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outline [2016/09/24 16:22] nikolaj |
outline [2016/10/15 14:22] nikolaj |
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| | [[An apple pie from scratch]] $\succ$ Outline $\succ$ [[Drawing arrows and coding functions]] | | | [[An apple pie from scratch]] $\succ$ Outline $\succ$ [[Drawing arrows and coding functions]] | | ||
| ==== Guide ==== | ==== Guide ==== | ||
| - | The content of this wiki is a presentation of mathematical concepts in a top-down way. | + | Here is an outline structure (work in progress): |
| - | The focus is on how "mathematical data" can be set up in //set theory// and I also use //category theory// for "structural characterizations". | + | |
| - | + | ||
| - | (As foundational paradigms, both set- and category theory have strong merits and disadvantages. While it's possible to develop a version of categories, functors and natural transformations in set theory and a version of sets in category theory, I rather use both paradigms early on. As a side note, it's also possible to axiomatize categories in logic directly and also to specify sets in type theory, but that's pretty nonstandard and more difficult. In discussion sections, I will often use categorcal language to to characterize sets a the category of sets.) | + | |
| - | + | ||
| - | To be self-contained, I start out with an more or less informal explanation of formal languages and foundational theories and common axioms. The structure of the presentation is summarized below. The primitive notions in this wiki, discussed in the first block, are summarized in [[Domain of discourse]]. | + | |
| - | + | ||
| - | "Two models principle": | + | |
| - | For each abstract definition, | + | |
| - | I'll try to exemplify it with two different structures. | + | |
| - | + | ||
| - | ----- | + | |
| - | + | ||
| - | Here the structure: | + | |
| === Computation and logic (presented bottom-up) === | === Computation and logic (presented bottom-up) === | ||
