Location: Bowdoin / Mathematics / Courses / Spring 2013

Mathematics

Spring 2013

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050. Quantitative Reasoning
Eric Gaze T 1:00 - 2:25, TH 1:00 - 2:25 Searles-223
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
Raj Saha T 8:30 - 9:55, TH 8:30 - 9:55 Searles-113
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
Abukuse Mbirika M 11:30 - 12:55, W 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.

165. Biostatistics
Jack O'Brien M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 11:25 Searles-217
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. An average of four to five hours of class meetings and computer laboratory sessions per week. Not open to students who have credit for or are concurrently enrolled in Mathematics 155, Psychology 252, or Economics 257.

171. Integral Calculus
Manuel Reyes T 10:00 - 11:25, TH 10:00 - 11:25 Searles-113
The definite integral; the Fundamental theorems; improper integrals; applications of the definite integral; differential equations; and approximations including Taylor polynomials and Fourier series. An average of four to five hours of class meetings and computer laboratory sessions per week.

171. Integral Calculus
Michael Penn M 11:30 - 12:55, W 11:30 - 12:55 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. An average of four to five hours of class meetings and computer laboratory sessions per week.

181. Multivariate Calculus
Adam Levy T 11:30 - 12:55, TH 11:30 - 12:55 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. An average of four to five hours of class meetings and computer laboratory sessions per week.

181. Multivariate Calculus
Michael King M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25 Searles-215
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. An average of four to five hours of class meetings and computer laboratory sessions per week.

181. Multivariate Calculus
Sarah Iams T 10:00 - 11:25, TH 10:00 - 11:25 Searles-115
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. An average of four to five hours of class meetings and computer laboratory sessions per week.

200. Introduction to Mathematical Reasoning
Thomas Pietraho M 1:00 - 2:25, W 1:00 - 2:25 Searles-113
An introduction to logical deductive reasoning and mathematical proof through diverse topics in higher mathematics. Specific topics include set and function theory, modular arithmetic, proof by induction, and the cardinality of infinite sets. May also consider additional topics such as graph theory, number theory, and finite state automata.

200. Introduction to Mathematical Reasoning
Michael King M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 11:25 Searles-113
An introduction to logical deductive reasoning and mathematical proof through diverse topics in higher mathematics. Specific topics include set and function theory, modular arithmetic, proof by induction, and the cardinality of infinite sets. May also consider additional topics such as graph theory, number theory, and finite state automata.

201. Linear Algebra
Sarah Iams T 8:30 - 9:55, TH 8:30 - 9:55 Searles-217
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.

225. Probability
Jack O'Brien M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25 Searles-217
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

229. Optimization
Adam Levy T 10:00 - 11:25, TH 10:00 - 11:25 Searles-217
A study of optimization problems arising in a variety of situations in the social and natural sciences. Analytic and numerical methods are used to study problems in mathematical programming, including linear models, but with an emphasis on modern nonlinear models. Issues of duality and sensitivity to data perturbations are covered, and there are extensive applications to real-world problems.

231. Intermediate Linear Algebra
Thomas Pietraho M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25 Searles-213
A continuation of Linear Algebra focused on the interplay of algebra and geometry as well as mathematical theory and its applications. Topics include matrix decompositions, eigenvalues and spectral theory, vector and Hilbert spaces, norms and low-rank approximations. Applications to biology, computer science, economics, and statistics, including artificial learning and pattern recognition, principal component analysis, and stochastic systems. Course and laboratory work balanced between theory and application.

241. Mathematics and Music
Leon Harkleroad T 8:30 - 9:55, TH 8:30 - 9:55 Gibson-101 Tillotson Room
Examines ways in which Fourier series, Markov chains, groups, and other mathematical objects have been used to describe, analyze, and create music. Applies mathematics to such musical contexts as tuning systems, change-ringing, serial and aleatoric composition, and contradances. No musical background required.

247. Geometry
William Barker T 11:30 - 12:55, TH 11:30 - 12:55 Searles-113
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.

262. Introduction to Algebraic Structures
Michael Penn M 8:00 - 9:25, W 8:00 - 9:25, F 8:00 - 9:25 Searles-113
An introduction to the theory of finite and infinite groups, with examples ranging from symmetry groups to groups of polynomials and matrices. Properties of mappings that preserve algebraic structures are studied. Topics include cyclic groups, homomorphisms and isomorphisms, normal subgroups, factor groups, the structure of finite abelian groups, and Sylow theorems.

265. Statistics
Rosemary Roberts T 2:30 - 3:55, TH 2:30 - 3:55 Searles-213
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 M 11:30 - 12:55, W 11:30 - 12:55 Searles-113
One or more selected topics from advanced analysis. Possible topics include Lebesque measure and integration theory, Fourier analysis, Hilbert and Banach space theory, and stochastic calculus with applications to mathematical finance.

318. Advanced Topics in Modeling
Mary Zeeman T 11:30 - 12:55, TH 11:30 - 12:55 Searles-213
Development, analysis and simulation of mathematical models. Application topics drawn from a variety of disciplines such as biology, environmental sciences, earth and oceanographic sciences, climate and sustainability. Analysis topics include oscillation, chaos, bistability, bifurcation, perturbation, resilience and their consequences for prediction. Three hours of class meetings and 1.5 hours of computer laboratory sessions per week. Not open to students who have credit for Mathematics 304.