Location: Bowdoin / Mathematics / Courses / Fall 2009

Mathematics

Fall 2009

155. Introduction to Statistics and Data Analysis
Rosemary Roberts T 2:30 - 3:55, TH 2:30 - 3:55 Searles-113
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
William Barker T 11:30 - 12:55, TH 11:30 - 12:55 Searles-217
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
Noah Kieserman M 11:30 - 12:55, W 11:30 - 12:55 Searles-215
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
Mohammad Tajdari M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25 Searles-213
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
Mohammad Tajdari M 11:30 - 12:25, W 11:30 - 12:25, F 11:30 - 12:25 Searles-213
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.

172. Integral Calculus, Advanced Section
Thomas Pietraho T 1:00 - 2:25, TH 1:00 - 2:25 Searles-215
A review of the exponential and logarithmic functions, techniques of integration, and numerical integration. Improper integrals. Approximations using Taylor polynomials and infinite series. Emphasis on differential equation models and their solutions. Four to five hours of class meetings and computer laboratory sessions per week, on average. Open to students whose backgrounds include the equivalent of Mathematics 161 and the first half of Mathematics 171. Designed for first-year students who have completed an AB Advanced Placement calculus course in their secondary schools.

172. Integral Calculus, Advanced Section
Michael King T 10:00 - 11:25, TH 10:00 - 11:25 Searles-217
A review of the exponential and logarithmic functions, techniques of integration, and numerical integration. Improper integrals. Approximations using Taylor polynomials and infinite series. Emphasis on differential equation models and their solutions. Four to five hours of class meetings and computer laboratory sessions per week, on average. Open to students whose backgrounds include the equivalent of Mathematics 161 and the first half of Mathematics 171. Designed for first-year students who have completed an AB Advanced Placement calculus course in their secondary schools.

181. Multivariate Calculus
Adam Levy M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 11:25 Searles-217
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
Michael King T 1:00 - 2:25, TH 1:00 - 2:25 Searles-217
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.

200. Introduction to Mathematical Reasoning
Jennifer Taback M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25 Searles-217
An introduction to logical deductive reasoning, mathematical proof, and the fundamental concepts of higher mathematics. Specific topics include set theory, induction, infinite sets, permutations, and combinations. An active, guided discovery classroom format.

201. Linear Algebra
Mary Zeeman M 2:30 - 3:55, W 2:30 - 3:55 Searles-113
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.

204. Biomathematics
Mary Zeeman M 11:30 - 12:55, W 11:30 - 12:55 Searles-113
A study of mathematical methods driven by questions in biology. Biological questions are drawn from a broad range of topics, including disease, ecology, genetics, population dynamics, neurobiology, endocrinology and biomechanics. Mathematical methods include compartmental models, matrices, linear transformations, eigenvalues, eigenvectors, matrix iteration and simulation; ODE models and simulation, stability analysis, attractors, oscillations and limiting behavior, mathematical consequences of feedback, and multiple time-scales. Three hours of class meetings and two hours of computer laboratory sessions per week. Within the biology major, this course may count as the mathematics credit or as biology credit, but not both. Students are expected to have taken a year of high school or college biology prior to this course. Formerly Mathematics 174.

225. Probability
Leon Harkleroad T 1:00 - 2:25, TH 1:00 - 2:25 Searles-113
A study of the mathematical models used to formalize nondeterministic or “chance” phenomena. General topics include combinatorial models, probability spaces, conditional probability, discrete and continuous random variables, independence and expected values. Specific probability densities, such as the binomial, Poisson, exponential, and normal, are discussed in depth.

233. Functions of a Complex Variable
Thomas Pietraho T 10:00 - 11:25, TH 10:00 - 11:25 Searles-213
The differential and integral calculus of functions of a complex variable. Cauchy’s theorem and Cauchy’s integral formula, power series, singularities, Taylor’s theorem, Laurent’s theorem, the residue calculus, harmonic functions, and conformal mapping.

262. Introduction to Algebraic Structures
Jennifer Taback M 11:30 - 12:55, W 11:30 - 12:55 Searles-217
A study of the basic arithmetic and algebraic structure of the common number systems, polynomials, and matrices. Axioms for groups, rings, and fields, and an investigation into general abstract systems that satisfy certain arithmetic axioms. Properties of mappings that preserve algebraic structure.

264. Applied Mathematics: Partial Differential Equations
Adam Levy M 1:00 - 2:25, W 1:00 - 2:25 Searles-213
A study of some of the partial differential equations that model a variety of systems in the natural and social sciences. Classical methods for solving partial differential equations, with an emphasis where appropriate on modern, qualitative techniques for studying the behavior of solutions. Applications to the analysis of a broad set of topics, including air quality, traffic flow, and imaging. Computer software is used as an important tool, but no prior programming background is assumed.

305. Advanced Topics in Probability and Statistics
Rosemary Roberts T 11:30 - 12:55, TH 11:30 - 12:55 Searles-113
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 8:30 - 9:55, TH 8:30 - 9:55 Searles-113
A survey of affine, projective, and non-Euclidean geometries in two-dimensions, unified by the transformational viewpoint of Klein’s Erlanger Program. Special focus will be placed on conic sections. Additional topics: complex numbers in Euclidean geometry, quaternions in three-dimensional geometry, and the geometry of four-dimensional space-time in special relativity. Mathematics 247 is helpful but not required.