Mathematics and Statistics
Note: the courses on this page reflect Summer Term 2008 offerings.
Please check back on December 15 for a list of courses available during Summer Term 2009.
College of Arts and Sciences
CAS MA 113 Elementary Statistics
Basic concepts of estimation and tests of hypotheses, ideas from probability;
one-, two-, and multiple-sample problems. Applications in social sciences.
Primarily for students in the social sciences who require a one-semester introduction
to statistics; others should consider CAS MA 115 or MA 213. Meets MCS divisional
studies requirement. 4 cr.
Note: MA 113 may not be taken for credit by any student who has completed
any MA course numbered 300 or higher. Students may receive credit for not more
than one of the following courses: MA 113, MA 115, or MA 213.
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CAS MA 115 Statistics I
Numerical and graphical summaries of univariate and bivariate data. Basic probability,
random variables, binomial distribution, normal distribution. One-sample statistical
inference for normal means and binomial probabilities. Primarily for students
in the social sciences with limited mathematics preparation. Meets MCS divisional
studies requirement. 4 cr.
Note: MA 115 may not be taken for credit by any student who has completed
any MA course numbered 300 or higher. Students may receive credit for not more
than one of the following: MA 113, MA 115, or MA 213.
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CAS MA 116 Statistics II
Prereq: CAS MA 115 or equivalent. One- or two-sample inference for normal
means and binomial probabilities, analysis of variance, simple linear regression,
multiple regression, analysis of categorical data. Introduction to survey design
and design of experiments. Primarily for students in the social sciences with
limited mathematics preparation. Meets MCS divisional
studies requirement. 4 cr.
Note: MA 116 may not be taken for credit by any student who has completed
any MA course numbered 300 or higher. Students may receive credit for not more
than one of the following: MA 116, MA 214, or MA 614.
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CAS MA 118 College Algebra and Trigonometry
Functions and graphs. Linear and quadratic equations. Exponents; logarithms.
Right and oblique triangles; trigonometric functions. Optimization. Specifically
intended to prepare students with insufficient background in mathematics for
the study of calculus. This course may not be used in fulfillment of the divisional
studies requirement. Satisfies the mathematics requirement in the College program.
4 cr.
Note: MA 118 may not be taken for credit by any student who has completed
any MA course numbered 121 or higher.
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CAS MA 120 Applied Mathematics for Social and Management Sciences
Linear equations, systems of linear equations, matrix algebra, exponential
functions and logarithms, elements of differential calculus, optimization,
probability. Applications in economics, finance, and management. Satisfies
mathematics requirement and meets MCS divisional
studies requirement.. 4 cr.
Note: MA 120 may not be taken for credit by any student who has completed
any MA course numbered 124 or higher.
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CAS MA 121 Calculus for Life and Social Sciences I
Differentiation and integration of functions of one variable. Same topics
as CAS MA 123, but with less emphasis on mathematical generality and more on
application. Especially suitable for students concentrating in the biological
and social sciences. Meets MCS divisional
studies requirement. 4 cr.
Note: Students may receive credit for either CAS MA 121 or 123, but not both.
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CAS MA 122 Calculus for Life and Social Sciences II
Prereq: CAS MA 121 or MA 123. Continuation of CAS MA 121. Review of
univariate calculus, calculus of the elementary transcendental functions, elementary
differential
equations, elementary multivariate calculus. Applications to exponential growth,
optimization, equilibrium, and dynamic modeling problems. Meets MCS divisional
studies requirement. 4 cr.
Note: Students may receive credit for not more than one of the following:
MA 122, MA 124, MA 127, or MA 129.
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CAS MA 123 Calculus I
Limits; derivatives; differentiation of algebraic functions. Applications
to maxima, minima, and convexity of functions. The definite integral; the fundamental
theorem of integral calculus; applications of integration. Meets MCS divisional
studies requirement. 4 cr.
Note: Students may receive credit for either CAS MA 121 or 123, but not both.
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CAS MA 124 Calculus II
Prereq: CAS MA 121 or MA 123. Logarithmic, exponential, and trigonometric
functions. Sequences and series; Taylor's series with the remainder. Methods
of integration. Calculus I and II together constitute an introduction to calculus
of a function of a single real variable. Meets MCS divisional
studies requirement. 4 cr.
Note: Students may receive credit for not more than one of the following:
MA 122, MA 124, MA 127, or MA 129.
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CAS MA 142 Introduction to Linear Algebra
Coreq: CAS MA 122, MA 124, MA 127, or MA 129. Systems of linear equations;
matrices. Vector spaces and linear transformations. Determinants. Eigenvalues
and eigenvectors. Applications. 2 cr.
