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The second digit in mathematical sciences course numbers is coded as follows:
Cat. I
This course presents vector topics and discusses partial differentiation.
Topics covered include: vector algebra, vector and scalar functions,
software for functions of two variables, partial derivatives, total
derivative, and extrema.
A knowledge of MA 1023 is assumed. Although the course will make use
of computers, no programming experience is assumed or needed.
Credit cannot be received for both MA 1004 and
MA 1014.
Cat. I (14-week course)
This course includes the topics of MA 1021 and also presents selected
topics from algebra, trigonometry, and analytic geometry.
This course, which extends for 14 weeks and offers 1/3 unit of credit,
is designed for students whose precalculus mathematics is not adequate
for MA 1021.
Cat. I
This course provides an introduction to differentiation and its
applications.
Topics covered include: functions and their graphs, sequences, limits,
continuity, differentiation, linear approximation, Newton's method,
chain rule, parametric curves, antiderivatives and projectile
problems.
A knowledge of algebra, trigonometry and analytic geometry is
assumed. Although the course will make use of computers, no
programming experience is assumed.
Credit cannot be received for both MA 1021 and
MA 1001.
Cat. I
This course provides an introduction to integration and its applications.
Topics covered include: trigonometric and inverse trigonometric
functions, numerical integration, Riemann sums, fundamental theorem of
calculus, basic techniques of integration, volumes of revolution, arc
length, exponential and logarithmic functions, and applications.
A knowledge of MA 1021 is assumed. Although the course will make use
of computers, no programming experience is assumed.
Credit cannot be received for both MA 1022 and
MA 1002.
Cat. I
This course provides an introduction to series and optimization theory.
Topics covered include: max/min problems, curve sketching,
indeterminate forms, improper integrals, Taylor's theorem with
remainder, convergence of series and power series.
A knowledge of MA 1022 is assumed. Although the course will make use
of computers, no programming experience is assumed.
Credit cannot be received for both MA 1023 and
MA 1003.
Cat. I
This course provides an introduction to multivariable calculus.
Topics covered include: vector algebra and functions, partial
derivatives and gradient, optimization in two and three dimensions,
double and iterated integrals, polar coordinates, other coordinate
systems and applications.
A knowledge of MA 1023 is assumed. Although the course will make use
of computers, no programming experience is assumed.
Credit cannot be received for both MA 1024 and
MA 2005.
Cat. I
This course discusses integration of multivariable functions and gives
an introduction to vector calculus.
Topics covered include: multiple integration, integration software,
applications, additional techniques of integration, vector
differentiation, and line integrals.
A knowledge of MA 1004 is assumed. Although the course will make use
of computers, no programming experience is assumed or needed.
Credit cannot be received for both MA 1014 and
MA 2005.
Cat. I
This course develops techniques for solving ordinary differential
equations. Topics covered include: introduction to modeling using
first-order differential equations, solution methods for linear
higher-order equations, qualitative behavior of nonlinear first-order
equations, oscillatory phenomena including spring-mass system and
RLC-circuits and Laplace transform. Additional topics may be chosen
from power series method, methods for solving systems of equations and
numerical methods for solving ordinary differential equations.
A knowledge of MA 1004 or
MA 1024 is assumed.
Cat. I
This course provides a study of computational techniques of matrix
algebra and an introduction to vector spaces.
Topics covered include: matrix algebra, systems of linear equations,
eigenvalues and eigenvectors, least squares, vector spaces, inner
products, and introduction to numerical techniques, and applications
of linear algebra.
A knowledge of MA 1022 is assumed.
Cat I.
This course serves as an introduction to some of the more important
concepts, techniques, and structures of discrete mathematics providing
a bridge between computer science and mathematics.
Topics include functions and relations, sets, countability, groups,
graphs, propositional and predicate calculus, and permutations and
combinations.
Students will be expected to develop simple proofs for problems drawn
primarily from computer science and applied mathematics.
Intended audience: computer science and mathematical sciences majors.
Recommended background: none.
Cat. I
This course introduces students to the principles of decision theory
as applied to the planning, design and management of complex
projects. It will be useful to students in all areas of engineering,
actuarial mathematics as well as those in such interdisciplinary areas
as environmental studies. It emphasizes quantitative, analytic
approaches to decision making using the tools of applied mathematics,
operations research, probability and computations. Topics covered
include: the systems approach, mathematical modeling, optimization and
decision analyses. Case studies from various areas of engineering or
actuarial mathematics are used to illustrate applications of the
materials covered in this course.
A knowledge of MA 1004 or
MA 1024 is assumed. Familiarity with vectors
and matrices is helpful. Although the course makes use of computers,
no programming experience is assumed. Students who have received
credit for CE 2010 may not receive credit for
MA 2210.
