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| | | | | thatsmaths.com | |
| | | | | There are numerous branches of mathematics, from arithmetic, geometry and algebra at an elementary level to more advanced fields like number theory, topology and complex analysis. Each branch has its own distinct set of axioms, or fundamental assumptions, from which theorems are derived by logical processes. While each branch has its own flavour, character and... | |
| | | | | jdh.hamkins.org | |
| | | | | This will be a series of self-contained lectures on the philosophy of mathematics, given at Oxford University in Michaelmas term 2019. We will be meeting in the Radcliffe Humanities Lecture Room at | |
| | | | | www.logicmatters.net | |
| | | | | A standard menu for a first mathematical logic course might be something like this: (1) A treatment of the syntax and semantics of FOL, presenting a proof system or two, leading up to a proof of a Gödel's completeness theorem (and then a glance at e.g. the compactness theorem and some initial implications). (2) An [...] | |
| | | | | mathematicaloddsandends.wordpress.com | |
| | | I recently came across this theorem on John Cook's blog that I wanted to keep for myself for future reference: Theorem. Let $latex f$ be a function so that $latex f^{(n+1)}$ is continuous on $latex [a,b]$ and satisfies $latex |f^{(n+1)}(x)| \leq M$. Let $latex p$ be a polynomial of degree $latex \leq n$ that interpolates... | ||