Graduate level course offerings: Mathematics
MA 323 Geometric Modeling 4R-0L-4C W (even
years)
Prerequisite: MA 113
Covers some of the mathematical methods for describing physical or
virtual objects in computer aided geometric design (CAGD) and
computer graphics. Emphasizes methods for curve and surface
modeling, and discusses both the underlying geometric concepts and
the practical aspects of constructing geometric models of objects.
Topics covered include Bezier curves, Hermite curves, B-splines,
Bezier patches, subdivision surfaces. In discussing these, ideas
from analytic geometry, differential geometry, affine geometry,
combinatorial geometry, and projective geometry will be
introduced.
MA 325 Fractals and Chaotic Dynamical
Systems 4R-0L-4C S
Prerequisite: CSSE 220 and MA 222
Emphasis on the mathematical and computer graphics foundations
behind fractal images and the relationship between chaotic dynamics
and fractal geometry. Self-similar fractals, random fractals with
Brownian motion, and fractals generated from dynamical systems.
Fractal dimensions. Iterated function systems. Chaos in
one-dimensional maps. Controlling chaos. Mandelbrot and Julia sets.
Computer graphics. Same as CSSE 325.
MA 327 Low Dimensional Topology 4R-0L-4C
W
Prerequisite: MA 113 or consent of instructor
An introduction to the topology of one-, two-, and
three-dimensional manifolds and its application to other areas of
mathematics and science. Topics may include, but are not restricted
to, classification of curves and surfaces, Euler characteristic,
tiling and coloring theorems, graph embeddings, vector fields,
knots and links, and elementary algebraic topology. Intended for
science and engineering majors as well as mathematics majors.
MA 330 Vector Calculus 4R-0L-4C F
Prerequisite: MA 113
Calculus of vector- valued functions of one and several variables.
Topics include differentiation (divergence, gradient and curl of a
vector field) and integration (line integrals and surface
integrals). Applications of Green's theorem, Stokes' theorem and
the divergence theorem to potential theory and/or fluid mechanics
will be provided.
MA 333 Introduction to Parallel Computing 4R-0L-4CS
(odd years)
Prerequisite: MA221 and programming experience
Principles of scientific computation on parallel computers.
Algorithms for the solution of linear systems and other scientific
computing problems on parallel machines. Course includes a major
project on RHIT's parallel cluster.
MA 336 Boundary Value Problems 4R-0L-4C
S
Prerequisite: MA 222
Introduction to boundary value problems and partial differential
equations. Emphasis on boundary values problems that arise from the
wave equation, diffusion equation, and Laplace's equation in one,
two and three dimensions. Solutions to such boundary value problems
will be discussed using Fourier series, numerical techniques, and
integral transforms.
MA 341 Topics in Mathematical Modeling 4R-0L-4C W
(even years)
Prerequisite: MA 222 or consent of instructor
An introduction to techniques of mathematical modeling involved in
the analysis of meaningful and practical problems arising in many
disciplines including mathematical sciences, operations research,
engineering, and the management and life sciences. Topics include
creative and empirical model construction, model fitting, models
requiring optimization, and modeling dynamic behavior. Student
participation in significant individual and group projects will be
emphasized.
MA 348 Continuous Optimization 4R-0L-4C S (even
years)
Prerequisite: MA 222
Optimization of nonlinear functions of real variables: algorithms
for univariate optimization; Golden section, parabolic
interpolation, hybrid methods; Newton's Method and variations for
multivariate functions; conjugate gradients and quasi-Newton
methods; line search strategies; penalty functions for constrained
optimization; modeling and applications of optimization.
MA 366 Functions of a Real Variable 4R-0L-4C
W
Prerequisite: MA 275 and MA 113
Calculus of functions of a single variable. A more careful
development of the basic concepts of analysis, including sequences,
limits, continuity, differentiability, integration, infinite
series, power series, Taylor's Theorem, and uniform
convergence.
MA 367 Functions of a Complex Variable 4R-0L-4C
S
Prerequisite: MA 221
Elementary properties of analytic functions including Cauchy's
theorem and its consequences, Laurent series, the Residue Theorem,
and mapping properties of analytic functions.
