Support for Student Projects. Members of the Class of and their senior thesis topics, alphabetically by department. Winners of the competition from left first runner-up Sabrina Yurkofsky '15, second runner-up M. Ficarra '15 and champion Lisbeth DaBramo ' Feminist Scholarly Approaches vs. Can it be Maintained? Ledesma Arias , Why people study a foreign language? Can gaokao reforms create a brighter tomorrow for Chinese youth?
How College Students prefer to share their political opinions in the 21st Century J. Evaluating gender representations in television Alicja B. Jamie Lee , The Economics of Deception: Literary Appetite in M. The Origins of Environmentalism M. Lourie, How will the Atlantic Oyster C. Morgan , Expedition Geology: Soo , Transgresiones de la heteronormatividad: Stephan , Las representaciones audiovisuales del Cid: Is Mindfulness Linked to Attentional Filtering?
Sarah Izzo , Seeing God in the Shadows: The Key to Drug Addiction? Genesis Melo , Violence: These models assume that the parameters of a model are themselves random variables and therefore that they have a probability distribution. Bayesian models may begin with prior assumptions about these distributions, and may incorporate data from previous studies, as a starting point for inference based on current data.
This project would investigate the conceptual and theoretical underpinnings of this approach, and compare it to the traditional tools of mathematical statistics as studied in Ma It could culminate in an application that uses real data to illustrate the power of the Bayesian approach.
Oxford University Press, New York. Bayesian Statistics for Evaluation Research: Measurements which arise from one or more categorical variables that define groups are often analyzed using ANOVA Analysis of Variance.
Linear models specify parameters that account for the differences among the groups. Sometimes these differences exhibit more variability than can be explained by these "fixed effects", and then the parameters are permitted to come from a random distribution, giving "random effects.
This modeling approach has proved useful and powerful for analyzing multiple data sets that arise from different research teams in different places. For example the "meta-analysis" of data from medical research studies or from social science studies often employs random effects models.
This project would investigate random effects models and their applications. MA , with a plus. Because a computer is deterministic, it cannot generate truly random numbers. A thesis project could explore methods of generating pseudo-random numbers from a variety of discrete and continuous probability distributions. The art of tilings has been studied a great deal, but the science of the designs is a relatively new field of mathematics.
Some possible topics in this area are: The problems in this area are easy to state and understand, although not always easy to solve. The pictures are great and the history of tilings and patterns goes back to antiquity.
An example of a specific problem that a thesis might investigate is: Devise a scheme for the description and classification of all tilings by angle-regular hexagons. Roughly speaking, a contraction of the plane is a transformation f: With a little effort CF can even be made to look like a tree or a flower!!
A thesis in this area would involve learning about these contraction mapping theorems in the plane and in other metric spaces, learning how the choice of contractions effects the shape of CF and possibly writing computer programs to generate CF from F. Consider a population of individuals which produce offspring of the same kind. Associating a probability distribution with the number of offspring an individual will produce in each generation gives rise to a stochastic i.
The earliest applications concerned the disappearance of "family names," as passed on from fathers to sons. Modern applications involve inheritance of genetic traits, propagation of jobs in a computer network, and particle decay in nuclear chain reactions. A key tool in the study of branching processes is the theory of generating functions, which is an interesting area of study in its own right.
Branching processes with biological applications. The Poisson Process is a fundamental building block for continuous time probability models. The process counts the number of "events" that occur during the time interval [0, T ], where the times between successive events are independent and have a common exponential distribution. Incoming calls to a telephone switchboard, decays of radioactive particles, or student arrivals to the Proctor lunch line are all events that might be modeled in this way.
Poisson processes in space rather than time have been used to model distributions of stars and galaxies, or positions of mutations along a chromosome. Starting with characterizations of the Poisson process, a thesis might develop some of its important properties and applications. Wiley, , Chapter 1. Two famous problems in elementary probability are the "Birthday Problem" and the "Coupon Collector's Problem.
For the second, imagine that each box of your favorite breakfast cereal contains a coupon bearing one of the letters "P", "R", "I", "Z" and "E". Now suppose that the "equally likely" assumptions are dropped. But how does one prove such claims? A thesis might investigate the theory of majorization, which provides important tools for establishing these and other inequalities.
