Mathematical Finance and The Rise of the Modern Financial Marketplace

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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A Course in the Philosophy and Foundations of Mathematics

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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Sensors and Systems


… Integrating Sensors into the Ubiquitous Computing Stack

“Smart dust”, tiny leaf sensors, wearable computing — these and a host of other sensors that make measurements and communicate without requiring human intervention can now be readily integrated into dispersed systems to provide ambient intelligence, situational awareness, and the capability for adaptive behaviors or intelligent process automation.

Whether the sensor’s output is used to control the opening and closing of relays or thermostats, or to automatically raise alerts — the integration of sensors into systems is at the heart of the promise of ubiquitous computing. And with the ability to place hundreds of embedded sensors within a given coverage area, each wirelessly streaming information, the possibility of self-organizing sensor networks is increasingly becoming a reality.

This article takes a look at the sensor layer of a basic ubiquitous computing stack.

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Catalysts in the Development of Mathematics

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.
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The Development of Mathematics

… 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…
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Mathematics in Pre-History

…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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