MA 371 Linear Algebra I 4R-0L-4C F,
S
Prerequisite: MA 221 or consent of instructor
Similar to MA373, but with an emphasis on the theory behind
matrices and vector spaces. Systems of linear equations, Gaussian
elimination, and the LU decomposition of a matrix. Projections,
least squares approximations, and the Gram-Schmidt process.
Eigenvalues and eigenvectors of a matrix. The diagonalization
theorem. The singular value decomposition of a matrix. Introduction
to vector spaces. Some proof writing will be required. Those
interested in applications of matrices and vector spaces should
take MA373. A student cannot take both MA 371 and MA 373 for
credit.
MA 373 Applied Linear Algebra for
Engineers 4R-0L-4C F, S
Prerequisite: MA 221 or consent of instructor
Similar to MA 371, but with emphasis on applications of matrices
and vector spaces. Systems of linear equations, Gaussian
elimination, and the LU decomposition of a matrix. Projections,
least squares approximations, and the Gram-Schmidt process.
Eigenvalues and eigenvectors of a matrix. The diagonalization
theorem. The singular value decomposition of a matrix. Those
interested in the theory behind matrices and vector spaces should
take MA 371. A student cannot take both MA 371 and MA 373 for
credit.
MA 375 Discrete and Combinatorial Algebra
II 4R-0L-4C W, S
Prerequisite: MA 275
A continuation of MA 275. Relations. An introduction to finite
state machines. More advanced enumeration techniques including
recurrence relations, generating functions and the principle of
inclusion and exclusion.
MA 376 Abstract Algebra 4R-0L-4C S
Prerequisite: MA 275
An introduction to modern abstract algebra and algebraic
structures. Topics include congruence and modular arithmetic;
rings, ideals, and quotient rings; fields, finite fields, and
subfields; groups and subgroups; homomorphisms and isomorphisms.
Other topics may also be introduced according to time and student
interest.
MA 378 Number Theory 4R-0L-4C S
Prerequisite: consent of instructor
Divisibility, congruences, prime numbers, factorization algorithms,
RSA encryption, solutions of equations in integers, quadratic
residues, reciprocity, generating functions, multiplicative and
other important functions of elementary number theory. Mathematical
conjecture and proof, mathematical induction.
MA 381 Introduction to Probability with Applications to
Statistics 4R-0L-4C F, W, S
Prerequisite: MA 113
Introduction to probability theory; axioms of probability, sample
spaces, and probability laws (including conditional probabilities).
Univariate random variables (discrete and continuous) and their
expectations including these distributions: binomial, Poisson,
geometric, uniform, exponential, and normal. Introduction to moment
generating functions. Introduction to jointly distributed random
variables. Univariate and joint transformations of random
variables. The distribution of linear combinations of random
variables and an introduction to the Central Limit Theorem.
Applications of probability to statistics.
MA 382 Introduction to Statistics with
Probability 4R-0L-4C F
Prerequisite: MA 381
This is an introductory course in statistical data analysis and
mathematical statistics.Topics covered include descriptive
statistics, Sampling distributions (including the entral Limit
Theorem), point estimation, Hypothesis testing and confidence
intervals for both one and two populations, linear regression, and
analysis of variance. Emphasis will be placed on both data analysis
and mathematical derivations of statistical techniques. A computer
package will be used for statistical analysis and simulation.
Experimental data from a variety of fields of interest will also be
used to illustrate statistical concepts and facilitate the
development of the student's statistical thinking. A student cannot
take both MA 223 and MA 382 for credit.
MA 383 Engineering Statistics II 4R-0L-4C
F
Prerequisite: MA 223 or MA 382
Hypothesis testing, confidence intervals, sample size
determination, and power calculations for means and proportions;
two factor analysis of variance (with and without interactions);
analysis of several proportions; confidence and prediction
intervals for estimated values using simple linear regression;
Pearson (linear) correlation coefficient; introduction to multiple
regression to include polynomial regression; review of fundamental
prerequisite statistics will be included as necessary.
MA 385 Quality Methods 4R-0L-4C S
Prerequisite: MA 223, or MA 382
Introduction to various aspects of statistical quality control and
statistical process control to include the following topics:
importance of variance reduction and probability concepts
influencing product quality and reliability; development and
application of control charts (P-charts, NP-charts, C-charts,
U-charts, individual's charts, moving range charts, X-bar and R as
well as X-bar and S charts); process capability indices (their use
and misuse); introduction to acceptance sampling. Other topics to
be included as time allows: 6 sigma thinking, gauge reproducibility
and repeatability, and total quality management with the
philosophies of Deming, Juran, and Crosby. Review of fundamental
prerequisite statistics will be included as necessary. Same as CHE
385.
