Mathematics Commons^™

Julian Cecil Stanley Papers, Zach S. Henderson Library, Special Collections

Finding Aids

This collection consists of the research materials of Johns Hopkins professor of psychology, Julian C. Stanley. Materials range from 1950-2005 and include his published reprints, abstracts, reports, letters, and seminar papers. The collection also includes reviews of research materials and articles by prominent psychologists in similar fields.

Find this collection in the University Libraries' catalog.

Newton, Maclaurin, And The Authority Of Mathematics, Judith V. Grabiner

Pitzer Faculty Publications and Research

Sir Isaac Newton revolutionized physics and astronomy in his Principia. How did he do it? Would his method work on any area of inquiry, not only in science, but also about society and religion? We look at how some Newtonians, most notably Colin Maclaurin, combined sophisticated mathematical modeling and empirical data in what has come to be called the "Newtonian Style." We argue that this style was responsible not only for Maclaurin’s scientific success but for his ability to solve problems ranging from taxation to insurance to theology. We show how Maclaurin’s work strengthened the prestige of Newtonianism and …

Cultural Topology: An Introduction To Postmodern Mathematics, Brent M. Blackwell

Reconstruction: Studies in Contemporary Culture

[Editors' Introduction]

This essay develops a new way of thinking about the cultural relationships among and within the sciences and the arts through a new understanding of the term postmodernism that at once derives from literary theory and the mathematical discipline of topology. While topology forms the main vertebra of this connective approach in its capacity as the mathematics of connectivity, quantum mechanics and non-Euclidean geometry -- the atlas and axis of this spinal column -- form the context through which this “postmodern” approach will develop. However, in order to position topology as a “postmodern” branch of mathematics, some brief …

Of Parts And Wholes: Self-Similarity And Synecdoche In Science, Culture And Literature, Dirk Vanderbeke

Reconstruction: Studies in Contemporary Culture

[Editors' Introduction]

The discussion here centers on how self-similarity, or parts resembling a whole, has been a recurring aspect in the most diverse fields of human thinking from antiquity to the present. Primary examples are drawn from physics, biology, cybernetics, alchemy, philosophy, myth and, of course, language and literature. The author argues that self-similar patterns are one of the persistent ways in which the human mind structures its experience and knowledge of the world, and then examines some of the questions that arise when an almost ubiquitous concept, structure or linguistic and literary phenomenon resurfaces in a new guise in …

Man's Cards And God's Dice: A Conceptual Analysis Of Probability For The Advanced Student, Elie Feder

Humanistic Mathematics Network Journal

No abstract provided.

A Linear Perspective To Art, Sarah Littler

Humanistic Mathematics Network Journal

No abstract provided.

Base And Subbase In A Number System, Walter S. Sizer

Humanistic Mathematics Network Journal

No abstract provided.

Tesselland: A Mathematical Oddment, Martin Glover

Humanistic Mathematics Network Journal

No abstract provided.

Bridging To Infinity, Mike Pinter

Humanistic Mathematics Network Journal

The author's own experiences as a mathematics student and teacher have influenced how he thinks about the infinite. Author Madeleine L'Engle has also shaped his thinking with her writing. The author offers some thoughts that connect some of L'Engle's writing with his experience.

Mathematics, The Liberal Arts, And Slavish Devotions, J. D. Phillips

Humanistic Mathematics Network Journal

No abstract provided.

A Brief Look At Mathematics And Theology, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Fermat's Enigma By Simon Singh, Matthew Becker

Humanistic Mathematics Network Journal

No abstract provided.

Neutrosophic Dialogues, Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

Thanks to Dr. Smarandache for his interest in Chinese culture. I cannot decline his warm request to write the preface, even with my fragments of knowledge – no insight nor wisdom, and therefore can be misleading. I have been extremely regretful for my ideological errors and mistakes in previous publications, especially those concerning Buddhism. As I mentioned in this book, I am not qualified. So please note that I am limited in my knowledge and enlightenment of the giant of Chinese heritage. I can express nothing more than my personal bias. In what aspect can Chinese culture be distinctive from …

Objectivity, Information, And Maxwell's Demon, Steven Weinstein

Dartmouth Scholarship

This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information‐content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwell's Demon.

Sylvester: Ushering In The Modern Era Of Research On Odd Perfect Numbers, Steven Gimbel, John Jaroma

Philosophy Faculty Publications

In 1888, James Joseph Sylvester (1814-1897) published a series of papers that he hoped would pave the way for a general proof of the nonexistence of an odd perfect number (OPN). Seemingly unaware that more than fifty years earlier Benjamin Peirce had proved that an odd perfect number must have at least four distinct prime divisors, Sylvester began his fundamental assault on the problem by establishing the same result. Later that same year, he strengthened his conclusion to five. These findings would help to mark the beginning of the modern era of research on odd perfect numbers. Sylvester's bound stood …

Sos Checks And Career Management, Russell W. Howell

ACMS Conference Proceedings 2003

This paper compares the careers of King Saul and King David in the Bible and how they inform the career management methods of a Christian.

