|
MACS500. LINEAR VECTOR SPACES (I) |
| Finite dimensional vector spaces and subspaces: dimension, dual bases,
annihilators. Linear transformations, matrices, projections, change of basis,
similarity. Determinants, eigenvalues, multiplicity. Jordan form. Inner
products and inner product spaces with orthogonality and completeness. |
Prerequisite: MACS401.
3 hours lecture; 3 semester hours. |
|
MACS502. REAL AND ABSTRACT ANALYSIS (I) |
| Introduction to metric and topological spaces. Lebesgue measure and
measurable functions and sets. Types of convergence, Lebesgue integration
and its relation to other integrals. Integral convergence theorems. Absolute
continuity and related concepts. |
Prerequisite: MACS401.
3 hours lecture; 3 semester hours. |
|
MACS503. FUNCTIONAL ANALYSIS (II) |
| Normed linear spaces, linear operators on normed linear spaces, Banach
spaces, inner product and Hilbert spaces, orthonormal bases, duality,
orthogonality, adjoint of a linear operator, spectral analysis of linear
operators. |
Prerequisite: MACS502.
3 hours lecture; 3 semester hours. |
|
MACS506. COMPLEX ANALYSIS II (II) |
| Analytic functions. Conformal mapping and applications. Analytic
continuation. Schlicht functions. Approximation theorems in the complex
domain. |
Prerequisite: MACS454.
3 hours lecture; 3 semester hours. |
|
MACS510. ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS (I) |
| Topics to be covered: basic existence and uniqueness theory, systems of
equations, stability, differential inequalities, Poincare-Bendixon theory,
linearization. Other topics from: Hamiltonian systems, periodic and almost
periodic systems, integral manifolds, Lyapunov functions, bifurcations,
homoclinic points and chaos theory. |
Prerequisites: MACS315 and MACS332 or equivalent.
3 hours lecture; 3 semester hours. |
|
MACS514. APPLIED MATHEMATICS I (I) |
| The major theme in this course is various non-numerical techniques for
dealing with partial differential equations which arise in science and
engineering problems. Topics include transform techniques, Green’s functions
and partial differential equations. Stress is on applications to boundary
value problems and wave theory. |
Prerequisite: MACS455 or equivalent.
3 hours lecture; 3 semester hours. |
|
MACS515. APPLIED MATHEMATICS II (II) |
| Topics include integral equations, applied complex variables, an
introduction to asymptotics, linear spaces and the calculus of variations.
Stress is on applications to boundary value problems and wave theory, with
additional applications to engineering and physical problems. |
Prerequisite: MACS514.
3 hours lecture; 3 semester hours. |
|
MACS530. STATISTICAL METHODS I (I) |
| Introduction to probability, random variables, and discrete and
continuous probability models. Elementary simulation. Data summarization
and analysis. Confidence intervals and hypothesis testing for means and
variances. Chi square tests. Distribution-free techniques and regression
analysis. |
Prerequisite: MACS213 or equivalent.
3 hours lecture; 3 semester hours. |
|
MACS531. STATISTICAL METHODS II (II) |
| Continuation of MACS 530. Multiple regression and trend surface analysis.
Analysis of variance. Experimental design (latin squares, factorial designs,
confounding, fractional replication, etc.). Nonparametric analysis of
variance. Topics selected from multivariate analysis, sequential analysis or
time series analysis. |
Prerequisite: MACS 323 or 530 or 535.
3 hours lecture; 3 semester hours. |
|
MACS534. MATHEMATICAL STATISTICS I (I) |
| The basics of probability, fundamental discrete, and continuous
probability distributions, sampling distributions, including order statistics,
and basic limit theorems, including the continuity theorem and the central
limit theorem, are covered. |
Prerequisite: Consent of Department.
3 hours lecture; 3 semester hours. |
|
MACS535. MATHEMATICAL STATISTICS II (II) |
| The basics of hypothesis testing using likelihood ratios, point and
interval estimation, including consistency, efficiency, and sufficient
statistics, and some nonparametric methods are presented. |
Prerequisite: MACS534 or equivalent.