MA 386 Statistical
Programming 4R-0L-4C
Prerequisite: previous programming course and either MA 223 or
MA 382
Database management and statistical analysis using SAS and
possibly, R/S+. Topics will include database management
(including SQL), data step programming, macro programming, standard
data analysis methods (from MA223 or higher level courses), and
coding of advanced and/or computationally intense modern
algorithms, e.g., bootstrapping and Monte Carlo methods.
MA 387 Statistical Methods in Six
Sigma 4R-0L-4C
Prerequisite: MA 223 or MA 382A course on statistical methods
used in the Six Sigma /DMAIC (Define, Measure, Analyze, Improve,
Control) paradigm.
Topics will include, but are not limited to, gauge repeatability
and reproducibility, control charts, regression, design of
experiments, and response surface optimization.
MA 423 Topics in Geometry 4R-0L-4C
(arranged)
Prerequisite: MA 371 or MA 373 or consent of
instructor
An advanced course in geometry. Topics could include from
projective geometry, computational geometry, differential geometry,
Riemannian geometry, algebraic geometry, Euclidean geometry and
non-Euclidean geometry.
MA 431 Calculus of Variations 4R-0L-4C
(arranged)
Prerequisite: MA 330
Euler-Lagrange and Hamiltonian equations, with possible
applications in mechanics, electrostatics, optics, quantum
mechanics and elasticity theory. An introduction to "direct
methods." Applications will be chosen in accordance with the
interest of the students. Both classical and numerical methods have
their place in this course.
MA 433 Numerical Analysis 4R-0L-4C W
Prerequisite: MA 222
Root-finding, computational matrix algebra, nonlinear optimization,
polynomial interpolation, splines, numerical integration, numerical
solution of ordinary differential equations. Principles of error
analysis and scientific computation. Selection of appropriate
algorithms based on the numerical problem and on the software and
hardware (such as parallel machines) available.
MA 434 Topics in Numerical Analysis 4R-0L-4C
(arranged)
Prerequisite: MA 433
An extension of the material presented in MA 433. Topics might
include numerical eigenproblems, numerical solution of partial
differential equations (finite differences, finite elements,
spectral methods), sparse matrices, global optimization,
approximation theory.
MA 436 Introduction to Partial Differential
Equations 4R-0L-4C F (even years)
Prerequisite: MA 336
Partial differential equations, elliptic, hyperbolic, and parabolic
equations. Boundary and initial value problems. Separation of
variables, special functions. Eigenfunction expansions. Existence
and uniqueness of solutions. Sturm-Liouville theory, Green's
function.
MA 439 Mathematical Methods of Image
Processing 4R-0L-4C F (odd years)
Prerequisite: MA222
Mathematical formulation and development of methods used in image
processing, especially compression. Vector space models of signals
and images, one- and two-dimensional discrete Fourier transforms,
the discrete cosine transform, and block transforms. Frequency
domain, basis waveforms, and frequency domain representation of
signals and images. Convolution and filtering. Filter banks,
wavelets and the discrete wavelet transform. Application to Fourier
based and wavelet based compression such as the JPEG compression
standard. Compression concepts such as scalar quantization and
measures of performance.
MA 444 Deterministic Models in Operations
Research 4R-0L-4C W
Prerequisite: MA 221 or MA 371/373
Formulation of various deterministic problems as mathematical
optimization models and the derivation of algorithms to solve them.
Optimization models studied include linear programs, integer
programs, and various network models. Emphasis on model formulation
and algorithm development "from the ground up."
MA 445 Stochastic Models in Operations
Research 4R-0L-4C S (even years)
Prerequisite: MA 223 or MA 381
Introduction to stochastic mathematical models and techniques that
aid in the decision-making process. Topics covered include a review
of conditional probability, discrete and continuous Markov chains,
Poisson processes, queueing theory (waiting line problems), and
reliability.
MA 446 Combinatorial Optimization 4R-0L-4C S (even
years)
Prerequisite: MA 375
An introduction to graph- and network-based optimization models,
including spanning trees, network flow, and matching problems.
