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You'd probably enjoy studying *type theory*. Type theory is a form of category theory applied to languages and sentences. It allows formal definitions of what constitutes a proof, and is used for structuring computer languages designed for error checking and debugging. Category theory, in turn, is an offshoot of abstract algebra which has applications all over mathematics. Of those applications, perhaps categorical logic would be of particular interest to you.

Emily Riehl wrote the book Category Theory in Context recently. You might find it helpful. It's available free on her website, and will be published by Dover later this year: http://www.math.jhu.edu/~eriehl/727/context.pdf [Broken]

Emily Riehl wrote the book Category Theory in Context recently. You might find it helpful. It's available free on her website, and will be published by Dover later this year: http://www.math.jhu.edu/~eriehl/727/context.pdf [Broken]

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I'm not all that convinced that you're looking for category theory, although it is definitely worth looking into.

Other things you might want to try are universal algebra. For example see http://www.math.hawaii.edu/~ralph/Classes/619/univ-algebra.pdf

You also might want to check out algebraic logic which establishes a link between logic and algebraic structures. See Rasiowa and Sikorski: https://www.amazon.com/dp/B005JGKZXW/?tag=pfamazon01-20

As for category theory, take a look at Aswodey's very neat book: https://www.amazon.com/dp/0199237182/?tag=pfamazon01-20&tag=pfamazon01-20 or try to get into topos theory with Goldblatt's beautiful book: https://www.amazon.com/dp/0486450260/?tag=pfamazon01-20&tag=pfamazon01-20

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chiro

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You might want to look at specific applications of algorithms in a mathematical context (i.e. - based on abstract algebra and theoretical computer science).

Mathematical cryptography in a very rigorous form might be up your alley since they have to understand all of these issues and have some idea of how to enforce the computational complexity of things like one way functions (i.e. easy to do, hard to undo without the necessary piece of information which is the basis for a lot of asymmetric cryptography).

If you can find an abstract algebraic treatment of cryptography along with the computer science (theoretical) treatment and combine them yourself (or find another who can combine it for you or has already done so) then it might meet your needs.

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Would universal algebra really be what I'm looking for, more than category theory?I'm not all that convinced that you're looking for category theory, although it is definitely worth looking into.

Other things you might want to try are universal algebra. For example see http://www.math.hawaii.edu/~ralph/Classes/619/univ-algebra.pdf

You also might want to check out algebraic logic which establishes a link between logic and algebraic structures. See Rasiowa and Sikorski: https://www.amazon.com/dp/B005JGKZXW/?tag=pfamazon01-20

As for category theory, take a look at Aswodey's very neat book: https://www.amazon.com/dp/0199237182/?tag=pfamazon01-20&tag=pfamazon01-20 or try to get into topos theory with Goldblatt's beautiful book: https://www.amazon.com/dp/0486450260/?tag=pfamazon01-20&tag=pfamazon01-20

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Don't know. Take a look at both fields and see what you like best.Would universal algebra really be what I'm looking for, more than category theory?

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