Analysis versus Computer Science

Somebody from the industry was asking me what is the use of Analysis (whether Real or Complex or Functional or Harmonic or related) in Computer Science. Being an EE major, I could not answer his  question. But, one of my contacts, Mr. Sankeerth Rao, (quite junior to me in age), with both breadth and depth of knowledge in Math, CS and EE gave me the following motivational reply:

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Analysis is very useful in Computer Science. For instance many areas of theoretical computer science use analysis – like check Pseudo randomness, Polynomial Threshold functions,…. its used everywhere.

Even hardcore discrete math uses heavy analysis – See Terence Tao’s book on Additive Combinatorics for instance. My advisor uses higher order fourier analysis to get results in theory of computer science.

Most of the theoretical results in Learning theory use analysis. All the convergence results use analysis.

At first it might appear that Computer Science only deals with discrete stuff – Nice algos and counting problems but once you go deep enough most of the latest tools use analysis. To get a feel for this have a look at the book Probabilistic Methods by Noga Alon or Additive Combinatorics by Terence Tao.

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More later,

Nalin Pithwa

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