Page 172 of Boston College 2005-2006 University Catalog by Boston College University

MT 290 Number Theory for Teachers (Fall: 3) Prerequisites: MT 190-191 This course is intended to focus on the wealth of topics that relate specifically to the natural numbers. These will be treated as motivational problems to be used in an activity-oriented approach to mathematics in grades K-9. The course will demonstrate effective ways to use the calculator and computer in mathematics education. Topics include prime number facts and conjectures, magic squares, Pascals triangle, Fibonacci numbers, modular arithmetic, and mathematical art. MT 291 Geometry for Teachers (Spring: 3) Prerequisites: MT 190-191 This course is intended to fill a basic need of all teachers of grades K-9. Geometry now occupies a significant role in the elementary mathematics curriculum. The course will treat content, but ideas for presenting geometry as an activity-based program will also be stressed. Topics to be covered include the geoboard and other key manipulatives, elements of motion and Euclidean geometry, and suggestions for using Logo as a tool to enhance teaching geometry. MT 305 Advanced Calculus (Science Majors) (Spring: 4) Prerequisite: MT 202 MT 305 is required for Geology-Geophysics, Geophysics, and Physics majors. It is also recommended for Chemistry majors. Topics include linear second order differential equations, series solutions of differential equations including Bessel functions and Legendre polynomials, and solutions of the diffusion and wave equations in several dimensions. MT 310 Introduction to Abstract Algebra (Fall/Spring: 3) Prerequisites: MT 210 and MT 216 This course studies four fundamental algebraic structures: groups, including subgroups, cyclic groups, permutation groups, symmetry groups and Lagranges Theorem; rings, including subrings, integral domains, and unique factorization domains; polynomials, including a discussion of unique factorization and methods for finding roots; and fields, introducing the basic ideas of field extensions and ruler and compass constructions. MT 320 Introduction to Analysis (Fall/Spring: 3) Prerequisite: MT 202 and MT 216 The purpose of this course is to give students the theoretical foundations for the topics taught in MT 102-103. It will cover algebraic and order properties of the real numbers, the least upper bound axiom, limits, continuity, differentiation, the Riemann integral, sequences, and series. Definitions and proofs will be stressed throughout the course. MT 460 Complex Variables (Fall: 3) Prerequisites: MT 202 This course gives an introduction to the theory of functions of a complex variable, a fundamental and central area of mathematics. It is intended for mathematics majors and well-prepared science majors. Topics covered include: complex numbers and their properties, analytic functions and the Cauchy-Riemann equations, the logarithm and other elementary functions of a complex variable, integration of complex functions, the Cauchy integral theorem and its consequences, power series representation of analytic functions, the residue theorem and applications to definite integrals. MT 499 Readings and Research (Fall/Spring: 3) Department permission is required. This is an independent study course, taken under the supervision of a Mathematics Department faculty member. Interested students should see the Chairperson. MT 695 Honors Seminar (Spring: 3) Department permission is required. This is a seminar course required of students in the Departmental Honors program. Other interested students may also participate in the seminar, with permission of the instructor. Undergraduate and Graduate Course Offerings MT 326 Mathematics for Statistics (Fall: 3) MT 410 Differential Equations (Fall/Spring: 3) Prerequisites: MT 202 and MT 210 This course is a junior-senior elective intended primarily for the general student who is interested in seeing applications of mathematics. Among the topics covered will be the following: first order linear equations, higher order linear equations with constant coefficients, linear systems, qualitative analysis of non-linear systems, and an introduction to stability and bifurcations. MT 414 Numerical Analysis (Spring: 3) Prerequisites: MT 202, MT 210, and familiarity with the Mathematica programming language Topics include the solution of linear and nonlinear algebraic equations, interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, approximation theory. MT 426 Probability (Fall/Spring: 3) Prerequisites: MT 202, familiarity with the Mathematica programming language This course provides a general introduction to modern probability theory. Topics include probability spaces, discrete and continuous random variables, joint and conditional distributions, mathematical expectation, the central limit theorem, and the weak law of large numbers. Applications to real data will be stressed, and we will use the computer to explore many concepts. MT 427 Mathematical Statistics (Fall/Spring: 3) Prerequisites: MT 426 and familiarity with the Mathematica programming language Topics studied include the following: sampling distributions, parametric point and interval estimation, hypothesis testing, goodnessof-fit, parametric and nonparametric two-sample analysis. Applications to real data will be stressed, and the computer will be used to explore concepts and analyze data. MT 430 Introduction to Number Theory (Spring: 3) Prerequisite: MT 216 Topics covered include divisibility, unique factorization, congruences, number-theoretic functions, primitive roots, diophantine equations, continued fractions, quadratic residues, and the distribution of primes. An attempt will be made to provide historical background for various problems and to provide examples useful in the secondary school curriculum. MT 435 Mathematical Programming I (Fall: 3) Prerequisite: MT 210 The MT 435-436 sequence demonstrates how mathematical theory can be developed and applied to solve problems from management, The Boston College Catalog 2005-2006 169 ARTS AND SCIENCES

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