Applications of Set Theory in engineering?

[Garry Go]

Hey everyone,

I'm currently taking a mathematics course in set theory at my university as a general elective. I was wondering does set theory have any practical applications in engineering?

 

[Stephen Tashi]

In my opinion, there isn't much application of set theory as a "stand-alone" tool in engineeering. It's main use for engineers is enable the mathematics they use to be treated precisely.

 

[mathman]

Although it is not exactly the same, the mathematics of logic circuits is very similar to that of set theory.

 

[StatOnTheSide]

Noise analysis in circuit design is completely based on Stochastic Differential Equations.
Many engineers start with Measure Theoretic Probability but to rigorously understand the stuff, you need to know Measure Thoery which in turn requires Real Analysis which basically requires Set Thoery.
I suppose you can learn the required material by starting from Measure Theoretic Probability the way most EE graduates do. They nevertheless learn the required amount of Set Theory, Real Analysis and Measure Theory while studying Measure Theoretic Probability.

 

[quantum123]

Interesting. Never knew that Measure theory is requited in engineering...wow cool

 

[StatOnTheSide]

Research in Engineering is possible to a large extent by learning Signal Processing and related topics. You need not learn Measure Theoretic Probability at all. A good analog circuit designer usually has a strong hold on Signal Processing; however, systems are getting way too complicated these days and for the right reasons. There are two fantastic works which make use of advanced signal processing tools along with the tools in Statistics. You can find these papers by typing "serial requantizer ashok swaminathan" in google and the very first page (a pdf file) leads you to that paper.
The second paper which is by far the most elegant use of math can be found by typing "phase noise in oscillators a unifying theory Jaijeet Roychowdhury" in google and the very first pdf you find will be that paper. I can't copy paste links for some reason. This paper basically models the oscillator phase noise using Floquet Theory and Stochastic Differential Equations. ALL the circuit design simulation tools use this principle today to simulate the phase noise in oscillators. Without this method, there would not have been this much of progress in RF design in the industry.

Statistical nature of signals has made it mandatory for any Circuit Desginer or Wireless Engineer to learn Measure Theoretic Probability. These Abstract Dynamical Systems have been designed for a certain reason but as they are so complicated to understand them clearly, there is not other go but to simply learn the required mathematical tools.

Going forward, research in Circuit Design will involve a lot of Statistical Signal Processing for both analysis and for design. I highly recommend that a person seeking a solid career in EE go through a course in Measure Thoeretic Probability, Statistical Signal Processing and maybe also Abstract Dynamical Systems in case it is needed for the particular case as is the case in Oscillator Phase Noise Analysis.

 

[Bacle2]

Although it is not exactly the same, the mathematics of logic circuits is very similar to that of set theory.

Isn't it more like Boolean Algebra than like Set Theory?