(Statistics and Data Mining II)
Automated decision problems are frequently encountered in statistical data processing and data mining. An heuristic filter or heuristic classifier typically has a limited set of input data from which to arrive at a set of conclusions and make a decision: REJECT, ACCEPT, or UNDETERMINED. In such cases, pre-processing the [...]
(Statistics and Data Mining I)
For a variety of reasons, meaningful website visitation and visitor behavior statistics are an elusive data set to generate. This article introduces the visitor statistics problem, and describes seven challenges that must be overcome by statistical and data analysis techniques aiming for accurate estimates. Along the way, we’ll encounter [...]
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 [...]
(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 [...]
(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 [...]
(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 [...]
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 [...]
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 [...]
(Discrete Mathematics Techniques III)
Abstract
We find a direct closed-form solution, i.e. one that does not require iteration, for the general case of the finite-summation-of-integer-powers problem . Having established in Part 2 that the closed-form solution is a polynomial, the summation is here rewritten as the sum of the independent monomials (), where the [...]
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 [...]
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Articles by Topic Professional Tools
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