Browsing Mathematics Senior Individualized Projects by Issue Date
Now showing items 120 of 249

The SelbergErdos Elementary Proof of the Prime Number Theorem
(Kalamazoo College, 1962)This is a paper dealing with a proof in the theory of numbers in particular it is from prime number theory dealing with the distributions of the primes. Unlike many other branches of number theory, distributional prime ... 
Wind and Current Study at Detroit's Metropolitan Beach
(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 ... 
Mathematical Existence in the Theory of Sets
(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 ... 
On Curves of Constant Breadth
(Kalamazoo College, 1963)This paper is concerned with figures of constant breadth. When the term constant width is used it is to mean the same as constant breadth. The terms are used interchangeably in the field. To provide a certain amount of ... 
Elementary Transcendental Functions of a Real and Complex Variable
(Kalamazoo College, 1964)The first chapter contains a description, rather than a development, of the real number system, and ends with some ideas about rational approximation to irrational numbers. This chapter serves primarily as an introduction ... 
An Introduction to the Mathematical Theory of Linear Programming
(Kalamazoo College, 1964)This paper is an attempt to provide a relatively selfcontained and basic mathematical justification for the LP problem and the simplex method of solving it. The first two parts of the paper outline the aspects of the ... 
Linear Programming: An introduction with emphasis on the cycling phenomenon of linear programming
(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 ... 
A Study of the Differences between Consecutive Prime Numbers
(Kalamazoo College, 1964)This paper will present heuristic arguments concerning the distribution of prime numbers and the spacings between consecutive primes. So that the reader will be familiar with some of the background material for this ... 
An Exposition of Hadamard Matrices
(Kalamazoo College, 1964)The purpose and aim of this paper will be to acquaint the reader with the development of these matrices and the methods used to determine their existence. The beginning section will consist of definitions which are intended ... 
Odd Perfect Numbers
(Kalamazoo College, 19640420) 
A Development of the Loop Concept
(Kalamazoo College, 19640421)The purpose of this thesis is to present in as lucid a manner as possible, the various properties of the abstract binary system defined as a loop. Special emphasis will be placed on the comparative development of other ... 
Design
(Kalamazoo College, 1965) 
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, ... 
A Generalized Program in Numerical Analysis
(Kalamazoo College, 1965)The first section, "Use of the Program", describes how to do various types of problems with the program. It is written for a person with a minimal knowledge of computer operation and no knowledge of programming. The ... 
An Introductory Study of Hyperbolic Geometry
(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 ... 
Euclid's Parallel Postulate
(Kalamazoo College, 1965)The development of the paper proceeds chronologically, with a few minor exceptions, from the beginnings of geometry up to the discovery of nonEuclidean geometry, of which a short summary is appended. No knowledge of ... 
The Origin of PointSet Topology
(Kalamazoo College, 1965)I have restricted my researches to the origin of general topology and carried my work past 1900. Within this framework, going back before Cantor's conception of set theory (18791884) is of little specific importance; ... 
Mathematical Proportions in Modern Architecture
(Kalamazoo College, 1965)This thesis combines the history of symmetry and proportion with a practical application of each to modern architecture. This application of knowledge and skills gained through research was introduced in the hope that ... 
A History of Some Polynomial Equations
(Kalamazoo College, 1965)This paper is an historical tracing of the beginnings of certain mathematical ideas through Greek, Indian, Muslim, Italian, and finally modern European mathematics. Not in the least sense is part of mathematics studied ... 
A Comparison of Three "New" High School FirstYear Algebra Courses
(Kalamazoo College, 1965)It is the intention of this thesis to compare the abovementioned curricula in the various areas that are covered in the firstyear algebra course. It shall also be shown how these new methods are superior to the ...