Digital Commons Network^™

Mathematical Reflections: Standing On The Shoulders Of Giants, Karl J. Smith

ACMS Conference Proceedings 1987

The layperson's response to mathematics is often that of desperation. When we tell people our occupation, do we more often than not hear about their unpleasant experiences with mathematics. They often tell us, "I studied algebra in high school and haven't used it since!" Indeed, that may be true. However, we can reply, "How many times has algebra been used on you?" We are all restricted, and protected, by the formulas of mathematics. In the mysterious metaphors we have agreed to cal mathematics, all creation is involved, from the symbol-happy logician down to the cunning geometers, the bees. When I …

Observations On Mathematics And The Christian Faith, W. David Laverell, Carl J. Sinke

ACMS Conference Proceedings 1987

There is little doubt that mathematicians are becoming more concerned with the foundations on which their discipline rests, the meaning of their work, and the philosophical stance implicit in what they do. This concern is prompted by serious questions which have been raised in recent years, questions dealing with the nature of mathematical truth, the nature of proof, certainty (or lack thereof) in mathematics, and the relationship of mathematics to the physical world. This has been particularly true for those of us involved in teaching since it is apparent that good mathematics education cannot ignore these issures.

Proof And Intution, Michael Detlefsen

ACMS Conference Proceedings 1987

This paper discusses various perspectives on proof and intuition by examing two epistemic systems, Intuition Intensive and Logic Intensive, and Jules Henri Poincaré's objections to the latter.

Logic And Proof For Mathematics: A Twentieth Century Perspective, Calvin Jongsma

ACMS Conference Proceedings 1987

This talk reports on the author's experience in teaching college mathematics students the basics of logic and proof in preparation for their transitioning to upper-level proof-based mathematics courses, following that up with a philosophical and historical analysis of mathematicians' attitudes toward such a project going back to nineteenth- and twentieth-century developments in logic and foundations (De Morgan, Boole, Frege, Russell, and Hilbert). The natural deduction approach to logic and inference developed in the mid-twentieth century by Jaskowski and Fitch is recommended as a much better focused approach for learning how to do proofs in mathematics. This idea is systematically developed …

Riesz Spaces And Their Applications In Economics, Calvin E. Piston

ACMS Conference Proceedings 1987

We will examine an economic model of pure exchange and some results concerning different notions of equilibrium. In particular, we will focus on the role played by the theory of Riesz space.

Variations On A Theme, Robert Creighton Buck

ACMS Conference Proceedings 1987

An autobiographical narration by Robert Creighton Buck, detailing his experiences in the field of mathematics, and the various questions and themes reoccurring in the mathematical sciences.

The Role Of Computer Science In A Liberal Arts College, Russell C. Bjork

ACMS Conference Proceedings 1987

The question the panel has been asked to discuss actually encompasses two related, but distinct, questions - each of which, in turn, has two subquestions.

The first question concerns the place of a computer science as a major program of study among the offerings of a liberal arts college. The two subquestions here are as follows: First, is computer science an appropriate field of study to offer in a liberal arts college? (Is it a liberal art?) Second, is a liberal arts college an appropriate home for a computer science program? (Can a high quality program be offered in such …

Another Look At Pick's Theorem, Dale Varberg

ACMS Conference Proceedings 1987

In this paper, the author discusses his experience building a proof for Pick's Theorem and theorem's history.

Computer Science In Liberal Arts Colleges, James Bradley

ACMS Conference Proceedings 1987

This paper looks at the strengths and weaknesses of computer science curricula and how liberal arts colleges can best teach the concepts of mathematics required in computer science.

An Activist Model Of The Metaphysics Of Mathematics, Christopher Menzel

ACMS Conference Proceedings 1987

No abstract provided.

Conic Sections In Ip, Richard Laatsch

ACMS Conference Proceedings 1987

No abstract provided.

3:16 - An Approach To Bible Study, Donald E. Knuth

ACMS Conference Proceedings 1987

No abstract provided.

Introduction (1987), Paul Zwier

ACMS Conference Proceedings 1987

A Sixth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec

Table Of Contents (1987), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1987

A Sixth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec

Asymptotic Study Of Estimators In Some Discrete And Continuous Time Model., Arup Bose Dr.

