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I was always fascinated with pure math, but lately I've been increasingly more interested on applications of math (preferably algebra/topology but other fields would be interesting too) in the real world.

I am wondering if there are any books that discuss such applications, as I wasn't able to find any. To be clear, I'm not looking for detailed books at the research level. I'm looking for books that I can read in my leisure time just out of curiosity to see how concepts from algebra/toplogy/etc are related to the real world.

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    $\begingroup$ I don't know of any books off the top of my head that are the standard, but for applications of algebra, you might want to look into any cryptography book or an algebraic coding theory book. As for topology, you might want to find a book on topological data analysis. These are the main applications of algebra and topology that I am aware of; although I am sure that there are probably many others. $\endgroup$
    – Steven Creech
    Commented Oct 17, 2023 at 12:14

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Depending on what you mean by real-world, topology has many applications in physics, for example: cosmology (topology of spacetime) and extensively in condensed matter (e.g. topological insulators). Topology's also been used in biology, both from data analysis and theoretical standpoints, for example in molecular biology and in describing properties of DNA.

If you're interested in the physics, one to check out is "Topology and Physics" by Chen Ning Yang.

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