3 hours lecture; 3 semester hours. |
|
MACS542. SIMULATION (I) |
| Advanced study of simulation techniques, random number, and variate
generation. Monte Carlo techniques, simulation languages, simulation
experimental design, variance reduction, and other methods of increasing
efficiency, practice on actual problems. Offered every other year. |
Prerequisite: MACS262 (or equivalent), MACS323 (or MACS530
or equivalent), or permission of instructor.
3 hours lecture; 3 semester hours. |
|
MACS550. NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (II) |
| Numerical methods for solving partial differential equations. Explicit
and implicit finite difference methods; stability, convergence, and
consistency. Alternating direction implicit (ADI) methods. Weighted residual
and finite element methods. |
Prerequisites: MACS315, MACS332, or consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS551. COMPUTATIONAL LINEAR ALGEBRA (II) |
| Numerical analysis of algorithms for solving linear systems of equations,
least squares methods, the symmetric eigenproblem, singular value decomposition,
conjugate gradient iteration. Modification of algorithms to fit the
architecture. Error analysis, existing software packages. |
Prerequisite: MACS 332, MACS 407, or consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS556. MODELING WITH SYMBOLIC SOFTWARE (I) |
| Case studies of various models from mathematics, the sciences and
engineering through the use of a symbolic software package, such as MATHEMATICA.
Based on hands-on projects dealing with contemporary topics such as number
theory, discrete mathematics, complex analysis, special functions, classical
and quantum mechanics, relativity, dynamical systems, chaos and fractals,
solitons, wavelets, chemical reactions, population dynamics, pollution models,
electrical circuits, signal processing, optimization, control theory, and
industrial mathematics. The course is designed for graduate students and
scientists interested in modeling and using symbolic software as a programming
language and a research tool. It is taught in a computer laboratory. |
Prerequisite: Senior undergraduates need consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS561. THEORETICAL FOUNDATIONS OF COMPUTER SCIENCE (I) |
| Mathematical foundations of computer science. Models of computation,
including automata, pushdown automata, and Turing machines. Language models,
including alphabets, strings, regular expressions, grammars, and formal
languages. Predicate logic. Complexity analysis. |
Prerequisites: MACS262, MACS358.
3 hours lecture; 3 semester hours. |
|
MACS562. APPLIED ALGORITHMS AND DATA STRUCTURES (II) |
| Industry competitiveness in certain areas is often based on the use of
better algorithms and data structures. The objective of this class is to survey
some interesting application areas and to understand the core algorithms and
data structures that support these applications. Application areas could change
with each offering of the class, but would include some of the following: VLSI
design automation, computational biology, mobile computing, computer security,
data compression, web search engines, geographical information systems. |
Prerequisites: MACS406, or consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS563. PARALLEL COMPUTING FOR SCIENTISTS AND ENGINEERS (I) |
| Students are taught how to use parallel computing to solve complex
scientific problems. They learn how to develop parallel programs, how to analyze
their performance, and how to optimize program performance. The course covers the
classification of parallel computers, shared memory versus distributed memory
machines, software issues, and hardware issues in parallel computing. Students
write programs for state of the art high performance supercomputers, which are
accessed over the network. |
Prerequisite: Programming experience in C, consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS564. ADVANCED COMPUTER ARCHITECTURE (I) |
| The objective of this class is to gain a detailed understanding about the
options available to a computer architect when designing a computer system along
with quantitative justifications for the options. All aspects of modern computer
architectures including instruction sets, processor design, memory system design,
storage system design, multiprocessors, and software approaches will be
discussed. |
Prerequisites: MACS341, or consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS565. DISTRIBUTED COMPUTING SYSTEMS (II) |
| Introduction to the design and use of distributed computer systems based on
networks of workstations and server computers. Topics include theory,
applications, systems and case studies describing current approaches. |
Prerequisite: Undergraduate machine architecture or consent of
instructor.
