Category theory has been championed as a means of unifying nearly all branches of physics and mathematics under a relatively small number of core concepts. While such claims almost certainly go too far, the wide scope provided by the ``categorical perspective'' is unquestionably valuable for abstracting and understanding relations within and between systems. As we will exemplify throughout the course, category theory is absolutely applicable to tangible problems that engineers face in system design. With the rapidly increasing power of algorithmic methods to handle complex computation and content generation, these sorts of questions seem likely to become increasingly relevant over the coming decade.
PHS6953JE introduces category theory as a language for describing formal relations---a method for organizing and layering mathematical models. Through examples drawn from database integration, topology, network analysis and logic, the core ideas of functors, natural transformations, universality, representability, and adjunctions are developed from multiple perspectives. The goal here is to get acquainted with how category theory can be used in practice---not to develop the theory as far as possible. No specific mathematical background is necessary or assumed.
PHS6953JE introduces category theory as a language for describing formal relations---a method for organizing and layering mathematical models. Through examples drawn from database integration, topology, network analysis and logic, the core ideas of functors, natural transformations, universality, representability, and adjunctions are developed from multiple perspectives. The goal here is to get acquainted with how category theory can be used in practice---not to develop the theory as far as possible. No specific mathematical background is necessary or assumed.
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