Location: Bowdoin / Mathematics / Courses / Fall 2010

Mathematics

Fall 2010

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
Rosemary Roberts T  11:30 - 12:55
TH 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, or Economics 257.

161. Differential Calculus
William Barker T  11:30 - 12:55
TH 11:30 - 12:55
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
Abukuse Mbirika M  1:00 - 2:25
W  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.

171. Integral Calculus
Jennifer Taback 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. Four to five hours of class meetings and computer laboratory sessions per week, on average.

171. Integral Calculus
Mohammad Tajdari 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. Four to five hours of class meetings and computer laboratory sessions per week, on average.

172. Integral Calculus, Advanced Section
Thomas Pietraho T  10:00 - 11:25
TH 10:00 - 11:25
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. Four to five hours of class meetings and computer laboratory sessions per week, on average. 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
Michael King 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. Four to five hours of class meetings and computer laboratory sessions per week, on average.

181. Multivariate Calculus
Mohammad Tajdari T  2:30 - 3:55
TH 2:30 - 3:55
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. Four to five hours of class meetings and computer laboratory sessions per week, on average.

200. Introduction to Mathematical Reasoning
Jennifer Taback M  11:30 - 12:55
W  11:30 - 12:55
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.

201. Linear Algebra
Leon Harkleroad T  8:30 - 9:55
TH 8:30 - 9:55
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. Formerly Mathematics 222.

201. Linear Algebra
Leon Harkleroad T  1:00 - 2:25
TH 1:00 - 2:25
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. Formerly Mathematics 222.

204. Biomathematics
Mary Zeeman M  1:00 - 2:25
W  1:00 - 2:25
A study of mathematical methods driven by questions in biology. Biological questions are drawn from a broad range of topics, including disease, ecology, genetics, population dynamics, neurobiology, endocrinology and biomechanics. Mathematical methods include compartmental models, matrices, linear transformations, eigenvalues, eigenvectors, matrix iteration and simulation; ODE models and simulation, stability analysis, attractors, oscillations and limiting behavior, mathematical consequences of feedback, and multiple time-scales. Three hours of class meetings and two 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. Formerly Mathematics 174.

225. Probability
Rosemary Roberts T  2:30 - 3:55
TH 2:30 - 3:55
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 T  10:00 - 11:25
TH 10:00 - 11:25
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 T  8:30 - 9:55
TH 8:30 - 9:55
A study of the fundamental concepts of vector calculus based on linear algebra. Topics include the derivative as best affine approximation; higher order derivatives and Taylor approximations; multiple integration and change of variables; vector fields, curl, and divergence; line and surface integration; the integral theorems of Green, Gauss, and Stokes; conservative vector fields; differential forms and the generalized Stokes' theorem; applications in the physical sciences and economics.

263. Introduction to Analysis
Thomas Pietraho T  1:00 - 2:25
TH 1:00 - 2:25
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.

304. Advanced Topics in Applied Mathematics
Mary Zeeman M  10:00 - 11:25
W  10:00 - 11:25
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.