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Articles 2341 - 2370 of 2379

Full-Text Articles in Mathematics

Intuitionism, Terence H. Perciante Jun 1979

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.

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Two Philosophical Problems About Mathematics, Stephen Barker Jun 1979

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 …

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Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma Jun 1979

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 …

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Non-Standard Calculus, Ron Friewald Jun 1979

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.

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Computer Usage In The College Curriculum, Dick A. Wood Jun 1979

Computer Usage In The College Curriculum, Dick A. Wood

ACMS Conference Proceedings 1979

No abstract provided.

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Math & Society: An Introduction To Mathematical Thought, Verbal Snook Jun 1979

Math & Society: An Introduction To Mathematical Thought, Verbal Snook

ACMS Conference Proceedings 1979

No abstract provided.

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Mathematics And Christian Faith - Some Personal Perceptions, Richard Laatsch Jun 1979

Mathematics And Christian Faith - Some Personal Perceptions, Richard Laatsch

ACMS Conference Proceedings 1979

No abstract provided.

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Implications Of Recent Developments In Philosophy Of Science For An Axiological Approach To Foundations Of Mathematics, Harold Heie Jun 1979

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.

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Logic In The Mathematics Curriculum, Nigel Cutland Jun 1979

Logic In The Mathematics Curriculum, Nigel Cutland

ACMS Conference Proceedings 1979

No abstract provided.

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Introduction (1979), Robert Brabenec May 1979

Introduction (1979), Robert Brabenec

ACMS Conference Proceedings 1979

No abstract provided.

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Table Of Contents (1979), Association Of Christians In The Mathematical Sciences May 1979

Table Of Contents (1979), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1979

A Second Conference on the Foundations of Mathematics

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Ua66/16/2 Ogden Instructional Computing Newsletter, Vol. 1, No. 1, Wku Mathematics & Computer Science Apr 1979

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.

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Optimal 2,3-Trees, Nicholas J. Pippenger, Raymond E. Miller, Arnold L. Rosenberg, Lawrence Snyder Jan 1979

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.

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Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier Jan 1979

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.

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On The Application Of Coding Theory To Hashing, Nicholas Pippenger Jan 1979

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.

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The Total Negation Of A Topological Property, Paul Bankston Jan 1979

The Total Negation Of A Topological Property, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

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An Investigation Of Montmort's "Probleme De Recontres" And Generalizations, Ronald I. Greenberg Dec 1978

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.

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Generalized Connectors, Nicholas Pippenger Jan 1978

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 …

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Existence In Mathematics, Willis Alberda Apr 1977

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 …

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Infinity & Reality, John W. Warner Apr 1977

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.

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Epistomology To Ontology, Charles R. Hampton Apr 1977

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.

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Recent Problems In The Foundationsof Mathematics, Terence H. Perciante Apr 1977

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 …

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The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis Apr 1977

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, …

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A Brief Introduction To Gödel’S Theorems, Michael Detlefsen Apr 1977

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.

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Current Work On Mathematical Truth, Michael Detlefsen Apr 1977

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.

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Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley Apr 1977

Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley

ACMS Conference Proceedings 1977

Following World War I European philosophy of science formed an alliance with mathematics culminating in an attitude of certainty and autonomy that rejected all non empirical claims to truth and purported to make all science presupposition less. The rise and fall of logical positivism has been one of the major themes of of twentieth century thought and illustrates the danger of placing too much emphasis on science and mathematics as an ideal for all knowledge. The restriction of rational inquiry to the modes of scientific verification and the processes of mathematical logic was far too confining for the containment of …

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Formalizing The Liar Paradox, Frank Meyer Apr 1977

Formalizing The Liar Paradox, Frank Meyer

ACMS Conference Proceedings 1977

No abstract provided.

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God: All Sufficient Or Infinite, Thomas E. Iverson Apr 1977

God: All Sufficient Or Infinite, Thomas E. Iverson

ACMS Conference Proceedings 1977

No abstract provided.

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Getting Their Interest - Initiating Students Into The Study Of Foundational Issues In Mathematics, Harold Heie Apr 1977

Getting Their Interest - Initiating Students Into The Study Of Foundational Issues In Mathematics, Harold Heie

ACMS Conference Proceedings 1977

No abstract provided.

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Wanted: Christian Perspectives In The Philosophy Of Mathematics, Arthur F. Holmes Apr 1977

Wanted: Christian Perspectives In The Philosophy Of Mathematics, Arthur F. Holmes

ACMS Conference Proceedings 1977

This paper describes the three types of theory about universals, beginning in each case with a classical historical formulation and moving to its restatement in recent analytic philosophy. It will then suggest ways in which Christian perspectives bear on theories of universals and so on mathematics.

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