Browsing Mathematics Senior Individualized Projects by Title
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Bases for Integer Generalized Splines on Graphs, an Investigation
(Kalamazoo College, 2017)Let R be a ring and G a graph whose edges are labeled by ideals of R. A vertex labeling of G by elements of the ring is called a generalized spline if for each edge, the difference of the labels of the two connected vertices ... 
Bursting Oscillations along the Axon of a Neuron
(Kalamazoo College, 1993)The body transfers electrical signals from one part to another by means of neurons. The first relatively complete mathematical model of nerve conduction was published by Hodgkin and Huxley. They. subsequently won the ... 
Calculating Equivariant Homotopy Groups
(Kalamazoo College, 2003)The study of algebraic invariants of topological spaces is an important part of topology. We find, for example, that the problem of distinguishing spaces from each other can often be answered by examining homotopy gro ... 
Characteristic Behavior of Dynamics on the Interval : From Cycles to Chaos
(Kalamazoo College, 2000)Presents examples and proofs for the Tent Map, with Periodic Points, Chaotic Points, and Inverse Limit Spaces. 
A Characterization of the Irreducible Representations of the Group of Rotations
(Kalamazoo College, 1973)The theory of group representation is a powerful synthesis of the properties of matrices and groups. It was developed at the turn of the century by the German mathematician F.G. Frobenius. Several contributions were also ... 
A Climatological Investigation of Global Dimming at Blue Hill Observatory, Milton, MA
(Kalamazoo College, 2008)Although much less heralded than global warming, global dimming is an equally remarkable and important climataological phenomenon. Throughout a majority of the second half of the 20th century a widespread and significant ... 
A Clinical Study of an Automated Regional Citrate Anticoagulation Protocol in Patients with Severe Renal Failure
(Kalamazoo College, 2010)Regional citrate anticoagulation (RCA) in sustained, lowefficiency, dialysis (SLED), has been found to be a more safe and effective alternative to hemodialysis. The Division of Nephrology and Hypertension at Henry Ford ... 
Code Generating Programs: Using the Computer to Instruct Itself
(Kalamazoo College, 1981)Asgrow Seeds, a subsidiary of the Upjohn Company, is a nationwide distributor of corn, sorghum and soybean seeds. In a continuing effort to improve the quality of their products Asgrow helps sponsor tests run by independent ... 
Combinatorial Optimization: The Traveling Salesman Problem
(Kalamazoo College, 1991)Optimization is the process of finding the best (or optimal) solution to a problem. For many realworld problems. there may be a large number of possible solutions, even an infinite number. Optimization seeks to find ... 
Communication Links to Superconputers: Automating the Distribution of Output
(Kalamazoo College, 1983)My SIP quarter was spent at Argonne National Laboratory as a participant in the Student Research Program. Argonne National Laboratory is a contract laboratory of the United States Department of Energy, located near Chicago. ... 
Commutativity of the Heisenberg Group
(Kalamazoo College, 2010)The Heisenberg group, named for Werner Heisenberg, is the group of upper triangular 3x3 matrices with ones down the diagonal. The group is not abelian, but shows many signs of"commutativity. It's center and commutator ... 
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 ... 
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 ... 
Complex Behavior in a Nerve Conduction Model
(Kalamazoo College, 1993)The phenomenon of bursting oscillations, a behavior found in many biological and chemical systems, consists of complex periodic oscillations (active phases) separated by quasisteady states (silent phases). Many of the ... 
Computer Simulation of Weak Shock Propagation in a ShockTube
(1974)The purpose of this research was to become familiar with the iterative method and to apply this technique to further the understanding of the previous shocktube experiments. It was anticipated that the previous results ... 
The Conjugacy Classes of SL2 (IR)
(Kalamazoo College, 1998)This paper is the result of my participation in the Undergraduate Program of the 1998 Park City Mathematics Institute Summer Session, as well as my individual work with Dr. John Fink for the remainder of that summer. ... 
Connected Sums and Decompositions of Plane Curves
(Kalamazoo College, 2000)Despite recent advances, the problem of plane curve classification remains unsolved. One possible aid in classification would be to examine compositions and decompositions of curves. We use the connected sum action to do ... 
Continued Fraction Theory
(Kalamazoo College, 1970)I have divided this paper on the theory of continued actions into five sections. The first section consists of general basic theorems in the theory, many of which  in particular, theorem 1.1  are used throughout the ... 
Cost Versus Quality of Care: Hospitalists and Their Impact on Eight Diagnosis Related Groups
(Kalamazoo College, 2002)This study will attempt to analyze some of the quantitative differences between the inpatient management performance of hospitalists, primary care physicians, and teaching service physicians using several factors for ... 
Covering Theorems in the Alternating Group
(Kalamazoo College, 1978)It was shown by Ore [1951] that each element of A n, the alternating group on n letters, is a commutator, abalb1 for some a and b in S n. Xu (1965] went further and showed that, given an element a in A n then, given any ...