3 hours lecture; 3 semester hours. |
|
MACS566. ADVANCED DATABASE MANAGEMENT (II) |
| Advanced issues in database management, with emphasis on their application
to scientific data. Topics to be covered include: object-oriented database
management, database rules, distributed databases, database design, transaction
management, query optimization, concurrency control, and management of
scientific data. Each student develops a course project, as a vehicle for
exploring and applying a database research issue. |
Prerequisite: MACS 403 or equivalent.
3 hours lecture; 3 semester hours. |
|
MACS567. ADVANCED OBJECT ORIENTED SOFTWARE ENGINEERING (I) |
| Advanced software engineering concepts, with emphasis on how to develop
object-oriented application programs. The entire software lifecycle is
discussed: requirements analysis, program design, implementation, debugging,
and testing. Seamless program development is emphasized, in which the
development process is an incremental refinement of a computer model of
real-world objects. Examples in the course are from scientific application
programs. The object-oriented use of the C++ language is taught and used in
assignments. |
Prerequisite: Knowledge of C or C++.
3 hours lecture; 3 semester hours. |
|
MACS568. DATA MINING (II) |
| This course is an introductory course in data mining. It covers
fundamentals of data mining theories and techniques. We will discuss
association rule mining and its applications, overview of classification and
clustering, data preprocessing, and several application-specific data mining
tasks. We will also discuss practical data mining using a data mining
software. Project assignments include implementation of existing data mining
algorithms, data mining with or without data mining software, and study of
data mining-related research issues. |
Prerequisite: MACS262 or permission of instructor.
3 hours lecture; 3 semester hours. |
|
MACS570. NEURAL NETWORKS (I) |
| This course explores the theory behind neural networks, and focuses on
the application of this technology to real problems in areas as diverse as
DNA pattern recognition, robot control, hazardous waste remediation, and
forensics. For the prepared student, this course also facilitates a
transition from doing coursework to producing publishable research. Skills
required to understand, critique, and extend existing research are emphasized.
An introductory series of lectures is followed by more in-depth study of
current research topics. Depending on a student’s background, the course
project is either a literature survey or application or exploration of a
neural network method of the student’s choice. |
Prerequisite: MACS404.
3 hours lecture; 3 semester hours. |
|
MACS571. ARTIFICIAL INTELLIGENCE (I) |
| Artificial Intelligence (AI) is the subfield of computer science that
studies how to automate tasks for which people currently exhibit superior
performance over computers. Historically, AI has studied problems such as
machine learning, language understanding, game playing, planning, robotics,
and machine vision. AI techniques include those for uncertainty management,
automated theorem proving, heuristic search, neural networks, and simulation
of expert performance in specialized domains like medical diagnosis. This
course provides an overview of the field of Artificial Intelligence.
Particular attention will be paid to learning the LISP language for AI
programming. |
Prerequisite: MACS262.
3 hours lecture; 3 semester hours. |
|
MACS572. COMPUTER NETWORKS II (II) |
| This introduction to computer networks covers the fundamentals of
computer communications, using TCP/IP standardized protocols as the main case
study. This second course on computer networks covers the network layer, data
link layer, and physical layer of communication protocols in depth. Detailed
topics include routing (unicast, multicast, and broadcast), one hop error
detection and correction, and physical topologies. Other topics include the
history of computer communications and protocols for emerging networks (e.g.,
ad hoc networks and sensor networks). In addition, students will program
client/server network applications and simulate a network protocol in a network
simulator. |
Prerequisite: MACS471.
3 hours lecture; 3 semester hours. |
|
MACS575. MACHINE LEARNING (II) |
| The goal of machine learning research is to build computer systems that
learn from experience and that adapt to their environments. Machine learning
systems do not have to be programmed by humans to solve a problem; instead,
they essentially program themselves based on examples of how they should behave,
or based on trial and error experience trying to solve the problem. This
course will focus on the methods that have proven valuable and successful in
practical applications. The course will also contrast the various methods,
with the aim of explaining the situations in which each is most appropriate. |
Prerequisites: MACS262, MACS323, or consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS598. SPECIAL TOPICS (I,II,S) |
| Pilot course or special topics course. Topics chosen from special interests
of instructor(s) and student(s). Usually the course is only offered once. |
Prerequisite: Instructor consent.
