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An examination of mathematical methods and the search for mathematical meaning. During your studies of mathematics, physics and engineering, you may find yourself distracted or troubled by meta questions about mathematics — questions that fall outside the syllabi of most of the coursework that you’ll take. For those for whom this itch is persistent, what [...] The question of what value 0^0 should evaluate to has been discussed since the time of Euler (1700s). There are three candidate choices: 1,0, or “indeterminate” (i.e., throw an error). In this article, I argue that the only reasonable choice (for discrete mathematics) is 0^0=1 (), and I’ll give a tangible, feel-the-grit-in-your-palms reason [...] Good mathematical technique can bring the solution to certain mathematical questions within reach. By a proper formulation (one that is both tractable and that generalizes readily) and the use of mechanical techniques, one can often pass from a single insight to the solution of a family of problems, and in some cases, to the [...] Can a definition be given that captures the meaning of Mathematics across the millennia of its recorded history? What unites the practice of mathematics throughout its history and into the present time? In this article, I will try for a short answer by proceeding iteratively — convergence will be reached in two iterations…. The development of mathematics has had many encouraging forces: societal, technological, cultural. These have served to accelerate mathematics and have been accelerated in turn, in many cases the pair becoming locked into a mutually beneficial resonance that has dramatically energized both. In this article, I look at some of the significant catalysts, from the rise [...] … in a nutshell The development of mathematics is intimately interwoven with the progress of civilization, influencing the course of history through its application to science and technology. But mathematics has changed. Even the mathematics of the 1800s can seem quite strange now, so greatly has mathematics evolved in the past 100 years and [...] What are the characteristics of mathematics, especially contemporary mathematics? I’ll consider five groups of characteristics:
Applicability and Effectiveness, …Taking into account early human evolution, and in particular, the development of speech, it is likely that the understanding of counting and keeping time far pre-dates the discovered fossil evidence of Homo Sapiens from 30,000 years ago, and reaches back at least as far as 250,000 years ago, coincident with speech, fire, and cooperative hunting, [...] |
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© 2009-2010 Assad Ebrahim |
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