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Articles 2341 - 2370 of 2384
Full-Text Articles in Computer Sciences
Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier
Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier
ACMS Conference Proceedings 1979
This paper explores the pedagogical decisions made by those teaching mathematics by discussing the various values and priorities of a mathematics course.
Mathematics In The Christian Philosophy Of Life, C. Ralph Verno
Mathematics In The Christian Philosophy Of Life, C. Ralph Verno
ACMS Conference Proceedings 1979
It is universally agreed that mathematics is important, that it is indeed very significant in life. This would be admitted even by those who are ignorant of or who dislike mathematics. There would be much less agreement, however, about why mathematics is important or significant. Such disagreement exists even more among mathematicians and mathematics educators. Unhappily many of the Christians who think about such things (and there are not very many who think about them at all) basically share the utilitarian view of many non-Christian thinkers, although endeavoring to place it within a Christian context. They think it is wonderful …
Brief Position Paper For Panel Discussion On Relation Of Mathematics And Christianity, C. Ralph Verno
Brief Position Paper For Panel Discussion On Relation Of Mathematics And Christianity, C. Ralph Verno
ACMS Conference Proceedings 1979
Some people view a conjoining of Christianity and Mathematics as improper. They miss the point of the relationship. The content of mathematics is not affected by Christianity. The relationship does not concern what, or how (the Christian doesn’t solve equations or differentiate differently), but it concerns why. It concerns such things as the interpretation and appreciation of the beauty, the symmetries, the coincidences, the remarkable properties, man’s creative role, etc. This paper explores the relationship between Christianity and mathematics as part of a panel discussion on the topic.
On Kuyk’S Complementarity In Mathematics, Gene B. Chase
On Kuyk’S Complementarity In Mathematics, Gene B. Chase
ACMS Conference Proceedings 1979
This paper examines Willem Kuyk’s book, Complementarity in Mathematics, and the interplay between the subjects of mathematics.
Are Mathematical Objects Ontologically Real? Ideas And Suggestions, Frank R. Bernhart
Are Mathematical Objects Ontologically Real? Ideas And Suggestions, Frank R. Bernhart
ACMS Conference Proceedings 1979
This essay will consider a few ways that realism in the modern philosophy of mathematics might be understood and defined.
Intuitionism, Terence H. Perciante
Intuitionism, Terence H. Perciante
ACMS Conference Proceedings 1979
Intuitionism derives philosophically from Kant's Conceptualism -- the object of the mathematical knowledge only have reality within the mind, they do not have reality apart from our thinking. This paper examines the nature of intuitionism and its strengths.
Two Philosophical Problems About Mathematics, Stephen Barker
Two Philosophical Problems About Mathematics, Stephen Barker
ACMS Conference Proceedings 1979
Mathematics is a flourishing field of human endeavor, a field that is accorded great respect and high standing. For 2500 years or more, many of the best minds available have worked in this field; and the results produced have indirectly been of enormous value to other fields, such as physics, engineering, architecture, economics, and so on. But with is mathematics about? Physics studies moving bodies; engineering studies bridges; architecture studies buildings; economics studies commercial behavior: here there are phenomena we can point to that constitute the subject matter. But what does mathematics study? If you answer “Numbers”, or “Abstract types …
Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma
Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma
ACMS Conference Proceedings 1979
This article surveys the different views of mathematical methodology that occurred from ancient Greek times through the early modern period up until its codification around 1900. After summarizing the axiomatic approach advocated by Aristotle and implemented in mathematics by Euclid, the talk explores the character of analysis in ancient Greek times, its development into a symbolic algebra by Viete and Descartes, and its expansion into a calculus of fluxions and differentials by Newton and Leibniz. The article concludes by touching on the recovery and transformation of the deductive ideal for mathematics by Pasch, Peano, and Hilbert during the late nineteenth …
Non-Standard Calculus, Ron Friewald
Non-Standard Calculus, Ron Friewald
ACMS Conference Proceedings 1979
This paper is intended to provide a very cursory introduction to how “nonstandard calculus” works, giving a sketch of how elementary calculus can be presented using hyperreal numbers.
