An AB candidate at Princeton, she plans to major in math while completing premedical requirements. Prime Number Theorem Mathematicians since antiquity have tried to find order in the apparent irregular distribution of prime numbers.

Mathematical Models of Conventional Warfare Most defense spending and planning is determined by assessments of the conventional ie. Oxford University Press, New York.

Poisson processes in space rather than time have been used to model distributions of stars and galaxies, or positions of mutations along a chromosome. From this work came the proof that a general solution for fifth degree polynomial equations does not exist.

Why did Euler initially think that 1, was prime before rectifying his mistake? It is easy to produce maps requiring at least four colors, but the proof that four colors are always sufficient did not appear until From any square on the board, the rook has two available moves. But how does one prove such claims?

These models assume that the parameters of a model are themselves random variables and therefore that they have a probability distribution.

Nonstandard Analysis Would you like to see epsilons and deltas returned to Greekwhere they belong? Mathematics is Princeton math senior thesis a static, immutable body of knowledge. The thesis would not involve computer work. For Princeton math senior thesis future, she will choose between an academic career in physics and a performing career as a pianist.

Here is a simple example reported by Jay Emerson from his recent Ph. Moreover, their theory is intimately related to the solution of Diophantine equations, Farey fractions, and the approximation of irrationals by rational numbers. However, the theorem is one of algebra and a purely algebraic proof would be nice to find.

Serre, Linear Representations of Finite Groups. If you a potential advisor in mind, that person may well have other ideas.

For further information, see Bruce Peterson. Ramanujan or women in mathematicsthe history of mathematics in a specific region of the world e. Do numbers like make any sense?

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.

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.

Representation theory also has wide and profound applications outside mathematics. For instance, in how many ways can we write an integer as the sum of two squares? Recent results indicate that any "reasonable" voting procedure must either be dictatorial or subject to strategic manipulation.

Here N is the number of tumor cells at time t, K is the largest tumor size and b is a positive constant. 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? A thesis project could explore methods of generating pseudo-random numbers from a variety of discrete and continuous probability distributions.

However, in Viggo Brun proved the following: This project would investigate random effects models and their applications. Mawith Ma a plus. 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.

In what sense can one say that a product of infinitely many factors converges to a number? An axiomatic formulation of a decision problem uses loss functions, various decision criteria such as maximum likelihood and minimax, and Bayesian analysis to lead investigators to good decisions.

For further information, see Mike Olinick. Iterated Function Systems Roughly speaking, a contraction of the plane is a transformation f: The recipient of the George B. A thesis in this area might restrict itself to linear representation of finite groups.

For example the "meta-analysis" of data from medical research studies or from social science studies often employs random effects models. The pictures are great and the history of tilings and patterns goes back to antiquity.

A thesis might investigate the theory of majorization, which provides important tools for establishing these and other inequalities. The earliest applications concerned the disappearance of "family names," as passed on from fathers to sons.I excelled in math in high school, rising to the top of the tiered class track and dabbling in multivariable calculus before college.

I, however, immediately and subconsciously faltered in confidence when I reached Princeton. This program is ONLY for Math majors (i.e., students who will be either a junior or a senior at Princeton University in the following fall semester and have declared their major as mathematics).

Website. Before joining East Asian Studies, Sean worked with YaLa Young Leaders, an international alternative education and peace non-profit. More recently, he worked in Baltimore City as an educator, teaching 4th and 5th grade honors Math and then 5th grade English and Social Studies.

Sean is a New Jersey native. He received his Bachelors of Science in Psychology from Ursinus College. Computer Science is the only department at Princeton which offers both A.B.

and B.S.E. degrees. BSE vs AB. Printer Friendly However, A.B. majors are required to participate in four semesters of independent work (two junior year and a year-long senior thesis) and these do not count towards the 31 required courses.

Ashvin Swaminathan, Math, Princeton, Harvard, Harker. Department of Mathematics, Fine Hall. Skip to main content. Ashvin A. Swaminathan Department of Mathematics Princeton University Fine Hall, Washington Road Senior thesis, Department of Mathematics, Harvard University, God at Work: The History and Promise of the Faith at Work Movement 1st Edition.

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