Focus is on the development of both models for real-world
applications and algorithms for their solution.
MA 460 Topics in
Analysis 4R-0L-4C(arranged)
Prerequisite: consent of instructor
An advanced topics course in analysis. Topic of the course could be
advanced topics in real analysis, advanced topics in complex
analysis, analysis on manifolds, measure theory or an advanced
course in applied analysis (differential equations). May be taken
more than once provided topics are different.
MA 461 Topics in Topology 4R-0L-4C
(arranged)
Prerequisite: MA 366 or consent of instructor
Introduction to selected topics from point-set topology or
algebraic topology from a rigorous point of view. Possible topics
include metric spaces, general topological spaces, compactness,
connectedness, separation axioms, compactification and metrization
theorems, homotopy and homology, and covering spaces. Intended for
mathematics majors planning to pursue graduate study in
mathematics.
MA 466 Introduction to Functional Analysis 4R-0L-4C
(arranged)
Prerequisite: MA 366
An introduction to the theory of Banach spaces emphasizing
properties of Hilbert spaces and linear operators. Special
attention will be given to compact operators and integral
equations.
MA 470 Topics in Algebra 4R-0L-4C
(arranged)
Prerequisite: consent of instructor
An advanced topics course in algebra. Topic of the course
could be commutative algebra, Galois theory, algebraic geometry,
Lie groups and algebras, or other advanced topics in algebra.
May be taken more than once provided topics are
different.
MA 471 Linear Algebra II 4R-0L-4C S (even
years)
Prerequisite: MA 371 or MA 373
Continuation of Linear Algebra I. Properties of Hermitian and
positive definite matrices and factorization theorems (LU, QR,
spectral theorem, SVD). Linear transformations and vector
spaces.
MA 473 Design and Analysis of Algorithms 4R-0L-4C
F
Prerequisite: CSSE 230 and MA 375
Students study techniques for designing algorithms and for
analyzing the time and space efficiency of algorithms. The
algorithm design techniques include divide-and-conquer, greedy
algorithms, dynamic programming, randomized algorithms and parallel
algorithms. The algorithm analysis includes computational models,
best/average/worst case analysis, and computational complexity
(including lower bounds and NP-completeness). Same as CSSE 473.
MA 474 Theory of Computation 4R-0L-4C
W
Prerequisite: CSSE 230 and MA 375
Students study mathematical models by which to answer three
questions: What is a computer? What limits exist on what problems
computers can solve? What does it mean for a problem to be hard?
Topics include models of computation (including Turing machines),
undecidability (including the Halting Problem) and computational
complexity (including NP-completeness). Same as CSSE 474.
MA 475 Topics in Discrete Mathematics 4R-0L-4C
S
Prerequisite: MA 375
An extension of the material presented in MA 275 and 375. Topics
may include combinatorial design, Fibonacci numbers, or the
Probabilistic Method, among others.
MA 476 Algebraic Codes 4R-0L-4C S (odd
years)
Prerequisite: MA 375 or consent of instructor
Construction and theory of linear and nonlinear error correcting
codes. Generator matrices, parity check matrices, and the dual
code. Cyclic codes, quadratic residue codes, BCH codes,
Reed-Solomon codes, and derived codes. Weight enumeration and
information rate of optimum codes.
MA 477 Graph Theory 4R-0L-4C S (even
years)
Prerequisite: MA 375 or consent of instructor
An introduction to the theory and applications of directed and
undirected graphs. Possible topics include the following:
Connectivity, subgraphs, graph isomorphism, Euler trails and
circuits, planarity and the theorems of Kuratowski and Euler,
Hamilton paths and cycles, graph coloring and chromatic
polynomials, matchings, trees with applications to searching and
coding, and algorithms dealing with minimal spanning trees,
articulation points, and transport networks.
MA 478 Topics in Number Theory 4R-0L-4C
(arranged)
Prerequisite: MA 378 or MA 375 or consent of
instructor
Advanced topics in Number Theory. Topics may include elliptic curve
cryptography, the Fermat-Wiles Theorem, elliptic curves, modular
forms, p-adic numbers, Galois theory, diophantine approximations,
analytic number theory, algebraic number theory. A student
may take the course for credit more than once provided the topics
are different.