A Christian Appraisal Of Stephan Wolfram's A New Kind Of Science, Gene B. Chase

ACMS Conference Proceedings 2003

Wolfram exposes some ideas about informatics that relate to Christian Scholarship: Does Wolfram's definition of free will permit God to have free will? Will human souls resurrected to a new body–as described by St. Paul and Aquinas–by like software that is moved to new hardware? Jesus' incarnation as in-form-ation in the Aristotelian sense.

Linear Regression As A 1-Variable Optimization Exercise, Ken Constantine

ACMS Conference Proceedings 2003

Derivation of the least squares line for a set of bivariate data entails minimizing a function of two variables, say the line's slope and intercept. Imposing the requirement that the line pass through the mean point for the data reduces this problem to a 1-variable problem easily solved as a single-variable Calculus exercise. The solution to this problem is, in fact, the solution to the more general problem. We illustrate with a dataset involving charitable donations.

Exploiting The Confidence Interval-Hypothesis Test Equivalence In Basic Statistics Classes, Ken Constantine

ACMS Conference Proceedings 2003

An emphasis is offered for the inference portion of an elementary Statistics course: the equivalence between confidence intervals and tests of hypotheses. This equivalence is rarely mentioned in basic texts but seems helpful to students. Student reference sheets which employ this equivalence are available on-line.

Making Connections: Using Analogies To Enrich Understanding Of Mathematical Ideas And Biblical Truths, Ron Benbow

ACMS Conference Proceedings 2003

Recent standards and research, published by mathematics education professional organizations, place a great emphasis on “connections” in all grade levels. Through this emphasis on interrelatedness, students begin to see the subject not as a collection of separate strands, but rather as an integrated field of study. When linkages between diverse domains of knowledge are formed (by comparing, contrasting, analyzing, and applying), we have increased the likelihood that we develop deeper understandings within both domains. This paper explores some specific examples of the use of analogies to connect mathematical and Biblical concepts.

What Is A Random Event? A Project For Finite Math Or Statistics, Jeremy Case

ACMS Conference Proceedings 2003

Randomization is an important idea in Finite Mathematics and Statistics. One main idea in these courses is that events that appear to be performed in a random fashion are often not random. Here we present a simple project involving "randomly" opening the Bible. This activity leads to deeper philosophical questions such as how to study the Bible and whether an event can be considered random if God intervenes.

Creationism - A Viable Philosophy Of Mathematics, Jonathan Zderad

ACMS Conference Proceedings 2003

The purpose of this essay is to try to answer the ontological and epistemological question of mathematics. Specifically, "What, if any, of mathematics exists in the objective sense?" And, "How do we as humans know that our knowledge of mathematics is correct?" These questions will be investigated by looking at the applications or mathematics, the practice of mathematicians, and most telling, the content of mathematics. Mathematics, admittedly, can only go so far in answering its own philosophical questions, even when aided by recent developments in the field of logic. The overwhelming evidence, as will be shown, points toward a theistic, …

A Greater Tantalizer, Andrew Simoson

ACMS Conference Proceedings 2003

The children’s puzzle, sometimes called the Great Tantalizer, consists of four blocks each of whose faces have been colored with four colors; a solution consists in stacking the blocks so that on each stack face, all four colors appear. This article renders the puzzle as six octahedral blocks, each of which is colored with six colors, and describes a scheme to successfully stack all six.

Light Meals And Morsels From Mathematics Magazine, Paul Zorn

ACMS Conference Proceedings 2003

No abstract provided.

General-Education Mathematics Course From A Christian Perspective, Saburo Matsumoto, Ph.D.

ACMS Conference Proceedings 2003

No abstract provided.

Some Fibonacci Gems, Peter Rothmaler

ACMS Conference Proceedings 2003

No abstract provided.

A Christian Perspective On Mathematics - History Of Mathematics And Study Guides, Johan H. De Klerk

ACMS Conference Proceedings 2003

No abstract provided.

Learning To Construct Proofs In A First Course On Mathematical Proof, Peter R. Atwood, Ph.D.

ACMS Conference Proceedings 2003

No abstract provided.

The Search For The Real Josephus Problem, Eric Gossett

ACMS Conference Proceedings 2003

Many of the problems that mathematicians and computer scientists dearly love have been around for a long time. One such problem is known as the Josephus Problem, named after the first century Jewish historian Flavius Josephus. Josephus did not invent the problem. Instead, an event from his life served as the inspiration for the problem statement. Many current books refer to "Mathematical Recreations and Essays" by W. W. Rouse Ball [originally published in 1892] for the problem statement. The problem is quite interesting (and will be solved here). However, the story, as quoted in Bell, is not completely accurate.

The Inverse Problem: Christianity Through A Mathematical Lens, Sharon K. Robbert

ACMS Conference Proceedings 2003

An inverse problem is a partner problem that reverses some type of direct problem. Usually the inverse problem is more challenging to solve than the direct problem: integration is more challenging than differentiation, factoring large numbers is more challenging than multiplying numbers. In this paper, the author poses that using mathematical thinking to understand the concepts of theological principles is the direct problem to the much more challenging inverse problem of using theological thinking to influence understanding in mathematics. Acknowledging that a problem is difficult allows one to be satisfied with understanding small pieces and progressing slowly to a complete …