Location: Bowdoin / Mathematics / Courses / Spring 2012

Mathematics

Spring 2012

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
Mohammad Tajdari T 8:30 - 9:55, TH 8:30 - 9:55
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 T 1:00 - 2:25, TH 1:00 - 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
Leon Harkleroad T 10:00 - 11:25, TH 10:00 - 11:25
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
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
Abukuse Mbirika M 11:30 - 12:55, W 11:30 - 12:55
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
William Barker M 11:30 - 12:55, W 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. An average of four to five hours of class meetings and computer laboratory sessions per week.

181. Multivariate Calculus
Leon Harkleroad 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. An average of four to five hours of class meetings and computer laboratory sessions per week.

181. Multivariate Calculus
Michael King M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 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. An average of four to five hours of class meetings and computer laboratory sessions per week.

200. Introduction to Mathematical Reasoning
Jennifer Taback M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25
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
William Barker M 8:30 - 9:25, W 8:30 - 9:25, F 8:30 - 9:25
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 T 2:30 - 3:55, TH 2:30 - 3:55
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.

224. Applied Mathematics: Ordinary Differential Equations
Mary Zeeman T 11:30 - 12:55, TH 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.

244. Numerical Methods
Adam Levy T 8:30 - 9:55, TH 8:30 - 9:55
An introduction to the theory and application of numerical analysis. Topics include approximation theory, numerical integration and differentiation, iterative methods for solving equations, and numerical analysis of differential equations.

263. Introduction to Analysis
Jennifer Taback M 11:30 - 12:55, W 11:30 - 12:55
Building on the theoretical underpinnings of calculus, develops the rudiments of mathematical analysis. Concepts such as limits and convergence from calculus are made rigorous and extended to other contexts, such spaces of functions. Specific topics include metric spaces, point-set topology, sequences and series, continuity, differentiability, the theory of Riemann integration, and functional approximation and convergence.

264. Applied Mathematics: Partial Differential Equations
Adam Levy T 11:30 - 12:55, TH 11:30 - 12:55
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.

265. Statistics
Rosemary Roberts M 1:00 - 2:25, W 1:00 - 2:25
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.

267. Topology
Michael King M 2:30 - 3:55, W 2:30 - 3:55
Topology studies those properties of objects that are preserved under continuous changes. Examines abstract definition of a topology and examples of topological spaces, connectedness and compactness, countability and separation axioms, classification of surfaces, algebraic topology-- including homotopy, the fundamental group, covering spaces, and introductory category theory.

302. Advanced Topics in Algebra
Manuel Reyes T 1:00 - 2:25, TH 1:00 - 2:25
Introduction to rings and fields. Vector spaces over arbitrary fields. Additional topics may include Galois theory, algebraic number theory, finite fields, and symmetric functions.