notes - Making Mathematical Notes 1 Notes On Making...

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Making Mathematical Notes 1 Notes On Making Mathematical Notes For Your Course C.T.J. Dodson, School of Mathematics, Manchester University This is a summary of guidance notes for students on mathematical language, symbols, logic and proofs, and on how to make their own course notes useful. It suggests some essential skills that a student should acquire during a first semester at university. Language, symbols, logic and proofs 1. Language (i) Make sense to a computer ( not a telepath) using same axioms. (ii) Punctuate into sentences and paragraphs. Brackets are useful. (iii) Signpost arguments : before, during and after the development. 2. Symbols (i) Declare the sets in use; eg A = { x R m | (statement about x ) } . (ii) Introduce an element by declaring its origin and make clear how it was chosen or if arbitrary, from which set. (iii) Use ‘=’ as an abbreviation of aequare, ‘to equal’ (Descartes introduced it as α in the 17 th cen- tury). It can be used only between sets, or between elements of one set;
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notes - Making Mathematical Notes 1 Notes On Making...

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