Doctoral Theses

This thesis deals with an asymptotic study of estimatore in some discrete time and continuOus time models.The firet part deele with time eeriee date modelled by moving sverage and eutoregreseive proceseee. Higher order as ymptotioe beyond. as ymptotio normality, of the usual astimatore heve been dealt by Phillipe (1977,1978), Durbin (198o), Oohi (1983), Tanaka (1983), Fujikoshi and Ochi (1984). o(n-1/2) or o(n-1) expenaions ara 'obteined by these authore under the assumption of normality of orrors. The reason for this wes the lack of suitable. expaneions for normalized sums of dependent random vectora. Recently Gotza and Hipp (1983) heve been able …

Rise To Power Of Senator Joseph R. Mccarthy: Reflections Of The Cold War Mccarthy Era In American Film, Scott Lainer

Honors Theses

The common bond between much of the film industry and Joseph McCarthy was insecurity and the drive for national approval. If one grasps the specific characteristics of McCarthy the man, and the methods of these politically "inspired" movies, we can to better place the period into context and acknowledge the fact that, if the citizenry is not aware, and is again caught by an ever-building wave of trickle down sentiment, the 1950s might not prove to be an isolated period in American history. Insecurity was not a fifties novelty. It still exists, and could potentially escalate anti-Communist policy and sentiment …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Comparative Instructor Attitudes Toward College Level English And Mathematics Experiences For Gifted High School Students, Bruce Vickers

Masters Theses & Specialist Projects

Samples derived from a mailed questionnaire were compared. The sample represented high school, community college and university instructors of mathematics and English. The Kentucky public schools sampled were equally represented among high school, community colleges and universities. The research indicated that of those instructors sampled a very high percentage (97.7%) feel that those high school students shown to be academically gifted would benefit from a college experience before high school graduation. The attitudes of those instructors sampled indicated that multiple criteria – grades, recommendations, standardized test scores and personal interview – were considered the preferred method of selection (82.5%). The …

On Root Invariants Of Periodic Classes In Exta(Z/2,Z/2), Paul L. Shick

Mathematics and Computer Science

We prove that if a class in the cohomology of the mod 2 Steenrod algebra is υ_n-periodic in the sense of [10[, then its root invariant must be υ_n+1-periodic, where υ_n denotes the nth generator of π∗(ΒΡ).

Least-Change Secant Updates Of Non-Square Matrices, Samih Kassem Bourji

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In many problems involving the solution of a system of nonlinear equations, it is necessary to keep an approximation to the Jacobian matrix which is updated at each iteration. Computational experience indicates that the best updates are those that minimize some reasonable measure of the change to the current Jacobian approximation subject to the new approximation obeying a secant condition and perhaps some other approximation properties such as symmetry.

All of the updates obtained thus far deal with updating an approximation to an nxn Jacobian matrix. In this thesis we consider extending most of the popular updates to the non-square …

A Sharp Partitioning-Inequality For Non-Atomic Probability Measures Based On The Mass Of The Infimum Of The Measures, Theodore P. Hill

Research Scholars in Residence

If μ₁, ... ,μ_n are non-atomic probability measures on the same measurable space (S, F), then there is an F-measurable partition {A_i }ⁿ_{i = 1} of S so that μ₁ (A_i )≥ (n – 1 + m)^–1 for all i=1, ..., n, where m = ∥ Δⁿ_i=1 μ_i∥ is the total mass of the largest measure dominated by each of the μ_i's; moreover, this bound is attained for all n≥1 and all m in [0, 1]. …

Logic And Proof For Mathematicians: A Twentieth Century Perspective, Calvin Jongsma

Faculty Work Comprehensive List

If there is one aspect of mathematics education that frustrates both students and teachers alike, it has got to be learning how to do valid proofs. Students often feel they really know the mathematics they're studying but that their teachers place some unreasonably stringent demands upon their arguments. Teachers, on the other hand, can't understand where their students get some of the wacky arguments they come up with. They argue in circles, they end up proving a different result from what they claim, they make false statements, they draw invalid inferences - it can be quite exasperating at times! Unfortunately, …

Partitioning General Probability Measures, Theodore P. Hill

Research Scholars in Residence

Suppose μ₁, ..., μ_n are probability measures on the same measurable space (Ω, F). Then if all atoms of each μ_i have mass α or less, there is a measurable partition A₁,..., A_n of Ω so that μ_i(A_i) ≥ V_n(α) for all i = 1, ... , n, where V_n(•) is an explicitly given piecewise linear nonincreasing continuous function on [0, 1]. Moreover, the bound V_n(α) is attained for all n and all α. Applications are given to L₁ spaces, to …

