Physical Sciences and Mathematics Commons^™

Une Histoire De La Formation Mathématique En France: Les Réformes Et Les Philosophies De L’Enseignement Primaire Et Secondaire De 1420 Jusqu'À Aujourd’Hui, Rebecca Robinson

Honors Theses

France has produced many illustrious mathematicians who have profoundly impacted mathematics as they are today. While Descartes, Cauchy, and Borel (among others) viewed math as a lifelong pursuit, they began their education in an elementary school classroom with everybody else. In this study, I explore mathematical reforms and governmental documents throughout history to show how the education system has grown to emphasize a strong mathematical curriculum for all students and have consulted many philosophical articles on both the importance of math in a student’s education as well as different views on the manner in which mathematics should be taught to …

The Calculus Of Variations, Erin Whitney

Honors Theses

The Calculus of Variations is a highly applicable and advancing field. My thesis has only scraped the top of the applications and theoretical work that is possible within this branch of mathematics. To summarize, we began by exploring a general problem common to this field, finding the geodesic be-tween two given points. We then went on to define and explore terms and concepts needed to further delve into the subject matter. In Chapter 2, we examined a special set of smooth functions, inspired by the Calabi extremal metric, and used some general theory of convex functions in order to de-termine …

A Comparison Of Van Hiele Levels And Final Exam Grades Of Students At The University Of Southern Mississippi, Cononiah Watson

Honors Theses

This research analyzed students final exam scores in a college mathematics class with geometric components and their van Hiele levels upon entering the class. After the class was completed, each student’s final exam grade was calculated. The researcher used a Spearman correlation to compare the two; the result was a correlation coefficient of 0.742. The researcher then reported that the results of the van Hiele test are a major component in predicting a student’s success in such a class.

On A Problem Of Burnside, Matthew Mizuhara

Honors Theses

Burnside posed the question as to whether or not there exist groups having an external automorphism that behaves in a certain, specific way like an inner automorphism: we shall define such automorphisms to be nearly-inner.

NI-groups are fairly rare. With the aid of the computer algebra system Magma - in particular with the aid of its small group database - we set out to test this hypothesis.

Verifying Harder's Conjecture For Classical And Siegel Modular Forms, David Sulon

Honors Theses

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form.

Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Tower Families Of Ribbon Graphs, Jordan Keller

Honors Theses

No abstract provided.

Behavioral Economics And Physician Behavior, Allyssa S. Ward

Honors Theses

This study seeks to answer whether the availability heuristic leads physicians to utilize more medical care than is economically efficient. Do rare, salient events alter physicians' perceptions about the probability of patient harm? Do these events lead physicians to overutilize certain medical procedures? This study uses Pennsylvania inpatient hospital admissions data from 2009 aggregated at the physician level to investigate these questions. The data come from the 2009 Pennsylvania Health Care Cost Containment Council (PHC4).

The study is divided into two parts. In Part I, we examine whether bad outcomes during childbirth (defined as maternal mortality, an obstetric fistula or …

Mapping Of Stochastic Matrices Into Polynomial Form In The Complex Plane, Jordan Emile Cates

Honors Theses

This thesis originated from a specific problem from biology. Namely we need to study probabilistic models that represent molecular interactions that take place inside living cells, such as the number of molecular heat-shock proteins present in a cell. Because of the intrinsic discrete nature of the number of molecules present in cells, the fundamental mathematical models are based on Markov processes. For such processes a transition probability matrix describes the evolution of the state of the cell, whereas the state itself, i.e. the number of molecules present at a specific time, is described by a vector. The components of this …

Odd Or Even: Uncovering Parity Of Rank In A Family Of Rational Elliptic Curves, Anika Lindemann

Honors Theses

Puzzled by equations in multiple variables for centuries, mathematicians have made relatively few strides in solving these seemingly friendly, but unruly beasts. Currently, there is no systematic method for finding all rational values, that satisfy any equation with degree higher than a quadratic. This is bizarre. Solving these has preoccupied great minds since before the formal notion of an equation existed. Before any sort of mathematical formality, these questions were nested in plucky riddles and folded into folk tales. Because they are so simple to state, these equations are accessible to a very general audience. Yet an astounding amount of …

Excluded Minors For Apex Classes Of Graphs, Christine A. Derbins

Honors Theses

No abstract provided.

Recurrence Relations, Fractals, And Chaos: Implications For Analyzing Gene Structure, Sarah. M. Harmon

Honors Theses

The “chaos game” is a well-known algorithm by which one may construct a pictorial representation of an iterative process. The resulting sets are known as fractals and can be mathematically characterized by measures of dimension as well as by their associated recurrence relations. Using the chaos game algorithm, is it possible to derive meaningful structure out of our own genetic encoding, and that of other organisms? In this paper, I will present one method of applying the chaos game to biological data and subsequently will discuss both the mathematical and biological implications of the results.