Location: Bowdoin / Mathematics / Courses / Fall 2012

Mathematics

Fall 2012

  • Visit Anchor to search for courses by title, instructor, department, and more.
  • Login to Blackboard. Instructional materials are available on a course-by-course basis.
050. Quantitative Reasoning
Eric Gaze T 1:00 - 2:25, TH 1:00 - 2:25 Searles-117
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.

155. Introduction to Statistics and Data Analysis
Rosemary Roberts M 1:00 - 2:25, W 1:00 - 2:25 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
Raj Saha M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 11:25 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 11:30 - 12:55, W 11:30 - 12:55 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
None None T 10:00 - 11:25, TH 10:00 - 11:25 Searles-215
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
None None T 1:00 - 2:25, TH 1:00 - 2:25 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. An average of four to five hours of class meetings and computer laboratory sessions per week.

172. Integral Calculus, Advanced Section
Manuel Reyes M 2:30 - 3:55, W 2:30 - 3:55 Searles-213
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. An average of four to five hours of class meetings and computer laboratory sessions per week. 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
Leon Harkleroad T 10:00 - 11:25, TH 10:00 - 11:25 Searles-113
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. An average of four to five hours of class meetings and computer laboratory sessions per week. 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
Sarah Iams T 8:30 - 9:55, TH 8:30 - 9:55 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.

200. Introduction to Mathematical Reasoning
Manuel Reyes M 11:30 - 12:55, W 11:30 - 12:55 Searles-213
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
Leon Harkleroad T 11:30 - 12:55, TH 11:30 - 12:55 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.

201. Linear Algebra
Sarah Iams T 11:30 - 12:55, TH 11:30 - 12:55 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.

204. Biomathematics
Mary Zeeman T 10:00 - 11:25, TH 10:00 - 11:25 Searles-217
A study of mathematical modeling in biology, with a focus on translating back and forth between biological questions and their mathematical representation. Biological questions are drawn from a broad range of topics, including disease, ecology, genetics, population dynamics, and neurobiology. Mathematical methods include discrete and continuous (ODE) models and simulation, box models, linearization, stability analysis, attractors, oscillations, limiting behavior, feedback, and multiple time-scales. Three hours of class meetings and 1.5 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.

224. Ordinary Differential Equations
Mary Zeeman T 2:30 - 3:55, TH 2:30 - 3:55 Searles-217
A study of some of the ordinary differential equations that model a variety of systems in the physical, 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, oscillators and economic markets. Computer software is used as an important tool, but no prior programming background is assumed.

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.

232. Number Theory
Michael King M 11:30 - 12:55, W 11:30 - 12:55 Searles-113
A standard course in elementary number theory, which traces the historical development and includes the major contributions of Euclid, Fermat, Euler, Gauss, and Dirichlet. Prime numbers, factorization, and number-theoretic functions. Perfect numbers and Mersenne primes. Fermat’s theorem and its consequences. Congruences and the law of quadratic reciprocity. The problem of unique factorization in various number systems. Integer solutions to algebraic equations. Primes in arithmetic progressions. An effort is made to collect along the way a list of unsolved problems.

253. Vector Calculus
William Barker M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 11:25 Searles-113
A study of vector calculus based on linear algebra. The central unifying theme is the theory and application of differential forms. Topics include the derivative as a linear transformation between Euclidean spaces; the Inverse Function Theorem and the Implicit Function Theorem; multiple integration and the Change of Variables Theorem; vector fields, tenors, and differential forms; line and surface integration; integration of differential forms; the exterior derivative; closed and exact forms; the generalized Stokes’ Theorem; gradient, curl, divergence and the integral theorems of Green, Gauss, and Stokes; manifolds in Euclidean space; applications in the physical sciences.

258. Combinatorics and Graph Theory
Abukuse Mbirika T 1:00 - 2:25, TH 1:00 - 2:25 Searles-113
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.

263. Introduction to Analysis
William Barker M 8:00 - 9:25, W 8:00 - 9:25, F 8:00 - 9:25 Searles-113
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.

304. Advanced Topics in Applied Mathematics
Adam Levy T 11:30 - 12:55, TH 11:30 - 12:55 Searles-213
One or more selected topics in applied mathematics. Material selected from the following: Fourier series, partial differential equations, integral equations, optimal control, bifurcation theory, asymptotic analysis, applied functional analysis, and topics in mathematical physics.

304. Advanced Topics in Applied Mathematics
Adam Levy T 10:00 - 11:25, TH 10:00 - 11:25 Searles-213
One or more selected topics in applied mathematics. Material selected from the following: Fourier series, partial differential equations, integral equations, optimal control, bifurcation theory, asymptotic analysis, applied functional analysis, and topics in mathematical physics.