MA 479 Cryptography 4R-0L-4C S
Prerequisite: CSSE 220 and MA 275
Introduction to basic ideas of modern cryptography with emphasis on
mathematical background and practical implementation. Topics
include: the history of cryptography and cryptanalysis, public and
private key cryptography, digital signatures, and limitations of
modern cryptography. Touches upon some of the societal issues of
cryptography (same as CSSE 479).
MA 480 Topics in Probability or Statistics 4R-0L-4C
(arranged)
Prerequisite: consent of instructor
An advanced course in probability or statistics. Possible
topics include (but are not restricted to) reliability, discrete
event simulation, multivariate statistics, Bayesian statistics,
actuarial science, nonparametric statistics, categorical data
analysis, and time series analysis. May be taken more than
once provided topics are different.
MA 481 Mathematical Statistics 4R-0L-4C W (even
years)
Prerequisite: MA 382, or MA 381 and consent of
instructor
An introduction to mathematical statistics. Review of distributions
of functions of random variables. Moment generating functions.
Limiting distributions. Point estimation and sufficient statistics.
Fisher information and Rao-Cramer inequality. Theory of statistical
tests.
MA 482 Bioengineering Statistics 4R-0L-4C
S
Prerequisite: MA 223 or MA 382
Hypothesis testing and confidence intervals for two means, two
proportions, and two variances. Introduction to analysis of
variance to include one factor and two factors (with interaction)
designs. Presentation of simple linear and multiple linear
regression modeling; development of analysis of contingency table
to include logistic regression. Presentation of Log odds ratio as
well as several non-parametric techniques of hypothesis testing and
construction of non-parametric confidence intervals and correlation
coefficients. Review of fundamental prerequisite statistics will be
included as necessary. Same as BE 482.
MA 485 Applied Regression Analysis and Introduction to
Time Series 4R-0L-4C W (odd years)
Prerequisite: MA 221 and either MA 223 or MA 382
Review of simple linear regression; confidence and prediction
intervals for estimated values using simple linear regression;
introduction to such concepts as model fit, misspecification,
multi-collinearity, heterogeneous variances and transformation of
both independent and dependent variables; introduction to multiple
regression to include polynomial regression; use of dummy variables
and diagnostics based on residuals; sequential variable selection
to include forward inclusion and backward exclusion of variables;
best subset regression; introduction to time series;
autocorrelation; moving averages and exponential smoothing.
MA 487 Design of Experiments 4R-0L-4C W (even
years)
Prerequisite: MA 223 or MA 382
Review of one factor analysis of variance; tests for homogeneity of
variance and model assumptions; multiple comparisons, post hoc
comparisons, and orthogonal contrasts; two factor analysis of
variance (with and without interactions); three factor and higher
full factorial designs; analysis of covariance and repeated
measures designs; screening designs to include 2 to the k and 3 to
the k design; fractional factorial designs; introduction to General
Linear Models. Other topics that may be included as time allows:
fixed, random, and mixed designs as well as nested designs. Review
of fundamental prerequisite statistics will be included as
necessary.
Undergraduate/Graduate Courses
MA 534 Management Science 4R-OL-4C F (even
years)
Prerequisite: Senior or graduate standing
A study of the development and analysis of various mathematical
models useful in managerial decision-making. This includes
discussions of what models are, how to create them, how they are
used, and what insights they provide. Spreadsheets will be used to
do much of the computational work. Topics considered include
linear, integer, and nonlinear programming, network models,
inventory management, project management, and simulation models.
Examples from all areas of business and industry will be
investigated. We will also investigate how companies are using
these techniques to solve current problems. Same as EMGT 534.
MA 580 Topics in Advanced Probability Theory and Its
Applications 4R-0L-4C (arranged)
Prerequisite: MA 381
Advanced topics in probability theory as well as applications that
are not offered in the listed courses.
MA 581 Topics in Advanced Statistics 4R-0L-4C
(arranged)
Prerequisite: MA 223 or MA 381 and consent of
instructor
This course will cover advanced topics in mathematical statistics
as well as applied statistics that are not offered in the listed
courses.
MA 590 Graduate Topics in Mathematics Variable
credit
Prerequisite: consent of instructor
This course will cover graduate-level topics in mathematics not
offered in listed courses.
Department of
Mathematics Website