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 solution of the general question itself. … Good mathematical technique has built within it the mathematical insight of the best of previous generations.
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…Thoughts on the Teaching of Exploratory, Topical Mathematics Mathematics is a richly spun tapestry threaded with interconnections from a multiplicity of endeavors, perspectives, and disciplines, both theoretical and applied. Contrary to its typical presentation, mathematics is not a linear subject. For an instructor, this presents a number of challenges: how best to address the non-linear, inter-woven nature of mathematical ideas while still maintaining sufficient pace through the material? … Co-opting the form of recent military jingoisms, I would ask: Are we winning the defense against the troublesomeness of having to engage with essentially non-mathematical questions, only to be losing the war on perception, and with it the hearts and minds of the majority of those who pass through our classrooms? 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 of the leisured class in ancient times to the impact of computing in modern times. …and the Emerging Technologies of the Next Decade Between Mathematics, Computer Science, Software Engineering, Electrical Engineering, and Statistics, is emerging an area of effort concerned, not just with using data or information gathered slowly over months or years, but with its real-time acquisition, interpretation and analysis, and its real-time use in appropriate decision-making, automatic adjustment, and intelligent response. For a team capable of bridging the disciplines involved, the potential for application is truly unlimited… … An Overview of Assembly Language Programming Assembly language programming often evokes images of a time when real programmers hurled boulders the size of small UNIVACs. The mystique is there for those whose computer science training is primarily in higher level languages. But programming is programming, and one language shouldn’t be much harder to pick up than another? In theory, perhaps. But in practice, there are a myriad of details. … for Assembly Language Programming To get started with assembly language on your x86 box, here is a set of open source (free) toolchain elements that play well together when host and target platforms are an x86 PC running a Windows (or Linux) operating system… … 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 so thoroughly has it been reworked in the post-modern approach. Despite its arcane appearance from the outside looking in, the present, abstract and highly specialized state of mathematics is the natural evolution of the subject, and there is much ahead that is exciting. Here, then, is the story of mathematics, in a nutshell… What are the characteristics of mathematics, especially contemporary mathematics? I’ll consider five groups of characteristics:
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…. …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, traits that marked the society of Homo Erectus… |
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© 2009-2012 Assad Ebrahim |
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