The statements of Gödel's incompleteness theorems are famous in mathematics, concerning the foundations of the eld. Whilst most mathematicians have heard of the theorems, few outside of mathematical logic would have gone through the technically sophisticated proofs. Instead of proving the original theorem for the theory of natural numbers and utilizing the notion of consistency, we prove a vers...

Engineering mathematics is traditionally conceived as a set of unambiguous mathematical tools applied to solving engineering problems, and it would seem that modern mathematical software is making the toolbox metaphor ever more appropriate. We question the validity of this metaphor, and make the case that engineers do in fact use mathematics as more than a set of passive tools—that mathematical...

Abstract Mathematical education, both mass and university education of non-mathematicians, are in an abominable state, rapidly degrading. We argue that the instruction non-mathematicians should be dramatically reformed as substance style. With traditional approach, such a transformation would take decades, with unclear results. But we do not have this time. The advent Computer Algebra Systems g...

Mathematicians have been fascinated for centuries by the properties and patterns of numbers. They noticed that some numbers are equal to sum all their factors (not including number itself). Such called perfect Thus a positive integer is if it its proper divisors. The search began in ancient times. four 6, 28, 496, 8128 seem known from In this paper, we will investigate important We give easy si...