Cat. I
This course introduces the student to vector and tensor calculus.
Topics covered include: scalar and vector functions and fields,
tensors, basic differential operations for vectors and tensors, line
and surface integrals, change of variable theorem in integration,
integral theorems of vector and tensor calculus. The theory will be
illustrated by applications to areas such as electrostatics, theory of
heat, electromagnetics, elasticity and fluid mechanics.
A knowledge of MA 1024 or
MA 2005 is assumed.
Cat. I
This course is designed to introduce the student to data analytic and
applied statistical methods commonly used in industrial and scientific
applications as well as in course and project work at WPI. Emphasis
will be on the practical aspects of statistics with students analyzing
real data sets on an interactive computer package.
Topics covered include analytic and graphical representation of data,
introduction to least squares, discrete and continuous probability
models, the central limit theorem, elementary sampling theory, point
and interval estimation, and one sample hypothesis tests of means
including p-values and significance levels.
A knowledge of MA 1022 is assumed.
Cat. I
This course is a continuation of MA 2611.
Topics covered include tests of hypotheses, chi-square tests,
regression analysis, survey sampling, and design and analysis of one
factor experiments and, as time allows, of multifactor
experiments.
A knowledge of MA 2611 is assumed.
Cat. I
This course provides a deeper understanding of topics introduced in MA
2071 and also continues the development of those topics.
Topics covered include: abstract vector spaces, linear
transformations, matrix representations of a linear transformation,
characteristics and minimal polynomials, diagonalization, and Jordan
canonical form.
A knowledge of MA 2071 is assumed.
Cat. I
An introduction to actuarial mathematics is provided for those who may
be interested in the actuarial profession.
Topics usually included are: measurement of interest, including
accumulated and present value factors; annuities certain; amortization
schedules and sinking funds; and bonds.
A knowledge of MA 2051 with the ability to write computer programs is
assumed.
Cat. I
A continuation of a study of actuarial mathematics with emphasis on
the theory and application of contigency mathematics in the areas of
life insurance and annuities.
Topics usually included are: survival functions and life tables; life
insurance; life annuities; net premiums; and premium reserves.
A knowledge of MA 3211 and
MA 3613 is assumed.
Cat. I
Topics covered include: solution of nonlinear equations, finding roots
of polynomials, interpolation and polynomial approximation,
approximation theory, numerical differentiation and
integration. Numerical linear algebra and numerical solution of
differential equations will not be studied: see MA 4255 and
MA 4411
for these materials.
A knowledge of MA 2051 or of
MA 2071 and the ability to write programs
in a scientific language is assumed. Computer programming will be
necessary to utilize existing scientific subroutines for case studies
but the details of programming will not be emphasized.
Cat. II
This course introduces the concepts and techniques of graph theory-a
part of mathematics finding increasing application to diverse areas
such as management, computer science and electrical engineering.
Topics covered include: graphs and digraphs, paths and circuits, graph
and digraph algorithms, trees, cliques, planarity, duality and
colorability.
A knowledge of MA 2071 is assumed.
This course will be offered in 1996-97 and in alternate years thereafter.
Cat. II
This course introduces the concepts and techniques of combinatorics-a
part of mathematics with applications in computer science and in the
social, biological, and physical sciences. Emphasis will be given to
problem solving.
Topics will be selected from: basic counting methods,
inclusion-exclusion principle, generating functions, recurrence
relations, systems of distinct representatives, combinatorial designs,
combinatorial algorithms and applications of combinatorics.
A knowledge of MA 2071 is assumed.
This course will be offered in 1995-96 and in alternate years thereafter.
Cat. I
This course is primarily concerned with the study of physical and
biological models leading to systems of nonlinear ordinary
differential equations. Examples are taken from electrical and
mechanical oscillations, ecological models and reaction
kinetics. Students will learn how to turn a real-life physical or
biological problem into a mathematical one and to interpret the
mathematical results. The following mathematical topics will also be
covered in this course: solving systems of ordinary differential
equations using the matrix method, linear stability theory,
phase-plane analysis and limit cycles.
A knowledge of MA 1024 or
MA 2005,
MA 2051 and
MA 2071 is assumed.
Cat. I
This course is designed to introduce the student to probability.
Topics to be covered are: basic probability theory including Bayes
theorem; discrete and continuous random variables; special
distributions including the Bernoulli, Binomial, Geometric, Poisson,
Uniform, Normal, Exponential, Chi-square, Gamma, Weibull, and Beta
distributions; multivariate distributions; conditional and marginal
distributions; independence; expectation; transformations of
univariate random variables.
A knowledge of MA 1024 or
MA 2005 is assumed.
Cat. II
This course extends the student's knowledge of multiple regression,
ANOVA and experimental design beyond the levelof MA 2612.
