Este blog tem como objectivo levar a cabo o que indica o título - um passeio pela Matemática. Dar a conhecer a sua História, as suas leis, as suas personagens e curiosidades, enfim divulgar esta Ciência que, como disse Victor Duruy, é a chave de ouro com que podemos abrir todas as ciências.

quinta-feira, 21 de março de 2013

Prémio Abel 2013

«The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2013 to Pierre Deligne, Institute for Advanced Study, Princeton, New Jersey, USA. He receives the Abel Prize “for seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields”, to quote the Abel committee.»

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quinta-feira, 14 de março de 2013

Como celebrar o Dia do Pi

«Pi is a mathematical constant that is the ratio of a circle's circumference to its diameter, and it is also one of the most revered mathematical constants in the known world. Pi Day was first officially celebrated on a large scale in 1988 at the San Francisco Exploratorium. Since then, Pi Day has been celebrated by millions of students and math-lovers. The holiday is celebrated on 3/14, since 3, 1, and 4 are the three most significant digits in the decimal form of pi. If you'd like to learn how to celebrate pi in due fashion, read on and it will be as easy as pi.»

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domingo, 10 de março de 2013

"There’s more to mathematics than rigour and proofs"

«One can roughly divide mathematical education into three stages:

1- The “pre-rigorous” stage, in which mathematics is taught in an informal, intuitive manner, based on examples, fuzzy notions, and hand-waving. (For instance, calculus is usually first introduced in terms of slopes, areas, rates of change, and so forth.) The emphasis is more on computation than on theory. This stage generally lasts until the early undergraduate years.

2- The “rigorous” stage, in which one is now taught that in order to do maths “properly”, one needs to work and think in a much more precise and formal manner (e.g. re-doing calculus by using epsilons and deltas all over the place). The emphasis is now primarily on theory; and one is expected to be able to comfortably manipulate abstract mathematical objects without focusing too much on what such objects actually “mean”. This stage usually occupies the later undergraduate and early graduate years.

3- The “post-rigorous” stage, in which one has grown comfortable with all the rigorous foundations of one’s chosen field, and is now ready to revisit and refine one’s pre-rigorous intuition on the subject, but this time with the intuition solidly buttressed by rigorous theory. (For instance, in this stage one would be able to quickly and accurately perform computations in vector calculus by using analogies with scalar calculus, or informal and semi-rigorous use of infinitesimals, big-O notation, and so forth, and be able to convert all such calculations into a rigorous argument whenever required.) The emphasis is now on applications, intuition, and the “big picture”. This stage usually occupies the late graduate years and beyond.»

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