Abstract
One of the fascinating areas to arise recently in applied mathematics has been Mathematical Finance. From a technical point of view, Mathematical Finance uses a broad range of sophisticated mathematics for its financial models, and relies on state-of-the-art software engineering and computer hardware to implement these financial models, often in real-time.
Whether one is interested in technology or not, there is a kernel of core financial ideas at the heart of the global free market capitalist system that every literate citizen should understand. Whether we agree with their principles or with the inequities that are, arguably, the result, these ideas are in place across most of the world today. A closer look at mathematical finance will offer a better understanding of the mechanics of the modern financial world.
In this article, I’ll motivate the need for financial mathematics through a simplified account of the rise of the modern financial marketplace.
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(Mathematical Toolset Series: TeX & LaTeX, Part 1 of 3)
If symbols, formulas, and equations comprise a large portion of your professional communication, then becoming familiar with the LaTeX / TeX platform should be high on your to-do list. With the right tools and a little practice, the relative ease of creating beautiful documents with TeX may mean that you soon leave your favorite Office suite in favor of TeX for your technical writing.
This article introduces the LaTeX / TeX platform, illustrates its capabilities, and highlights the key differences between using TeX for document preparation and more commonly used word processing systems.
For those that like to know the human side of the tools they use, a little history of TeX, the philosophy motivating its development, and something about its legendary creator, is included.
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(Mathematical Toolset Series: TeX & LaTeX, Part 2 of 3)
LaTeX / TeX on Windows has had the rather unfortunate reputation of being difficult to install and use. But with the quality of today’s open source tools and references, this is no longer the case, and should not be a reason to deter you from trying it out.
This article takes you through the practical business of getting a LaTeX / TeX platform running on Windows, using free, open-source software. From downloading and installing, to providing reference materials and basic templates, this article should get you going quickly and provide a decent toolkit from which to build.
Note: All the steps in this article have been tested on Windows XP and Windows 7.
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(Mathematical Toolset Series: TeX & LaTeX, Part 3 of 3)
If you write frequently, it is likely that you have certain stock or administrative material that is included in each of your documents. You also likely spend a substantial portion of your overall effort re-writing, editing, or re-arranging material. In this situation, one of the best ways of preserving your time and your sanity is to adopt a modular approach to document development.
In this final article of the three part series on LaTeX / TeX, I will discuss a modular approach to document preparation using TeX. I’ll also provide modular templates that should make your use of TeX more efficient.
On the Value of Assembly Language, and Resources to get you started in Digital Logic, Computer Architecture, and Assembly Language programming.
Despite advances in programming technologies since the 1970s, there are still reasons to understand and learn assembly language programming. Contrary to what one may imagine, Assembly Language is not a relic of the past, even though a typical applications programmer will almost never need to drop into assembly.
In this article, we’ll look at practical situations in embedded systems development in which assembly language programming is still used, pedagogical reasons to learn assembly language, and provide resources and projects for gaining a working knowledge of digital logic, computer architecture, and assembly language programming.
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Abstract
“It seems that students who are hard-working and otherwise successful, but whose milieu (peers, mentors, and home environment) are at once non-technical and disengaged from the ideas behind science and technology, are at a higher risk of disorientation, dissatisfaction, or disillusionment with mathematics and science.”
In this article, I will explore this conjecture, and suggest a potential course of action, rooted in the methods of inquiry of philosophy and the humanities, that may help reverse an otherwise tough pedagogical situation.
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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 follows is an outline and reading list for a Course in the Philosophy and Foundations of Mathematics. Among the topics included are the relation of mathematics to science, the examination of mathematical method, and the search for mathematical meaning.
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By Assad Ebrahim, on March 19th, 2010
Topic: Technology
The past five years have seen the emergence of a growing array of autonomous swimming, flying, and rolling vehicles, each highly sensored and capable of real-time communication with processors external to themselves. Practical designs are now commercially available for each of the four primary areas of our environment: terrestrial, marine (subsea, surface, and amphibian), atmospheric (gravity constrained), and space (orbital and planetary).
A look at a selection of these achievements in networked sensor systems will set the stage to discuss the communications layer of the ubiquitous computing stack.
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By Assad Ebrahim, on March 19th, 2010
Topic: Technology
A Versatile Tool for Marine Operations, and a Portable Undersea Platform for Small Sensors
Micro-ROVs (Remotely Operated Vehicles) are becoming increasingly capable even as their size and cost drop, opening up new possibilities for the application of undersea inspection, imaging, and measurement.
In this article, I’ll discuss four reasons why Micro-ROVs should be a routinely used part of a marine and water-side operations toolkit, and review some stand-out choices in the Micro-ROV category.
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. Having established in 
independent monomials 
(
), where the 
are unknown coefficients. Using the recurrence relation 
, we obtain a linear combination of the monomials, which reduces to an easily solvable 
-by-
of the closed-form polynomial solution.