final exam - Question 1: Reality of mathematics Euclidian...

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Question 1: Reality of mathematics Euclidian space – parallel lines- believed this was a ‘true’ answer, and was trying to describe this ‘reality’ Question 3:Cultural Interchange Greece Alexander the Great Traveled and conquered Left garrisons and build admin. Centres Started Alexandria to gather all info together Due to the fact that they traveled/traded and had prev. contact with other cultures, so understood the value of learning from other cultures, allows advancement of math Euclid After importance of logical argument, perhaps importance placed on putting information in coherent structure- let to “the Elements” Due to importance on philosophy Had learned knowledge from other countries, so able to focus on phil?? Plato Because had more time for philosophy, could contemplate ‘reality’ -associate it with divinity Egypt and Babylon Not as much ‘time’ on their hands as Greece, not the advantage of taking their knowledge from many previous cultures More practical Didn’t focus on ‘general algorithms’ and ‘proofs’ -specific examples, didn’t “care” as much about math other than its practical uses Didn’t achieve the reverence that the ‘philosophical’ Greeks did -Not divine Monolithic cultures Didn’t evolve their math- not many developments 1
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Stuck to their methods Need for symbols/positional system Egypt- symbols existed for numbers of practical use, not higher Grouped for convenient reading (no position) = from no devel. - even though had to write a LOT of symbols to convey a number Early Agricultural Civilizations Now had the need for taxes, property= inheritance, geometry (property and religion), calander for crops Practical need for math Early human development THEORY!!! (can’t be proven) -dev of man 1000’s of years before dev of culture!! Why? Even though man was developed enough, hadn’t developed a way to speak and communicate- pass down knowledge - so culture wasn’t possible These cultures weren’t ‘cultures’ until communication was possible Math developed (tallying) with devel of culture (bone dating) -regional differences in tallying- (link between math and culture) Dark Ages- West Roman Empire Fall of Rome People are left with no structure, no Roman culture New culture of Feudal System Serfs/nobles/monks -farmers and nobles don’t need math because just ‘protecting’ and ‘farming’ -monks are only literates 2
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can CHOOSE what to preserve as knowledge math knowledge is dependant on their religion’s “needs” preserving, not inventing + illiterate masses = less knowledge avail. than in past! East Roman Empire- Islam Mohammed – 600AD Preaching in Saudi Arabia Saudia Arabia conquests, Middle East etc Arabs were in contact with Greek knowledge Babylon- conquering muslims bring back Greek knowledge Islam isn’t threatened by new knowledge like RCC, so allows for them to learn ALL of previous knowledge (no censor) and value on dev. Of knowledge They are new, young and vigorous (compared to Romans)
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This note was uploaded on 05/24/2008 for the course MATH 363 taught by Professor Dover during the Winter '08 term at University of Alberta.

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final exam - Question 1: Reality of mathematics Euclidian...

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