Note: Cannot be taken for credit in addition to
CAS MA 242, MA 442 or ENG EK 102.
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CAS MA 213 Basic Statistics and Probability
Prereq: good background in high school algebra. Elementary treatment
of probability densities, means, variances, correlation, independence, the binomial
distribution,
the central limit theorem. Stresses understanding and theoretical manipulation
of statistical concepts. Meets MCS divisional
studies requirement. 4 cr.
Note: Students may receive credit for not more than one of the following:
MA 113, MA 115 or MA 213.
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CAS MA 214 Applied Statistics
Prereq: CAS MA 213 or consent of instructor. Inference about proportions,
goodness of fit, student's t-distribution, tests for normality; two-sample
comparisons, regression and correlation, tests for linearity and outliers,
residual analysis, contingency tables, analysis of variance. Meets MCS divisional
studies requirement. 4 cr.
Note: Students may receive credit for not more than one of the following:
MA 116, MA 214, or MA 614.
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CAS MA 225 Multivariate Calculus
Prereq: CAS MA 124, MA 127, or MA 129. Vectors, lines, planes. Multiple
integration, cylindrical and spherical coordinates. Partial derivatives, directional
derivatives, scalar and vector fields, the gradient, potentials, approximation,
multivariate minimization, Stokes's and related theorems. 4 cr.
Note: Cannot be taken
for
credit in addition to CAS MA 230.
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CAS MA 226 Differential Equations
Prereq: CAS MA 225 or MA 230. First-order linear and separable equations.
Second-order equations and first-order systems. Linear equations and linearization.
Numerical and qualitative analysis. Laplace transforms. Applications and modeling
of real phenomena throughout. 4 cr.
Note: Cannot be taken for credit in addition to CAS
MA 231.
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CAS MA 242 Linear Algebra
Coreq: CAS MA 122, MA 124, MA 127, or MA 129. Matrix algebra, solution
of linear systems, determinants, Gaussian elimination, fundamental theory, row-echelon
form. Vector spaces, bases, norms. Computer methods. Eigenvalues and eigenvectors,
canonical decomposition. Applications. 4 cr.
Note: Cannot be taken for credit in addition
to CAS MA 142, MA 442, or ENG EK 102.
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CAS MA 293 Discrete Mathematics I
Prereq: CAS MA 123. Propositional logic, set theory. Elementary probability
theory. Number theory. Combinatorics with applications. 4 cr.
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CAS MA 294 Applied Abstract Algebra
Prereq: CAS MA 293 or consent of instructor. Abstract algebra and its applications to combinatorics.
A first exposure to groups, rings, and fields via significant combinatorial applications.
Students who have already received credit for MA 541 or MA 542 may not subsequently
receive credit for MA 294. 4 cr.
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CAS MA 341 Introduction to Number Theory
Prereq: CAS MA 242
or consent of instructor. Study of integers and basic results of number theory.
Topics include Linear Diophantine equations, prime numbers and factorization,
congruences, and quadratic reciprocity. 4 cr.
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CAS MA 381 Elementary Probability
Prereq: CAS MA 225 or MA 230. A calculus-based introductory course in probability.
Language of probability, combinatorics, conditional probability, discrete
and
continuous random variables, the Poisson process, joint probability distribution,
moment generating function, law of large numbers and central limit theorem,
sample estimators for mean and variance. 4 cr.
Note: Cannot be taken for credit in
addition to CAS MA 581 or MA 590.
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CAS MA 411 Advanced Calculus
Prereq: CAS MA 225 or MA 230 and MA 242 or MA 442. Extends concepts and techniques
of calculus and develops further applications. Topics include higher dimensional
calculus, applications of vector analysis, uniform convergence of series, complex
series, improper integrals, gamma and beta functions, Stirling's formula, Fourier
series and transform. 4 cr.
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CAS MA 412 Complex Variables
Prereq: CAS MA 225 or MA 230. Basic concepts, results, and applications of
complex analysis. Emphasis on computation and applications. Complex plane and
functions, differentiability, Cauchy-Riemann conditions, contour integrals,
Cauchy formulas, complex series, residue calculus, applications. Extends the
concepts of the calculus to the complex setting. 4 cr.
