of any actual applications to life other than by helping mathematics, which is rather indirect.

I also heard once that real analysis is used in cryptography, can someone show me exactly in what capacity?

>> No.6297104

>>6297089
opening beer bottels

>> No.6297247

Nobody?

>> No.6297275

>>6297089
Quantum Mechanics man. Wavefunctions are complex. No "revolutionary life-changing engineering applications" like a "gravity reversal gizmo" or and "FTL newspaper delivery" though. Heck, we're still trying to wrap our heads around the implications of symmetry breaking in the imaginary part of the Higgs potential, but hey, stuff's working.

>> No.6297277

>>6297089

signal processing

>> No.6297284

Real analysis is useful in higher tier microecon

>> No.6297289

>>6297275
Thanks, I didn't assume there would be any ridiculous breakthroughs like anti-gravity or whatever because of analysis, but I was curious to see if any physicists or other scientists used analysis.

>> No.6297292
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6297292

Complex analysis is used extensively in control theory. However unlikely it sounds, stuff like argument principle finds applications, check out stability criterions of Nyquist.

Real analysis is a prerequisite for both complex, functional and fourier analysis, where the last two are pretty much the most applicable pieces of abstract mathematics that I've seen. Modern methods of numerical approximation are justified by functional analytic methods. You must have heard of the solutions to the heat equation that Fourier proposed. Fourier transform is absolutely fundamental in signal processing, it's fair to say that you always want to compute the Fourier transform of your data.

It's algebra that is used in cryptography. It's been fairly recently discovered how stuff like modules and Gröbner bases can be used to construct cryptosystems, more exactly I am talking about the Polly Cracker type. Famous RSA is a special case of this.

>> No.6297295

Real analysis is inevitable prerequisite for understanding stochastics, which is heavily used in mathematical finance.