Browsing Mathematics Senior Integrated Projects by Author "Bausch, Augustus Frank, 19201973"
Now showing items 120 of 20

Algorithms
Pirog, Diane Carole (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. ... 
Criticism of the Theory of Transfinite Numbers
Dickerson, Douglas Stephen (Kalamazoo College, 1970)This paper will attempt to deal with two aspects of Cantor's achievement. First it will give a brief survey of the theory of transfinite numbers, pointing out its use of the.axiom of choice which historically has been the ... 
The Development, Derivation, and Classical Application of the Utility Function in DecisionTheory
Wild, Gary Lauren (Kalamazoo College, 1965)This study was made to present a fairly unified and overall view of the utility concept in decision theory. As yet, only a small amount of literature has been presented from the mathematical standpoint, that deals with ... 
An Explication of System EI, The Pure Calculus of Entailment, developed by Alan Ross Anderson and Nuel D. Belnap Jr., with special attention given to their position concerning the paradoxes of implication
Steward, John Richard (Kalamazoo College, 1971)In this paper, we wi11 focus on system EI and the arguments, presented by Anderson and Belnap, for rejecting the paradoxes of implication, 1nc1ucling the disjunctive syllogism (p & (p v q)  q). We will also examine ... 
Fundamental Concepts of Category Theory
Hocker, Walter (Kalamazoo College, 1970)This paper will not go into what is being done in category theory. Its purpose is to give a clear picture of the essential terms of the theory: category, functor and natural transformation. 
Georg Cantor's MathematicalPhilosophical Theory: Selected Translated Excerpts
Davis, Gregory Mark (Kalamazoo College, 1970)The three essays that form the body of this paper were translated (from the German) as they appear in Georg Cantors Gesannnelte Abhandlungen (Cantor's collected works), edited by E. Zermelo (page·s 171183, 370377, 440442, ... 
Infinity
Belski, William (Kalamazoo College, 1971)In this paper we will trace the changing notion of infln1ty throughout Western thought. In the first part ideas from both mathematics and philosophy wl11 be brought together, for often in discussions on infinity the ... 
Introduction to the Theory of Games: Finite ZeroSum Two Person Games
Wolofski, Susan Mae (Kalamazoo College, 1968)The intent of this paper is to present an introduction to the theory of matrix games, with particular emphasis on the different approaches to the solution of such games. Although I have rearranged material and ... 
An Introductory Study of Hyperbolic Geometry
Foreman, Jack (Kalamazoo College, 1965)The object of this paper is to develop Hyperbolic geometry using, as tools, only the postulates and propositions of Euclid (excluding the ones dealing with parallel lines) and the tools of logic. To the best of my ... 
The Intuitionist Reconstruction of Mathematics
Nussbaum, Mitchell Steven (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 ... 
Linear Programming: An introduction with emphasis on the cycling phenomenon of linear programming
Hayward, Thomas J. (Kalamazoo College, 1964)It is the general intent of this thesis to, in the first part, develop and explain the procedure of Dantzig's simplex method in solving linear programming problems. The second part is devoted to an investigation into ... 
Logic in Practice: ModelTheoretic Completeness
Fay, Thomas (Kalamazoo College, 1971)Model theory is unusual as a field where the abstract and ''impractical" machinery of logic has concrete applications. The abstract quality of logic lends a generality to model theory which is a real asset, allowing a ... 
A Logical Development of Arithmetic as Based on the Theories of Guiseppe Peano and Gottlob Frege
Rudell, Lucinda Robbins, 19471990 (Kalamazoo College, 1969)The search for a foundation from which all of mathematics can be developed through prescribed motions is a pursuit that in the past has always failed. Even while concepts today considered elementary were causing arguments ... 
Mathematical Existence in the Theory of Sets
Walkoe, Wilbur J., Jr. (Kalamazoo College, 1963)The purpose of this paper is to trace some of the developments arising directly out of the crisis in set theory, in terms of the various views they embody of the nature and existence of their subject matter. Three viewpoints ... 
Mathematical Linguistics and the Rationalists
Opie, Lawrence Kenneth (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 ... 
On von Neumann's Model of an Expanding Economy
Howard, James M. (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. ... 
Random Walk Theories of the Stock Market
Kodiak, Karl Thomas (Kalamazoo College, 1972)If one could predict future prices of var10us stocks in the stock market, one could make a fortune. Because of this, many theories dealing with future stock price changes have been developed, but no single theory has ... 
The Sematic Definition of Truth in Formalized Languages
Huddlestone, John (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 ... 
Twelfth Grade Mathematics: A Summary of Changes and a Review of New Possibilities
Pifer, James Wright (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. ... 
Wind and Current Study at Detroit's Metropolitan Beach
Strong, Alan E. (Kalamazoo College, 1962)It was decided that pertinent studies to be carried out in the Beach area should be measurement of water current and wind. A current indicator was built early in t he summer. The unit built was a cylindrical structure about ...