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Difference Equations to Differential Equations
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This book covers the following topics: Sequences, limits, and difference equations; functions ...

This book covers the following topics: Sequences, limits, and difference equations; functions and their properties; best affine approximations; integration; polynomial approximations and Taylor series; transcendental functions; the complex plane; differential equations.

Material Type:
Textbook
Provider:
Furman University
Provider Set:
Individual Authors
Author:
Sloughter, Dan
Peirce And Fisher on the Place of Probability in Abductive Inference
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In his analysis of inference into three types, deduction, induction, and abduction, ...

In his analysis of inference into three types, deduction, induction, and abduction, C. S. Peirce maintains that probability plays an essential role in the first two, but not in the third. For a deductive argument, probability tells us the frequency with which the conclusion will hold given the premises; for an inductive argument, probability tells us the frequency with which the argument will hold true. However, probability has no role to play in abduction because there is, in Peirce's view, no common ground between the conclusion and the premises on which to base a calculation of frequencies. Nevertheless, there is something in the argument that makes the conclusion plausible to our mind. I will argue that this something is a probability which is, in many cases, quantifiable. This probability is the significance level of the statistical logic developed by R. A. Fisher in the 1920's.

Subject:
Statistics and Probability
Material Type:
Reading
Provider:
Furman University
Author:
Dan Sloughter
Peirce's Alternative Achilles Paradox
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A discussion of an alternative version of one of Zeno's paradoxes, and ...

A discussion of an alternative version of one of Zeno's paradoxes, and its connection to the nature of the continuum and the existence of infinitesimals. (Unpublished paper)

Material Type:
Reading
Provider:
Furman University
Author:
Dan Sloughter
Statistical Inference: Small Probabilities and Errors
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A discussion of how small probabilities license statistical inferences, and how frequentists ...

A discussion of how small probabilities license statistical inferences, and how frequentists C. S. Peirce, R. A. Fisher, J. Neyman, E. S. Pearson, and D. Mayo differ in their interpretations of the p-value of a statistical test. (Unpublished paper)

Subject:
Statistics and Probability
Material Type:
Reading
Provider:
Furman University
Provider Set:
Individual Authors
Author:
Sloughter, Dan
Yet Another Calculus Text
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I intend this book to be, firstly, a introduction to calculus based ...

I intend this book to be, firstly, a introduction to calculus based on the hyperreal number system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such as Abraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures on the Hyperreals. Secondly, I have aimed the text primarily at readers who already have some familiarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace is too fast for most of those without some acquaintance with the basic notions of calculus.

Subject:
Calculus
Material Type:
Textbook
Provider:
Furman University
Author:
Dan Sloughter