Location: Bowdoin / Mathematics / Courses / Spring 2005

Mathematics

Courses

Spring 2005

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055. Statistical Reasoning (formerly Mathematics 65): Raymond Fisher T 10:00 - 11:25, TH 10:00 - 11:25; An introduction to the ideas of statistics. Students learn how to reason statistically and how to interpret and draw conclusions from data. Designed for students who want to understand the nature of statistical information. Open to first-year students and sophomores who want to improve their quantitative skills. It is recommended that students with a background in calculus enroll in Mathematics 155 or 165. Not open to students who have credit for Mathematics 65.
155. Introduction to Statistics and Data Analysis: Rosemary Roberts M 11:30 - 12:55, W 11:30 - 12:55; 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, Economics 257, or AP Statistics.
161. Differential Calculus: James Ward 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.
161. Differential Calculus: Mark Rhodes M 11:30 - 12:25, W 11:30 - 12:25, F 11:30 - 12:25; 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.
LAB: James Ward TH 2:30 - 4:25; 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.
LAB: Mark Rhodes T 2:30 - 4:25; 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.
171. Integral Calculus: Rebecca Field TH 10:00 - 11:25, T 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. Four to five hours of class meetings and computer laboratory sessions per week, on average.
171. Integral Calculus: William Barker T 11:30 - 12:55, TH 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. Four to five hours of class meetings and computer laboratory sessions per week, on average.
LAB: Rebecca Field W 1:30 - 3:25; 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.
LAB: William Barker M 1:30 - 3:25; 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.
181. Multivariate Calculus: Mohammad Tajdari M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25; 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.
181. Multivariate Calculus: Mohammad Tajdari M 11:30 - 12:25, W 11:30 - 12:25, F 11:30 - 12:25; 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.
LAB: Mohammad Tajdari M 1:30 - 3:25; 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.
LAB: Mohammad Tajdari W 1:30 - 3:25; 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: Rebecca Field T 1:00 - 2:25, TH 1:00 - 2:25; 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.
222. Linear Algebra: Matthew Killough M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 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.
255. Applied Statistical Methods: Matthew Killough T 10:00 - 11:25, TH 10:00 - 11:25; An introduction to statistical modeling techniques with an emphasis on applications. Deals first with regression analysis: least square estimates of parameters; single and multiple linear regression; hypothesis testing and confidence intervals in linear regression models; and testing of models, data analysis, and appropriateness of models. Follows with a focus on time series: linear time series models; moving average, autoregressive, and ARIMA models; estimation, data analysis, and forecasting with time series models; and forecast errors and confidence intervals.
263. Introduction to Analysis: Mark Rhodes M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25; Emphasizes proof and develops the rudiments of mathematical analysis. Topics include an introduction to the theory of sets and topology of metric spaces, sequences and series, continuity, differentiability, and the theory of Riemann integration. Additional topics may be chosen as time permits.
264. Applied Mathematics: Partial Differential Equations: Adam Levy T 1:00 - 2:25, TH 1:00 - 2:25; 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 T 11:30 - 12:55, TH 11:30 - 12:55; 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.
302. Advanced Topics in Algebra: James Ward M 10:30 - 11:25, W 10:30 - 11:25, F 10:30 - 11:25; One or more specialized topics from abstract algebra and its applications. Topics may include group representation theory, coding theory, symmetries, ring theory, finite fields and field theory, algebraic numbers, and Diophantine equations.
307. Advanced Topics in Geometry: William Barker T 8:30 - 9:55, TH 8:30 - 9:55; A survey of analytic geometry, affine geometric, projective geometry, and the non-Euclidean geometries. Culminates in a rigorous development of the geometry of four-dimensional space-time in special relativity. The unifying theme is the transformational viewpoint of Klein’s Erlangen Program.