Location: Bowdoin / Mathematics / Courses / Spring 2011

Mathematics

Spring 2011

050. Quantitative Reasoning
Eric Gaze T 1:00 - 2:25, TH 1:00 - 2:25
Explores the ways and means by which we communicate with numbers; the everyday math we encounter on a regular basis. The fundamental quantitative skill set is covered in depth providing a firm foundation for further coursework in mathematics and the sciences. Topics include ratios, rates, percentages, units, descriptive statistics, linear and exponential modeling, correlation, logic, probability. A project-based course using Microsoft Excel, emphasizing conceptual understanding and application. Reading of current newspaper articles and exercises involving personal finance are incorporated to place the mathematics in real-world context.

161. Differential Calculus
Noah Kieserman M 1:30 - 2:25, W 1:30 - 2:25, F 1:30 - 2:25
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.

165. Biostatistics
Rosemary Roberts T 11:30 - 12:55, TH 11:30 - 12:55
An introduction to the statistical methods used in the life sciences. Emphasizes conceptual understanding and includes topics from exploratory data analysis, the planning and design of experiments, probability, and statistical inference. One and two sample t-procedures and their non-parametric analogs, one-way ANOVA, simple linear regression, goodness of fit tests, and the chi-square test for independence are discussed. Four to five hours of class meetings and computer laboratory sessions per week, on average. Not open to students who have credit for or are concurrently enrolled in Mathematics 155, Psychology 252, or Economics 257.

171. Integral Calculus
Michael King T 2:30 - 3:55, TH 2:30 - 3:55
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
Leon Harkleroad T 8:30 - 9:55, TH 8:30 - 9:55
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
Jennifer Taback M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25
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
William Barker T 11:30 - 12:55, TH 11:30 - 12:55
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 10:00 - 11:25, TH 10:00 - 11:25
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.

200. Introduction to Mathematical Reasoning
William Barker T 8:30 - 9:55, TH 8:30 - 9:55
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
Leon Harkleroad T 1:00 - 2:25, TH 1:00 - 2:25
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.

224. Applied Mathematics: Ordinary Differential Equations
Mary Zeeman 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.

247. Geometry
Noah Kieserman M 2:30 - 3:25, W 2:30 - 3:25, F 2:30 - 3:25
A survey of modern approaches to Euclidean geometry in two and three dimensions. Axiomatic foundations of metric geometry. Transformational geometry: isometries and similarities. Klein’s Erlangen Program. Symmetric figures. Scaling, measurement, and dimension.

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

258. Combinatorics and Graph Theory
Abukuse Mbirika M 1:00 - 2:25, W 1:00 - 2:25
An introduction to combinatorics and graph theory. Topics to be covered may include enumeration, matching theory, generating functions, partially ordered sets, Latin squares, designs, and graph algorithms.

262. Introduction to Algebraic Structures
Michael King T 10:00 - 11:25, TH 10:00 - 11:25
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.

265. Statistics
Rosemary Roberts T 2:30 - 3:55, TH 2:30 - 3:55
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.

303. Advanced Topics in Analysis
Thomas Pietraho T 11:30 - 12:55, TH 11:30 - 12:55
One or more selected topics from analysis. Possible topics include geometric measure theory, Lebesque general measure and integration theory, Fourier analysis, Hilbert and Banach space theory, and spectral theory.