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Mathematics

Courses

Fall 2008

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060. Introduction to College Mathematics: James Ward M 11:30 - 12:55, W 11:30 - 12:55; Material selected from the following topics: combinatorics, probability, modern algebra, logic, linear programming, and computer programming. This course, in conjunction with Mathematics 155 or 161, is intended as a one-year introduction to mathematics and is recommended for those students who intend to take only one year of college mathematics.
161. Differential Calculus: Mary Zeeman M 11:30 - 12:55, W 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: Helen Wong T 10:00 - 11:25, TH 10:00 - 11:25; 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: Rosemary Roberts T 11:30 - 12:55, TH 11:30 - 12:55; 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. Four to five hours of class meetings and computer laboratory sessions per week, on average. Not open to students who have credit for Mathematics 155, Psychology 252, or Economics 257.
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: Professor X T 8:30 - 9:55, TH 8:30 - 9:55; 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.
171. Integral Calculus: Professor X 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. Four to five hours of class meetings and computer laboratory sessions per week, on average.
172. Integral Calculus, Advanced Section: Thomas Pietraho T 1:00 - 2:25, TH 1:00 - 2:25; 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: Adam Levy 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. Four to five hours of class meetings and computer laboratory sessions per week, on average.
181. Multivariate Calculus: William Barker 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. 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 - 12:25, W 11:30 - 12:25, F 11:30 - 12:25; 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.
201. Linear Algebra: William Barker 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.
204. BioMathematics: Mary Zeeman M 8:00 - 9:25, W 8:00 - 9:25; 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. 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: James Ward M 9:30 - 10:25, W 9:30 - 10:25, F 9:30 - 10:25; 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. Formerly Mathematics 242.
235. Exploratory Multivariate Data Analysis: Stephen Fisk T 1:00 - 2:25, TH 1:00 - 2:25; Almost all data collected by researchers is multivariate. An introduction to the theory and techniques of exploratory multivariate data analysis. Topics include graphical techniques, scientific visualization, discriminant analysis, principle components, multi-dimensional scaling, classification, phylogeny trees and genomics, cluster analysis, and data mining. Students learn how to use the statistical system R. Formerly Mathematics 255.
263. Introduction to Analysis: Thomas Pietraho T 10:00 - 11:25, TH 10:00 - 11:25; 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: Adam Levy M 1:00 - 2:25, W 1:00 - 2:25; 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.