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Open Recruitment
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Hello Mathematics Citizenia,,
MEC is now holding open recruitment for new members of the 2009/2010 period.
Registration can be done online through blogs MEC by downloading the registration form on the menu Download, or can also register at the meeting,
We wait your participation.
Please Join Us
MEC is now holding open recruitment for new members of the 2009/2010 period.
Registration can be done online through blogs MEC by downloading the registration form on the menu Download, or can also register at the meeting,
We wait your participation.
Please Join Us
5 Categories Of Research In Mathematics
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According to the research object MAA (Mathematical Association of America) have a great line in the 5 categories of research which is abbreviated with Mathematics PEACE: Proof, Extension, Application, Characterization, & Existence .
Proof: Of course, every mathematical research project involves proof; in this context, proof is the focus of the project. For example, “Prove Fermat’s Last Theorem.” More generally, though, we note that reproof is also a valid line of mathematical research: Gauss, for example, earned his doctoral dissertation by providing a new proof of the Fundamental Theorem of Algebra. It might be argued that no rigorous proof existed before Gauss, but clearly Gauss felt that proving a theorem once was insufficient: he eventually gave four proofs of the Fundamental Theorem of Algebra and six proofs of the Law of Quadratic Reciprocity.
Extension: This takes some existing concept and extends it. For example, Newton took the expansion of (a + b)n, where n is a whole number, and extended it to the expansion of (a + b)n where n was a positive or negative rational number. The Lebesgue integral is another example of an extension.
Application: We may take an existing idea and apply it to a new area. This is frequently the focus of projects in applied mathematics, but it also can be used to originate new areas of pure mathematics: the application of algebra to problems in geometry led to Descartes’s creation of analytic geometry, while the application of power series techniques to problems in number theory led to Euler’s creation of analytic number theory.
Characterization: We can try to characterize or classify a mathematical object or concept. For example, Cauchy’s great contribution was to characterize what was really meant by continuity, differentiability, and integrability, while Cantor characterized the naive notions of “infinity,” and the Enormous Theorem is a classification of finite simple groups.
Existence: Strictly speaking, this is part of “characterization,” since one quality of an object is whether or not it exists. However, existence (or non-existence) theorems tend to be treated separately: this is reasonable, since unless the object exists, there is no point investigating its mathematics! Examples of existence results are Euclid’s proof of the existence of an infinite number of primes or Gödel’s incompleteness theorem (a non-existence proof).
Source: http://www.maa.org/features/112404howdoido.html
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