The matrix
formulation of the general linear model and its applications to
multiple regression will be discussed. Other topics include
diagnostics and remedial measures, regression model building methods,
blocking in experimental design, nested designs, repeated measures,
split plot, Latin square designs, and crossover designs. Special
emphasis will be given to fitting models to real data sets using
statistical software.
A knowledge of MA 2071 and
MA 2612 is assumed.
This course will be offered in 1996-97 and in alternate years thereafter.
Cat. II
This course covers one or more selected topics from such subjects as
time series analysis, nonparametric and robust methods, decision
theory, Bayesian inference, survival analysis, categorical data
analysis, modern data analysis, and statistical computing and
simulation.
Statistical software will be used wherever appropriate.
A knowledge of MA 2612 is assumed.
This course will be offered in 1995-96 and in alternate years thereafter.
Cat. II
This course provides an introduction to one of the major areas of
mathematics.
Topics will be selected from groups or from rings and fields. The
instructor should be consulted as to the specific topics to be
covered.
A knowledge of MA 2071 is assumed.
This course will be offered in 1995-96 and in alternate years thereafter.
Cat. I
Advanced Calculus is a two-part course giving a rigorous presentation
of the important concepts of classical real analysis.
Topics covered in the two-course sequence include: basic set theory,
elementary topology of Euclidean spaces, limits and continuity,
differentiation Reimann-Stieltjes integration, infinite series,
sequences of functions, and topics in multivariate calculus.
A knowledge of MA 2051 and
MA 2071 is assumed.
Cat. I
MA 3832 is a continuation of MA 3831.
For the contents of this course, see the description given for
MA 3831.
A knowledge of MA 3831 is assumed.
Cat. II
This course covers topics in risk theory as it is applied, under
specified assumptions, to insurance.
Topics covered include: economics of insurance, short term individual
risk models, single period and extended period collective risk models,
and applications.
A knowledge of MA 3212 is assumed.
This course will be offered in 1995-96 and in alternate years thereafter.
Cat. II
This course introduces the nature and properties of survival models
and techniques for life table construction are considered.
Topics covered include: parametric and tabular models, estimation
techniques for both model types from both complete and incomplete data
samples. For tabular models the actuarial, moment, and maximum
likelihood estimation techniques will be discussed. Parametric models
with concomitant variables will be introduced.
A knowledge of MA 3212 is assumed.
This course will be given in 1996-97 and alternate years thereafter.
Cat. I
This course considers the formulation of real-world optimization
problems as linear programs, the most important algorithms for their
solution, and techniques for their analysis.
Topics covered include: the primal and dual simplex algorithms,
duality theory, parametric analysis, network flow models and, as time
permits, bounded variable linear programs or interior methods.
A knowledge of MA 2071 is assumed.
Cat. II
This course develops specialized techniques to solve linear programs
having integer constraints and considers the application of these
techniques to problems in areas such as capital budgeting, scheduling,
project management, or routing decisions.
Topics covered include: branch and bound, out-of-kilter, network flow,
greedy, and dynamic programming algorithms. The complexity of the
algorithms will also be treated.
A knowledge of MA 4231 is assumed.
This course will be offered in 1996-97 and in alternate years thereafter.
Cat. II
This course explores theoretical conditions for the existence of
solutions and effective computational procedures to find these
solutions for optimization problems involving nonlinear functions.
Topics covered include: classical optimization techniques, Lagrange
multipliers and Kuhn-Tucker theory, duality in nonlinear programming,
and algorithms for constrained and unconstrained problems.
A knowledge of vector calculus at the level of MA 3251 is assumed.
This course will be offered in 1995-96 and in alternate years thereafter.
Cat. II
This course develops probabilistic methods useful to planners and
decision makers in such areas as strategic planning, service
facilities design, and failure of complex systems.
Topics covered include: decisions theory, inventory theory, queuing
theory, reliability theory, and simulation.
A knowledge of probability theory at the level of MA 3613 is assumed.
This course will be offered in 1995-96 and in alternate years thereafter.
Cat. II
The objective of this course is to acquaint the student with a broad
set of algorithms for the numerical solution of problems in linear
algebra and ordinary differential equations.
Topics covered include: direct and iterative algorithms for the
solution of systems of linear equations, the inverse of a matrix, the
eigenvalue problem for matrices, and initial and boundary value
problems for ordinary differential equations.
A knowledge of MA 3255 or
CS 3031 is assumed.
This course will be offered in 1995-96 and in alternate years thereafter.
Cat. I
This course provides an introduction to the ideas and techniques of
complex analysis that are frequently used by scientists and
engineers. The presentation will follow a middle ground between rigor
and intuition.