This is a modern topic combining ideas from probability and graph theory. A "cover time" is the expected time to visit all vertices when a random walk is performed on a connected graph. Here is a simple example reported by Jay Emerson from his recent Ph. Consider a rook moving on a 2x2 chessboard.
From any square on the board, the rook has two available moves. If the successive choices are made by tossing a coin, what is the expected number of moves until the rook has visited each square on the board? Reliability theory is concerned with computing the probability that a system, typically consisting of multiple components, will function properly e. The components are subject to deterioration and failure effects, which are modeled as random processes, and the status of the system is determined in some way by the status of the components.
For example, a series system functions if and only if each component functions, whereas a parallel system functions if and only if at least one component functions. In more complicated systems, it is not easy to express system reliability exactly as a function of component reliabilities, and one seeks instead various bounds on performance.
Specifically, in order to be Riemann integrable, a function must be continuous almost everywhere. However, many interesting functions that show up as limits of integrable functions or even as derivatives do not enjoy this property.
Certainly one would want at least every derivative to be integrable. To this end, Henri Lebesgue announced a new integral in that was completely divorced from the concept of continuity and instead depended on a concept referred to as measure theory. Interesting in their own right, the theorems of measure theory lead to facinating and paradoxical insight into the structure of sets.
That is, we want a set of sets from F such that any two sets have a non-empty intersection. What is the structure of such a sub-collection? The conjecture remains open, though some particular cases have been solved. For more information see John Schmitt Snark Hunting "We have sailed many months, we have sailed many weeks, Four weeks to the month you may mark , But never as yet 'tis your Captain who speaks Have we caught the least glimpse of a Snark!
When Martin Gardner applied the name to a particular class of graphs in , a time when only four graphs including the Petersen graph of course were known to be in the class, it was an appropriate name. Snarks were hunted by Bill Tutte while writing under the pseudonym Blanche Descartes as a way to approach the then unsolved Four Color Problem.
They were both an elusive and worthy prey. Now there exists several infinite classes of snarks and they have proved to be useful, though not yet in the way Tutte envisioned. Gardner , Penguin, Gardner, Mathematical games, Scientific American, , No. For more information see John Schmitt. Two-Dimensional Orbifolds Spheres and tori are examples of closed surfaces. There is a well-known classification theorem whereby we are able to completely characterize any surface based on only two pieces of information about the surface.
A 2-dimensional orbifold is a generalization of a surface. The main difference is that in general, an orbifold may have what are known as singular points. A thesis in this area could examine Thurston's generalization of the surface classification theorem to 2-dimensional orbifolds. Another direction could be an examination of groups of transformations of the 2-dimensional plane which are used to produce flat 2-orbifolds.
This subject is full of big ideas but can be pleasantly hands-on at the same time. For classification of 2-manifolds, see Wolf, p. Matrix Groups In linear algebra, we learn about n-by-n matrices and how they represent transformations of n-dimensional space.
In abstract algebra, we learn about how certain collections of n-by-n matrices form groups. These groups are very interesting in their own rights, both in understanding what geometric properties of n-dimensional space they preserve, and because of the fact that they are examples of objects known as manifolds.
There are many senior projects that could grow out of this rich subject. See, for example, 27 above. In the late 19th century, geometry was revolutionized by the realization that if Euclid's fifth axiom, the parallel postulate, was dropped, there were a number of alternate geometries that satisfied the first four axioms but that displayed behavior quite different from traditional Euclidean geometry. These geometries are called non-Euclidean geometries, and include projective, hyperbolic, and spherical geometries.
As the theory of these geometries began to develop, one of the great mathematicians of the day, Felix Klein, proposed his Erlangen Program, a new method for studying and characterizing these geometries based on group theory and symmetries.
A thesis in this area would study the various geometries, and the groups of transformations that define them. David Gans, Transformations and Geometries. For further information, see Emily Proctor. Skip to main content. Site Editor Log On. For further information, see Bruce Peterson. The Four Color Theorem For many years, perhaps the most famous unsolved problem in mathematics asked whether every possible map on the surface of a sphere could be colored in such a way that any two adjacent countries were distinguishable using only four colors.
