Courses

Courses

Spring 2008

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155. Introduction to Statistics and Data Analysis
Rosemary Roberts T 11:30 - 12:55, TH 11:30 - 12:55
A general introduction to statistics in which students learn to draw conclusions from data using statistical techniques. Examples are drawn from many different areas of application. The computer is used extensively. Topics include exploratory data analysis, planning and design of experiments, probability, one and two sample t-procedures, and simple linear regression. Not open to students who have credit for Mathematics 165, Psychology 252, or Economics 257.

161. Differential Calculus
James Ward M 11:30 - 12:25, W 11:30 - 12:25, F 11:30 - 12:25
Functions, including the trigonometric, exponential, and logarithmic functions; the derivative and the rules for differentiation; the anti-derivative; applications of the derivative and the anti-derivative. Four to five hours of class meetings and computer laboratory sessions per week, on average. Open to students who have taken at least three years of mathematics in secondary school.

161. Differential Calculus
Mohammad Tajdari M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25
Functions, including the trigonometric, exponential, and logarithmic functions; the derivative and the rules for differentiation; the anti-derivative; applications of the derivative and the anti-derivative. Four to five hours of class meetings and computer laboratory sessions per week, on average. Open to students who have taken at least three years of mathematics in secondary school.

171. Integral Calculus
Jennifer Taback M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25
The definite integral; the Fundamental theorems; improper integrals; applications of the definite integral; differential equations; and approximations including Taylor polynomials and Fourier series. Four to five hours of class meetings and computer laboratory sessions per week, on average.

171. Integral Calculus
Stephen Fisk T 1:00 - 2:25, TH 1:00 - 2:25
The definite integral; the Fundamental theorems; improper integrals; applications of the definite integral; differential equations; and approximations including Taylor polynomials and Fourier series. Four to five hours of class meetings and computer laboratory sessions per week, on average.

181. Multivariate Calculus
Adam Levy M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25
Multivariate calculus in two and three dimensions. Vectors and curves in two and three dimensions; partial and directional derivatives; the gradient; the chain rule in higher dimensions; double and triple integration; polar, cylindrical, and spherical coordinates; line integration; conservative vector fields; and Green’s theorem. Four to five hours of class meetings and computer laboratory sessions per week, on average.

181. Multivariate Calculus
Thomas Pietraho T 1:00 - 2:25, TH 1:00 - 2:25
Multivariate calculus in two and three dimensions. Vectors and curves in two and three dimensions; partial and directional derivatives; the gradient; the chain rule in higher dimensions; double and triple integration; polar, cylindrical, and spherical coordinates; line integration; conservative vector fields; and Green’s theorem. Four to five hours of class meetings and computer laboratory sessions per week, on average.

201. Linear Algebra
Adam Levy T 8:30 - 9:55, TH 8:30 - 9:55
Topics include vectors, matrices, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors, and quadratic forms. Applications to linear equations, discrete dynamical systems, Markov chains, least-squares approximation, and Fourier series. Formerly Mathematics 222.

201. Linear Algebra
James Ward M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25
Topics include vectors, matrices, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors, and quadratic forms. Applications to linear equations, discrete dynamical systems, Markov chains, least-squares approximation, and Fourier series. Formerly Mathematics 222.

224. Applied Mathematics: Ordinary Differential Equations
Mohammad Tajdari M 11:30 - 12:55, W 11:30 - 12:55
A study of some of the ordinary differential equations that model a variety of systems in the natural and social sciences. Classical methods for solving differential equations with an emphasis on modern, qualitative techniques for studying the behavior of solutions to differential equations. Applications to the analysis of a broad set of topics, including population dynamics, competitive economic markets, and design flaws. Computer software is used as an important tool, but no prior programming background is assumed.

227. Elementary Topics in Topology
Helen Wong M 1:00 - 2:25, W 1:00 - 2:25
Topology studies properties of geometric objects that do not change when the object is deformed. The course covers knot theory, surfaces, and other elementary areas of topology. Formerly Mathematics 207.

252. Mathematical Cryptography
Jennifer Taback M 11:30 - 12:55, W 11:30 - 12:55
Classical and modern methods of cryptography and cryptanalysis. Topics will include public key cryptography and the RSA encryption algorithm, factoring techniques and recently proposed cryptosystems based on group theory and graph theory.

263. Introduction to Analysis
William Barker T 8:30 - 9:55, TH 8:30 - 9:55
Emphasizes proof and develops the rudiments of mathematical analysis. Topics include an introduction to the theory of sets and topology of metric spaces, sequences and series, continuity, differentiability, and the theory of Riemann integration. Additional topics may be chosen as time permits.

265. Statistics
Thomas Pietraho T 10:00 - 11:25, TH 10:00 - 11:25
An introduction to the fundamentals of mathematical statistics. General topics include likelihood methods, point and interval estimation, and tests of significance. Applications include inference about binomial, Poisson, and exponential models, frequency data, and analysis of normal measurements.

302. Advanced Topics in Algebra
Stephen Fisk T 10:00 - 11:25, TH 10:00 - 11:25
One or more specialized topics from abstract algebra and its applications. Topics may include group representation theory, coding theory, symmetries, ring theory, finite fields and field theory, algebraic numbers, and Diophantine equations.

305. Advanced Topics in Probability and Statistics
Rosemary Roberts T 2:30 - 3:55, TH 2:30 - 3:55
One or more specialized topics in probability and statistics. Possible topics include regression analysis, nonparametric statistics, logistic regression, and other linear and nonlinear approaches to modeling data. Emphasis is on the mathematical derivation of the statistical procedures and on the application of the statistical theory to real-life problems.

307. Advanced Topics in Geometry
William Barker T 1:00 - 2:25, TH 1:00 - 2:25
A survey of three-dimensional Euclidean geometry, affine geometry, projective geometry, and non-Euclidean geometries. Culminates in the geometry of four-dimensional space-time in special relativity. The unifying theme is the transformational viewpoint of Klein’s Erlangen Program.