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CAS MA 547 Topics in Number Theory
Prereq: CAS MA 242. Coreq: CAS MA 548. An exploration of rational arithmetic
and its generalizations. Foundations of arithmetic, Euclid's algorithm, the
fundamental theorem of arithmetic, modulo arithmetic, continued fractions,
Diophantine approximation, Pell's equation, sums of squares, the arithmetic
of polynomials over a field, arithmetic in quadratic number field, lattice
point-free regions, Minkowski's theorem on convex bodies. This class is part
of the PROMYS program. Consent of instructor is required. Students must register for both
CAS MA 547 and MA 548. 4 cr.
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CAS MA 548 Problem Solving in Number Theory
Coreq: CAS MA 547. Mathematical heuristics, including good use of language
and symbolism, techniques of exploration and discovery. Through their intensive
work on a large assortment of unusually challenging problems in number theory,
students practice the art of mathematical discovery, numerical exploration,
formulation and critique of conjectures, and techniques of proof and generalization.
This class is part of the PROMYS program. Consent of instructor is required. Students must register for both CAS
MA 547 and MA 548. 4 cr.
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CAS MA 549 Geometry and Symmetry
Prereq: consent of instructor. Problem-oriented seminar in modern geometry
focusing on invariants of transformation groups. Specific
topics may include Euclidean and plane geometry, Hilbert's Axioms, conics,
tilings, finite, projective, spherical and/or hyperbolic geometry, tessellations,
applications to number theory, Platonic Solids. 4 cr.
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CAS MA 581 Probability
Prereq: CAS MA 225 or MA 230 or consent of instructor. Basic probability,
conditional probability, independence. Discrete and continuous random variables,
mean and variance, functions of random variables, moment generating function.
Jointly distributed random variables, conditional distributions, independent
random variables. Methods of transformations, law of large numbers, central
limit theorem. (Cannot be taken for credit in addition to MA 381 or MA 590.)
4 cr.
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Graduate School of Arts and Sciences
GRS MA 647 Research Methods in Mathematics I
Prereq: CAS MA 547 and CAS MA 548 or consent of instructor. Methods of mathematical
research via prolonged study of one selected mathematical topic. Topics are usually
chosen from number theory or combinatorics. Written and oral research presentations.
2 cr.
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Metropolitan College
MET AT 752 Group Insurance Applications of Actuarial Principles
Covers the application of basic actuarial principles to group life and group
health financial security systems. Material covered will include the purpose
of these systems, financial security product design and development, underwriting
and risk management, premium determination, and the funding and valuation
of group life and group health financial security systems. Group systems
in the United States are emphasized, but the course will also review the
Canadian health system. 4 cr.
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MET AT 782 Pension Mathematics and Mortality Tables
Prereq: MET MA 581 and MET AT 721. This course covers pension actuarial funding
methods and the use of life contingencies. Included are analyses of the funding
methods allowable under ERISA, their computation, and uses. We will also
review the use of mortality tables, and discuss the various actuarial functions
that are used in pension actuarial calculations. Finally, the course will
review implications for pension funding under the IRS. 4 cr.
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MET AT 982 Internship in Actuarial Science II
Prereq: successful completion of MET AT 722 and MET AT 731, and an overall
cumulative GPA of 3.3 or higher. Offered to students who seek practical applications
of actuarial principles in insurance companies, financial institutions, pension
consulting firms, and other related fields. Requires students to participate
in an internship program within the industry. Students need to submit monthly
progress reports and a final semester report to the Chairman, Department
of Actuarial Science at Boston University. Variable cr. per
credit
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MET CS 248 Introduction to Discrete Mathematics
Prereq: high school algebra or instructor's consent. Introduction to
first
order
logic:
propositions, predicates, logic sets, relations, and functions. Combinatorics.
Introduction
to graph theory. Monoids and groups; Boolean algebra; introduction to probability
theory. 4 cr.
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MET CS 534 Quantitative Methods for Information Systems
Prereq: high school algebra or instructor's consent.
The first part of this course lays down the mathematical foundation for the study
of Probability Theory and Statistics. Functions, Combinatorial Mathematics, Differentiation
and Integration fundamentals are covered. The second part of the course concentrates
on the study of Discrete and Continuous Distributions and Linear Regression.
4 cr.
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MET MA 603 SAS with Statistical Applications
Prereq: CAS CS 111, MET CS 201 or equivalent, and MET MA 214.
Offers a unified and in-depth coverage of the statistical computer package
SAS, and its statistical applications. Topics include the language of SAS,
data formatting, creating and storing SAS data sets, file manipulations,
macro procedure, and graphics. Also included are procedures for statistical
techniques selected from analysis of variance, regression, factor analysis,
scoring, and categorical data analysis. Several large data sets are used
as case studies emphasizing hands-on experience with SAS for Windows. Laboratory
course. 4 cr.
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