Computer Usage In The College Curriculum, Dick A. Wood
Computer Usage In The College Curriculum, Dick A. Wood
ACMS Conference Proceedings 1979
No abstract provided.
Math & Society: An Introduction To Mathematical Thought, Verbal Snook
Math & Society: An Introduction To Mathematical Thought, Verbal Snook
ACMS Conference Proceedings 1979
No abstract provided.
Mathematics And Christian Faith - Some Personal Perceptions, Richard Laatsch
Mathematics And Christian Faith - Some Personal Perceptions, Richard Laatsch
ACMS Conference Proceedings 1979
No abstract provided.
Implications Of Recent Developments In Philosophy Of Science For An Axiological Approach To Foundations Of Mathematics, Harold Heie
ACMS Conference Proceedings 1979
No abstract provided.
Logic In The Mathematics Curriculum, Nigel Cutland
Logic In The Mathematics Curriculum, Nigel Cutland
ACMS Conference Proceedings 1979
No abstract provided.
Introduction (1979), Robert Brabenec
Introduction (1979), Robert Brabenec
ACMS Conference Proceedings 1979
No abstract provided.
Table Of Contents (1979), Association Of Christians In The Mathematical Sciences
Table Of Contents (1979), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1979
A Second Conference on the Foundations of Mathematics
Ua66/16/2 Ogden Instructional Computing Newsletter, Vol. 1, No. 1, Wku Mathematics & Computer Science
Ua66/16/2 Ogden Instructional Computing Newsletter, Vol. 1, No. 1, Wku Mathematics & Computer Science
WKU Administration Documents
Newsletter created to promote the Ogden College Computer Laboratory. This issue is a review of some projects, courses, hardware and software available from the computer lab.
Optimal 2,3-Trees, Nicholas J. Pippenger, Raymond E. Miller, Arnold L. Rosenberg, Lawrence Snyder
Optimal 2,3-Trees, Nicholas J. Pippenger, Raymond E. Miller, Arnold L. Rosenberg, Lawrence Snyder
All HMC Faculty Publications and Research
The 2,3-trees that are optimal in the sense of having minimal expected number of nodes visited per access are characterized in terms of their “profiles”. The characterization leads directly to a linear-time algorithm for constructing a K-key optimal 2,3-tree for a sorted list of K keys. A number of results are derived that demonstrate how different in structure these optimal 2,3-trees are from their “average” cousins.
Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier
Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier
ACMS Journal 2004
This paper clearly presents eight aspects of mathematics and contrasting perspectives in each that will affect the teaching of mathematics and the design of curricula. It also presents a collection of affirmations that could reasonably characterize a Christian perspective on teaching mathematics.
On The Application Of Coding Theory To Hashing, Nicholas Pippenger
On The Application Of Coding Theory To Hashing, Nicholas Pippenger
All HMC Faculty Publications and Research
Quick proofs are given for the characterization (due to Schay, Raver, Hanan, and Palermo) of the collision distance of a linear hashing function and for a dual function (called the restriction distance), which relates to the accessibility of addresses by sets of keys and the uniform distribution of sets of keys over addresses.
The Total Negation Of A Topological Property, Paul Bankston
The Total Negation Of A Topological Property, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
No abstract provided.
An Investigation Of Montmort's "Probleme De Recontres" And Generalizations, Ronald I. Greenberg
An Investigation Of Montmort's "Probleme De Recontres" And Generalizations, Ronald I. Greenberg
Computer Science: Faculty Publications and Other Works
I have investigated a problem which may be phrased in many ways, such as finding the probability of answering a given number of questions correctly on a randomly-completed matching test which may have a number of extra "dud" answers. I have determined such probabilities, the average number of correct answers, and other allied results. I have also investigated a related problem involving the number of ways of choosing a different element from each of a certain collection of sets.
