Location: Bowdoin / Mathematics / Courses / Fall 2013

Mathematics

Fall 2013

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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.

155. Introduction to Statistics and Data Analysis
Michael King M 8:30 - 9:25, W 8:30 - 9:25, F 8:30 - 9:25
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 1300 {165}, Psychology 2520 {252}, or Economics 2557 {257}.

161. Differential Calculus
William Barker M 8:30 - 9:25, W 8:30 - 9:25, F 8:30 - 9:25
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
Jack O'Brien M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 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 1200 {155}, Psychology 252, or Economics 2557 {257}, or Psychology 2520 {252}.

171. Integral Calculus
Miriam Logan M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25
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
Mohammad Tajdari M 11:30 - 12:25, W 11:30 - 12:25, F 11:30 - 12:25
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.

172. Integral Calculus, Advanced Section
Manuel Reyes 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. 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 1600 {161} and the first half of Mathematics 1700 {171}. Designed for first-year students who have completed an AB Advanced Placement calculus course in their secondary schools.

172. Integral Calculus, Advanced Section
Miriam Logan T 11:30 - 12:55, TH 11:30 - 12:55
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 1600 {161} and the first half of Mathematics 1700 {171}. Designed for first-year students who have completed an AB Advanced Placement calculus course in their secondary schools.

181. Multivariate Calculus
Thomas Pietraho T 1:00 - 2:25, TH 1:00 - 2:25
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.

181. Multivariate Calculus
Amanda Redlich 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. 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
Thomas Pietraho T 11:30 - 12:55, TH 11:30 - 12:55
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
Manuel Reyes T 10:00 - 11:25, TH 10:00 - 11:25
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. Ordinary Differential Equations
Mohammad Tajdari T 8:30 - 9:55, TH 8:30 - 9:55
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
Amanda Redlich T 1:00 - 2:25, TH 1:00 - 2:25
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 8:30 - 9:55, TH 8:30 - 9:55
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.

233. Functions of a Complex Variable
Justin Marks M 1:00 - 2:25, W 1:00 - 2:25
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.

244. Numerical Methods
Adam Levy T 11:30 - 12:55, TH 11:30 - 12:55
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.

252. Mathematical Cryptography
Michael King T 10:00 - 11:25, TH 10:00 - 11:25
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.

262. Introduction to Algebraic Structures
Jennifer Taback M 11:30 - 12:55, W 11:30 - 12:55
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.

305. Advanced Topics in Probability and Statistics
Jack O'Brien M 11:30 - 12:25, W 11:30 - 12:25, F 11:30 - 12:25
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 M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 11:25
A survey of affine, projective, and non-Euclidean geometries in two-dimensions, unified by the transformational viewpoint of Klein’s Erlanger Programm. Special focus will be placed on conic sections and projective embeddings. Additional topics as time permits: complex numbers in plane geometry, quaternions in three-dimensional geometry, and the geometry of four-dimensional space-time in special relativity. Mathematics 2404 {247} is helpful but not required.