Topics covered include: complex numbers, analytic functions, Taylor
and Laurent expansions, Cauchy integral theorem, residue theory, and
conformal mappings.
A knowledge of MA 1024 or
MA 2005 and
MA 2051 is assumed.
Cat. II
Since most differential equations that arise in science and
engineering cannot be solved exactly in terms of elementary functions,
it is crucial to develop methods for obtaining approximate
solutions. This course is primarily concerned with developing such
approximate solutions. Other topics in numerical analysis are treated
in MA 3255 and
MA 4255.
Topics covered include: methods for the solution of initial value problems, stiff differential equations, shooting methods, finite differences and the numerical solution of boundary value problems. Additional advanced topics (such as the method of finite elements) will be included depending on student interest and time limitations.
A knowledge of MA 2051 and
MA 2071 is assumed. An ability to write computer programs in a scientific language is assumed. Students enrolling in this course must have knowledge either of numerical methods or of boundary value problems. The former can be obtained from MA 3255 or CS 3031; the latter may be obtained from MA 4451.
This course will be offered in l996-97 and in alternate years thereafter.
Cat. I
Science and engineering majors often encounter partial differential
equations in the study of heat flow, vibrations, electric circuits and
similar areas. Solution techniques for these types of problems will be
emphasized in this course.
Topics covered include: derivation of partial differential equations
as models of prototype problems in the areas mentioned above, Fourier
Series, solution of linear partial differential equations by
separation of variables, Fourier integrals and a study of Bessel
functions.
A knowledge of MA 1024 or
MA 2005 and
MA 2051 is assumed.
Cat. II
The first part of the course will cover existence and uniqueness of
solutions, continuous dependence of solutions on parameters and
initial conditions, maximal interval of existence of solutions,
Gronwall's inequality, linear systems and the variation of constants
formula, Floquet theory, stability of linear and perturbed linear
systems. The second part of the course will cover material selected by
the instructor. Possible topics include: Introduction to dynamical
systems, stability by Lyapunov's direct method, study of periodic
solutions, singular perturbation theory and nonlinear oscillation
theory.
A knowledge of MA 3431 and
MA 3832 is assumed.
This course will be offered in 1995-96 and in alternate years thereafter.
Cat. II
The first part of the course will cover the following topics: boundary
value problems in two and three dimensions using multiple Fourier
series, classification of partial differential equations, solving
single first order equations by the method of characteristics,
solutions of Laplace's and Poisson's equations including the
construction of Green's function, solutions of the heat equation
including the construction of the fundamental solution, maximum
principles for elliptic and parabolic equations. For the second part
of the course, the instructor may choose to expand on any one of the
above topics.
A knowledge of MA 4451 and
MA 3832 is assumed.
This course will be offered in 1996-97 and in alternate years thereafter.
Cat.II.
This course covers the calculus of variations and select topics from
optimal control theory. The purpose of the course is to expose
students to mathematical concepts and techniques needed to handle
various problems of design encountered in many fields,
e. g. electrical engineering, structural mechanics and
manufacturing.
Topics covered will include: derivation of the necessary conditions of
a minimum for simple variational problems and problems with
constraints, variational principles of mechanics and physics, direct
methods of minimization of functions, Pontryagin's maximum principle
in the theory of optimal control and elements of dynamic
programming.
A knowledge of MA 2051 and
MA 4451 will be assumed.
This course will be offered in 1996-97 and alternate years thereafter.
Cat. I (14 week course)
Intended for advanced undergraduates and beginning graduate students
in the mathematical sciences and for others intending to pursue the
mathematical study of probability and statistics, this course begins
by covering the material of MA 3613 at a more advanced
level. Additional topics covered are: one-to-one and many-to-one
transformations of random variables; sampling distributions; order
statistics, limit theorems.
A knowledge of MA 3613,
MA 3831 - MA 3832
is assumed.
Cat. I (14 week course)
This course is designed to complement MA 4631 and
provide background
in principles of statistics.
Topics covered include: point and interval estimation; sufficiency,
completeness, efficiency, consistency; the Rao-Blackwell theorem and
the Cramer-Rao bound; minimum variance unbiased estimators, maximum
likelihood estimators and Bayes estimators; tests of hypothesis
including uniformly most powerful, likelihood ratio, minimax and
bayesian tests.
A knowledge of MA 4631 is assumed.
Cat. II
This course provides an introduction to areas which have been part of
the traditional major in mathematics.
Topics will be selected from areas such as number theory, geometry,
topology, and modern algebra. The instructor should be consulted as to
the specific topics to be covered.
A knowledge of mathematics at the level of MA 3071 and
MA 3821-32 is
assumed.
This course will be offered in 1996-97 and in alternate years thereafter.
Cat. I