sp18

Spring 2018

Archived: 

Topics in Linear Algebra

Linear algebra in R^n, standard Euclidean inner product in R^n, general linear spaces, general inner product spaces, least squares, determinants, eigenvalues and eigenvectors, symmetric matrices

Introduction to Information Theory

The measurement and quantification of information. These ideas are applied to the probabilistic analysis of the transmission of information over a channel along which random distortion of the message occurs.

Mathematical Statistics II

Hypothesis testing, likelihood ratio tests, nonparametric tests, bivariate and multivariate normal distributions

Stochastic Processes II

Renewal theory, Poisson processes and continuous time Markov processes, including an introduction to Brownian motion and martingales

Introduction to Number Theory

Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.

Abstract Algebra II

Continuation of Abstract Algebra I, with emphasis on Galois theory, modules, polynomial fields, and the theory of linear associative algebra.

Abstract Algebra I

This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures." There will be a very strong emphasis on theory and proofs.

Senior Project II

The second of a two course sequence of faculty-directed independent research culminating in the writing of a senior thesis and its presentation.

Senior Project I

The first of a two course sequence of faculty-directed independent research culminating in the writing of a senior thesis and its presentation.

Combinatorial Analysis

Combinatorial problem-solving techniques including the use of generating functions, recurrence relations, Polya theory, combinatorial designs, Ramsey theory, matroids, and asymptotic analysis.

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