Periodic Phenomena In The Classical Adams Spectral Sequence, Mark Mahowald, Paul L. Shick

Mathematics and Computer Science

We investigate certain periodic phenomena in the classical Adams spectral sequence which are related to the polynomial generators υ_n in π∗(ΒΡ). We define the notion of a class α in Ext_Α(Ζ/2,Ζ/2) being υ_n-periodic or υ_n-torsion and prove that classes that are υ_n-torsion are also υ_κ-torsion for all κ such that 0 ≤ κ ≤ n. This allows us to define a chromatic filtration of Ext_Α(Ζ/2,Ζ/2) paralleling the chromatic filtration of the Novikov spectral sequence Ε₂-term …

Extensions Of Gromov Theory., Sumanta Guha Dr.

Doctoral Theses

Gromov formulated and proved a very general Smale - Hirsch - Phillips type theorem. The theorem concerns the claseification of a class of cross-sections o of a smooth fibre bundle E X over a non-closed manifold X such that each r-jet j(0) satisfies an openness condition as well es a stability condition. Briefly, the openness condition is that each j(a) is a cross-section of some preacribed open subbundle of the bundle of r-jets of local oross- sections of EX, and. the etability condition is that this subbundle remain invarient under the action of the paeudogroup of local diffeo- morphisme of …

Studies On Optimality Of Some Classes Of Designs., Rita Saharay Dr.

Doctoral Theses

la. General Dbaervations and Literature ReviewExperimentation playe an easential role in moet of the atatistioal investigations carried out for drawing inferences about certain unknown parametera of interest. If the eituation allowe for only one experiment to be executed out of a number of available alternative experiments, the experimenter ehould sim at perfoming the one which le optimum in This ie how the problem of ohooeing the beet experiment some sense. comes up.To judge the relative performances of various statistical exf mente, Blackwell (1951, 1953) and Blackwell and Girahiok (1954) introduced the concopt of sufficient experiments . However, in the ontext …

An Essay On The Formation And Dynamics Of The Marketed Surplus And Price Of Foodgrains., Vathsala Narasimhan Dr.

Doctoral Theses

The the sde is baadcally a methodological exploration of the field we have Celled the ti end d eted and price of foodgrains. The object ie basically to develop a framework of thought, developing alongaide the toola, concepte and methods necessary for the purpose. In doing this we keep entirely to the baaic structure of the field as ve see it, which is defined in reference to a few bare elenentary facts pertaining to our general context of reference the rest is simply abstracted from. Our whole approach 1a thus 8crictiy anRALA mothodology is oxplored within boundaries that we ourselves …

Estimation Of Demographic Parameters For India., S. Guha Roy Dr.

Doctoral Theses

There has been a peralstent empliasis both at the na tional and international levela on the developmont and application of techniques of estimation of demographio variablos from incomplete or inagcurute data in Coneietont wi th the theme of reuoaroh, the the lesu developed rogiona. present study tries to provide estimates of vital rates and prospective population trends in India and to form a basis for measuri.ng suoh hunan neede as vducation, employment, f'anily weltare,and few others in terms of population size,growth, ago s truature and nuptiality. The other major objectivu is to undertake furthor utilization of data generated by tihe …

Multisectoral Model Of Income Distribution Poverty And Growth:Some Policy Exercies For Indian Economy., Debdas Bandyopadhyay Dr.

Doctoral Theses

The extent of poverty in any country depends upon two factors vlz, the average level of income anxd the degree of inequality in its distribution. The central theme in the continuing debate on the relationship between growth and poverty is whether past growth process in the developing countries has caused any signi.licant benefit to the poor. Kuznets (1955) was first to observe from cross country data that procosa of development is likely to be accompanied by increase in inequality, whhich would reverse itself only at a relatively advanced stage. This hypothesis has been subsequently confirned to some extent by several …

Studies In Set Theoretic Hierarchies:From Borel Sets To R-Sets., Rana Barua Dr.

Doctoral Theses

The present thesis consists of three parts.Part I of the thesis is devoted to the study of regularity propertion of classes of sets obtained from 8-8 operations applied to the class of clopen set s. In particular, the classes of set s obtained by applying the hierarchy of increasingly complex R-operations {Rp,), are investing at ed. Our points of departure in this study are the recent works on R- sets by Hi nm an and Burgess. In this thesis we have unified the methods of Hinman and Burgess by extensively u sing the game quantifier and methods of inductive definability. …