Browsing Mathematics Senior Integrated Projects by Issue Date
Now showing items 2140 of 274

The Experimental Works of Jean Piaget and a Discussion of Their Educational Implications
(Kalamazoo College, 1965)The first part of this paper is a rather lengthy and detailed summary of the experimental works of Piaget in the areas of number and geometry. I had a number of reasons for making the summary so detailed. Unfortunately, ... 
The Intuitionist Reconstruction of Mathematics
(Kalamazoo College, 1966)The intent of this paper is to indicate some of the ways in which mathematics may be developed under intuitionist requirements. In Chapter 2, real numbers are developed informally, following Heyting 1956. In later chapters ... 
On von Neumann's Model of an Expanding Economy
(Kalamazoo College, 1966)In the present paper the method of proof is quite different from that in von Neumann's original article. The three proofs of existence herein involve game theory while the original proof involves elements of topology. ... 
Orthogonality and Related Ideas
(Kalamazoo College, 1966)The primary purpose of the following material was to provide a learning experience for the author by involving him in an area in which he had not previously worked, by posing, as a problem to him the explanation of some ... 
Twelfth Grade Mathematics: A Summary of Changes and a Review of New Possibilities
(Kalamazoo College, 1966)This paper evolved from my desire to learn more about new reforms in secondary school mathematics. Through conversations with Dr. Calloway, I decided that the twelfth grade offered the greatest number of possibilities. ... 
NonAssociative Number Theory: Meditations Upon an Article by T. Evans
(Kalamazoo College, 1966)The course of' learning tor a college math student is a search for unity. Throughout his four years of study, he is constantly trying to organize vectors, groups, differentials, integrals, and the like, into a meaningful. ... 
Programming the IBM 1620 Digital Computer to Bid Contract Bridge
(Kalamazoo College, 1966)It may be of interest to the reader to understand the goal of this project, if indeed, there was any one goal. The project was not undertaken in order to prove any hypothesis or reach any profound conclusions . It was ... 
Algorithms
(Kalamazoo College, 1966)This paper is concerned with the general problem of theorem proving within a first order predicate logic. The topic was chosen as a result of simultaneous but separate interests in symbolic logic and Computer sciences. ... 
The Sematic Definition of Truth in Formalized Languages
(Kalamazoo College, 19660505)In this paper I have attempted to survey the problem of defining the truth set in formalized languages. Although the intuitive conceptions involved are fairly simple, the technical requirements of the definition are ... 
Mathematical Aspects in the Freeway Merging Situation
(Kalamazoo College, 1967) 
A Comparison of Two "New Math" Geometry Texts and the Historical Development of their Foundations
(Kalamazoo College, 1967)The two "new math" texts which I am comparing in this paper are, The School Mathematics study Group (SMSG) high school geometry text, and the Ball State geometry text. I should qualify the use of "comparing", for I am ... 
Machine Translation of German to English
(Kalamazoo College, 1967)The purpose of this study was to look into the possib1l1ties of translating oonversat1onal German sentences into English sentences. Some computers are capable of translating upwards of 50,000 words per hour, while ... 
Solutions of Selected Problems as Posed by Walter Rudin in His Book: "Principles of Mathematical Analysis"
(Kalamazoo College, 1967)This paper cannot be read without the accompanying use of the second edition of Walter Rudin's Principles of Mathematical Analysis. The problems and chapters are both numbered in accordance with this book, and I have also ... 
Information Theory
(Kalamazoo College, 1967)This is a purely expository paper. The concepts come primarily from Shannon's intuitionbased proofs and Khinchlo's more rigorous ones; all definitions come from these sources. Intermediate steps and some short proofs ... 
Differential Forms
(Kalamazoo College, 1967) 
A Programmed Job Shop Simulator
(Kalamazoo College, 1967)This project has four main purposes. First, it was written to give the area engineers within the Upjohn Company a valuable tool for decision making concerning the job shops which they direct. Second, it is to ... 
A Gernalized Questionnaire Analyzer Program Specifically Used for the Danforth Study
(Kalamazoo College, 1967)In doing this this thesis I had the privilege of working with the Danforth Foundation in its evaluation of the total experience derived at Kalamazoo College. The greater emphasis was placed on the four years of academic ... 
The Structural Theorems on Infinite Abelian Groups
(Kalamazoo College, 1967)General Abelian group theory is a branch of algebra that has achieved several satisfactory structural theorems. The aim of this paper is to discuss the most important of these theorems so as to give an overview of this ... 
A Study of the nersenne Numbers
(Kalamazoo College, 1967)The purpose of this paper is, as the title suggests, to study the Mersenne numbers. This topic was chosen for, to my knowledge, there exist few papers which deal exclusively with the Mersenne numbers. Rather, there exist ... 
Mathematical Linguistics and the Rationalists
(Kalamazoo College, 1968)The purpose of this paper is to make clear the position of the Rationalist school of language study and its reliance on machinery provided by the Foundation of Mathematics. Thus the main thrust of this paper is at the ...