Generalized Connectors, Nicholas Pippenger
Generalized Connectors, Nicholas Pippenger
All HMC Faculty Publications and Research
An $n$-connector is an acyclic directed graph having $n$ inputs and $n$ outputs and satisfying the following condition: given any one-to-one correspondence between inputs and distinct outputs, there exists a set of vertex-disjoint paths that join each input to the corresponding output. It is known that the minimum possible number of edges in an $n$-connector lies between lower and upper bounds that are asymptotic to $3n\log _3 n$ and $6n\log _3 n$ respectively. A generalized $n$-connector satisfies the following stronger condition: given any one-to-many correspondence between inputs and disjoint sets of outputs, there exists a set of vertex-disjoint trees that …
Existence In Mathematics, Willis Alberda
Existence In Mathematics, Willis Alberda
ACMS Conference Proceedings 1977
Contemplation of the existence of mathematical entities for very apparent reasons generates a mental cycling of arguments dealing with the nature of mathematical truth, meaning in mathematics, and the obviously related question of which of these two problems should be solved first. The problem of the existence of mathematical entities dates from the first thoughts and ideas of a mathematical nature. The problem of existence in mathematics is fundamental to the domain of speculation and research on the foundations of mathematics. When we try to put ourselves in the place of those philosophers who first explored this problem we must …
Infinity & Reality, John W. Warner
Infinity & Reality, John W. Warner
ACMS Conference Proceedings 1977
This paper examines the topics of infinity and reality as relevant to the conference, proposing a possible relationship between the two in order to stimulate further discussions.
Epistomology To Ontology, Charles R. Hampton
Epistomology To Ontology, Charles R. Hampton
ACMS Conference Proceedings 1977
This paper offers commentary on the various philosophical approaches to the foundations of mathematics and then indicates how these ideas have implications in consideration of the existence question.
Recent Problems In The Foundationsof Mathematics, Terence H. Perciante
Recent Problems In The Foundationsof Mathematics, Terence H. Perciante
ACMS Conference Proceedings 1977
This paper examines the foundational crises that have haunted twentieth-century mathematics, beginning with a brief review of the effects generated by Gauss, Lobachevsky, and Bolyai who each developed non-Euclidean parallel axiom. Though of mathematical interest in their own right, the significance of the new geometries was greatly magnified when it was discerned that they could be used to adequately model physical space, even to the extent that Einstein’s theory of relativity later employed as its model a non-Euclidean geometry developed by Riemann. The question that obviously presented itself was how could any given geometry be called true when it and …
The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis
The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis
ACMS Conference Proceedings 1977
In teaching the foundations of mathematics within the framework of a Christian college, and particularly that of a Christian liberal arts college, there are two groups of students which must be served. The first consisted of the non-mathematics majors—those non-scientifically oriented “general anything” students who, as a catalog might put it, are to receive “an introduction to and an appreciation of the history, foundations, culture and applications of mathematics.” The second group consists of the mathematics majors, and the few science majors who have not been frightened away by the calculus. The gulf between these two groups is sufficiently large, …
A Brief Introduction To Gödel’S Theorems, Michael Detlefsen
A Brief Introduction To Gödel’S Theorems, Michael Detlefsen
ACMS Conference Proceedings 1977
Gödel’s two famous incompleteness theorems are results that have come up a number of times in the discussions at the 1977 ACMS conference. This paper provides a brief and relatively non-technical statement on these results and of their significance for the foundations of mathematics.
Current Work On Mathematical Truth, Michael Detlefsen
Current Work On Mathematical Truth, Michael Detlefsen
ACMS Conference Proceedings 1977
The overall aim of this paper is to serve as an introduction to the work currently being done on the topic of mathematical truth. It provides an overview of the major developments concerning mathematical truth and also evaluates those developments as potential contributions to mathematician’s understanding of the subject.