For additional information, see Bruce Peterson. Additive Number Theory We know a good deal about the multiplicative properties of the integers -- for example, every integer has a unique prime decomposition. For related ideas, see Waring's Problem topic Mersenne Primes and Perfect Numbers Numbers like 6 and 28 were called perfect by Greek mathematicians and numerologists since they are equal to the sum of their proper divisors e. Kelley, Arrow Impossibility Theorems.
For further information, see Mike Olinick. Mathematical Models of Conventional Warfare Most defense spending and planning is determined by assessments of the conventional ie. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra states that every non-constant polynomial with complex coefficients has a complex root. For further information, see Priscilla Bremser or David Dorman. Algebraic Numbers A real number r is "algebraic" if r is the root of a polynomial with integer coefficients.
For further information Peter Schumer, or David Dorman. Nonstandard Analysis Would you like to see epsilons and deltas returned to Greek , where they belong? Galois Theory The relation between fields, vector spaces, polynomials, and groups was exploited by Galois to give a beautiful characterization of the automorphisms of fields.
Prime Number Theorem Mathematicians since antiquity have tried to find order in the apparent irregular distribution of prime numbers. For further information, see Peter Schumer. Twin Primes Primes like 3 and 5 or and are called twin primes since their difference is only 2.
For further information, see Peter Schumer or David Dorman. Primality Testing and Factoring This topic involves simply determining whether a given integer n is prime or composite, and if composite, determining its prime factorization. Introduction to Analytic Number Theory Analytic number theory involves applying calculus and complex analysis to the study of the integers. Finite Fields A finite field is, naturally, a field with finitely many elements.
Representation Theory Representation theory is one of the most fruitful and useful areas of mathematics. Serre, Linear Representations of Finite Groups. For further information, see David Dorman. Lie Groups Lie groups are all around us. Quadratic Forms and Class Numbers The theory of quadratic forms introduced by Lagrange in the late 's and was formalized by Gauss in Davenport, The Higher Arithmetic. Generalizations of the Real Numbers Let R n be the vector space of n-tuples of real numbers with the usual vector addition and scalar multiplication.
A thesis in this area would involve learning about the discoveries of these various "composition algebras" and studying the main theorems: Frobenius' theorem on division algebras. The Arithmetic-Geometric Inequality and Other Famous Inequalities Inequalities are fundamental tools used by many practicing mathematicians on a regular basis.
For further information, see Bill Peterson. For further information, see Michael Olinick or Peter Schumer. Decision-Theoretic Analysis and Simulation Medical researchers and policy makers often face difficult decisions which require them to choose the best among two or more alternatives using whatever data are available.
Theory and Decision Making The power of modern computers has made possible the analysis of complex data set using Bayesian models and hierarchical models. MA , with Ma a plus. Ma , with Ma a plus. For further information, see John Emerson. Pseudo-Random Number Generation Because a computer is deterministic, it cannot generate truly random numbers.
For further information, see Priscilla Bremser. Iterated Function Systems Roughly speaking, a contraction of the plane is a transformation f: Branching Processes Consider a population of individuals which produce offspring of the same kind. For more information, see Bill Peterson. Cover Times This is a modern topic combining ideas from probability and graph theory.
Members of the Class of and their senior thesis topics, alphabetically by department.
Mar 01, · Ok, so i'm a Communications Major, and i'm taking Senior Thesis (which is a class I need to fully graduate). I have to do a page research paper on a communication topic about anything that deals with coachoutleta.cf: Resolved.
A master’s degree helps to prepare a student for work as a public relations manager, a journalist, a television producer and many other careers in communications. But, in order to earn the degree, a student must first complete a thesis. Consider five possible topics for a Master’s in Communication thesis. Every semester, communication seniors receive their cap and gown, finish their degree requirements and take part in the most daunting, yet rewarding of all: complete and defend their senior thesis, a rite of passage for Southeastern communication .
A senior thesis project could include a presentation of several different types of proof and a search for an algebraic one. References: Any text in complex analysis. Jun 19, · Paper topics should be developed in close consultation with the instructor.” To be quite honest, pages seems really short for a senior thesis. I’m sure there’s a lot of busy work for the course, but still.