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Full-Text Articles in Physical Sciences and Mathematics
A Qualitative Analysis Of Differential Equations Of Population Dynamics, Kevin Brenner
A Qualitative Analysis Of Differential Equations Of Population Dynamics, Kevin Brenner
Honors Theses, 1963-2015
An exploration of systems of equations modeling closed hypothetical ecosystems. Models are formed from biological assumptions about population. Models are constructed by combining or modifying simpler systems. The simple models used in constructing systems are the logistic, competition, and Lotka-Volterra models. Eigenvalues and eigenvectors are used to prove some results about the equilibria of the systems. Geometric perspectives of the systems are used to develop the intuitive approach of the work. Examples of graphed systems are included. Partial results are proven. Conjectures are formed. Difficulties in the work are described and suggestions for further work are given.
Nothing In Moderation, Everything In Excess: A New Weighted Statistic On Permutations, Ann Marie Paulukonis
Nothing In Moderation, Everything In Excess: A New Weighted Statistic On Permutations, Ann Marie Paulukonis
Honors Theses, 1963-2015
The major index is a well-known statistic on permutations which is computed by summing the positions of descents in a permutation. Instead of considering descents, this paper investigates what happens when excedances are weighted by position in a permutation. Several theorems are presented concerning various symmetries of the resulting distribution.
Irreducible Polynomials Over A Finite Field Zp, Brian Holbrook
Irreducible Polynomials Over A Finite Field Zp, Brian Holbrook
Honors Theses, 1963-2015
The topic of my thesis was counting irreducible polynomials. I began with some preliminary material including relevant theorems discovered in various math textbooks and data generated by a computer program that I wrote. I then used this data to calculate formulas for the number of polynomials which had zeroes in a field Zp of sufficiently low degree. Next, I explained why it would not be practical to use the formulas for lower degrees to synthesize formulas for high degrees. However, I was able to generate a new formula using a different counting technique: the inclusion-exclusion principle. Finally, I discussed the …
Triangles, Triangles And, Yes, More Triangles: Explorations In Euclidean Ramsey Theory, Kathleen Wilson
Triangles, Triangles And, Yes, More Triangles: Explorations In Euclidean Ramsey Theory, Kathleen Wilson
Honors Theses, 1963-2015
Several important general theorems of Euclidean Ramsey Theory are presented with an emphasis on trying to prove or disprove the 1973 conjecture of Erdös et al. that for all triangles, except for equilateral triangles, it is possible to find a monochromatic coloring of the vertices in any two colorings of the plane. Further investigation included looking at triangles in greater dimensions.
A Mathematical Analysis Of A Small Corporation: This Stuff Really Works?, Wade Olson
A Mathematical Analysis Of A Small Corporation: This Stuff Really Works?, Wade Olson
Honors Theses, 1963-2015
This thesis is a mathematical analysis of Foam Enterprises, a small corporation in the Twin Cities. Through interaction with the,. I heard of several problems occurring at that time which were being dealt with in a mathematical fashion. The first involves the profitability of two main clients of Foam Enterprises. The second deals with the production capacity of the two current plants and the distribution of products to customers. Each problem was then described in detail. The general mathematical approaches were stated for each problem and important circumstances which could affect the procedure were given. In turn, the results of …