THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world— explicating such facts presents philosophy with some of its subtlest problems. Let me begin by reminding you of some c...

A certain mathematician M, considering some hypothesis H, conclusion C and text P, can arrive at one of the following judgments: (1) P does not convince M of the fact that since H, it follows that C; (2) P is the proof that since H, it follows that C (judgment of the type"Proved"). Is it possible to replace such a mathematician with an arbitrary Turing machine? The paper provides a proof that t...

As time passed, numerous mathematicians gravitated towards universities. An emphasis on free thinking and trial had begun in Britain's oldest universities beginning the seventeenth century at Oxford with scientists Robert Hooke Boyle, Cambridge where Isaac Newton was Physics. Science mathematics Islamic world during Middle Periods followed colourful models modes of backing varied grounded prima...

in recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. these two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. in this paper i will consider the linear differential equations on the plane (phase diagram) and elements of nonl...

Tw o conflicting schools of thought have been dominating software engineering education. One school stresses on the popular software development methodologies, but horror stories on poorly designed systems are not uncommon. The other school advocates formal methods, but most practitioners regard them as impractical. We recommend that we should bridge the gap between the formal and informal by b...

In recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. These two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. In this paper I will consider the linear differential equations on the plane (phase diagram) and elements of nonl...