Variable Credit: 1 to 6 semester hours. |
|
MACS599. INDEPENDENT STUDY (I,II,S) |
| Individual research or special problem projects supervised by a faculty member,
when a student and instructor agree on a subject matter, content, and credit
hours. |
Prerequisite: Independent Study form must be completed and
submitted to the Registrar.
Variable Credit; 1 to 6 credit hours. |
|
MACS610. ADVANCED TOPICS IN DIFFERENTIAL EQUATIONS (II) |
| Topics from current research in ordinary and/or partial differential equations;
for example, dynamical systems, advanced asymptotic analysis, nonlinear wave
propagation, solitons. |
Prerequisite: Consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS614. ADVANCED TOPICS IN APPLIED MATHEMATICS (I) |
| Topics from current literature in applied mathematics; for example, wavelets
and their applications, calculus of variations, advanced applied functional
analysis, control theory. |
Prerequisite: Consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS616. INTRODUCTION TO MULTI-DIMENSIONAL SEISMIC INVERSION (II) |
| Introduction to high frequency inversion techniques. Emphasis on the
application of this theory to produce a reflector map of the earth’s interior
and estimates of changes in earth parameters across those reflectors from data
gathered in response to sources at the surface or in the interior of the earth.
Extensions to elastic media are discussed as well. Includes high frequency
modeling of the propagation of acoustic and elastic waves. |
Prerequisite: Partial differential equations, wave equation
in the time or frequency domain, complex function theory, contour integration.
Some knowledge of wave propagation: reflection, refraction, diffraction..
3 hours lecture; 3 semester hours. |
|
MACS650. ADVANCED TOPICS IN NUMERICAL ANALYSIS (II) |
| Topics from the current literature in numerical analysis and/or
computational mathematics; for example, advanced finite element method, sparse
matrix algorithms, applications of approximation theory, software for
initial value ODEs, numerical methods for integral equations. |
Prerequisite: Consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS660. ADVANCED TOPICS IN COMPUTER SYSTEMS (II) |
| Topics from the current literature in hardware and software computer
systems; for example, user interfaces, object oriented software engineering,
database management, computer architectures, supercomputing, parallel
processing, distributed processing, and algorithms. |
Prerequisite: Consent of instructor.
3 hours lecture; 3 semester hours. |
|
MACS691. GRADUATE SEMINAR (I) |
| Presentation of latest research results by guest lecturers, staff, and
advanced students. |
Prerequisite: Consent of department.
1 hour seminar; 1 semester hour. |
|
MACS692. GRADUATE SEMINAR (II) |
| Presentation of latest research results by guest lecturers, staff, and
advanced students. |
Prerequisite: Consent of Department Head.
1 hour seminar; 1 semester hour. |
|
MACS693 (GPGN551). WAVE PHENOMENA SEMINAR (I,II) |
| Students will probe a range of current methodologies and issues in
seismic data processing, with emphasis on underlying assumptions,
implications of these assumptions, and implications that would follow from
use of alternative assumptions. Such analysis should provide seed topics
for ongoing and subsequent research. Topic areas include: Statistics
estimation and compensation, deconvolution, multiple suppression,
suppression of other noises, wavelet estimation, imaging and inversion,
extraction of stratigraphics and lithologic information, and correlation
of surface and borehole seismic data with well log data. |
Prerequisite: Consent of department.
1 hour seminar; 1 semester hour. |
|
MACS698. SPECIAL TOPICS (I,II,S) |
| Pilot course or special topics course. Topics chosen from special
interests of instructor(s) and student(s). Usually the course is offered
only once. |
Prerequisite: Consent of Department Head.
1 to 3 semester hours. |
|
MACS699. INDEPENDENT STUDY (I,II,S) |
| Individual research or special problem projects supervised by a
faculty member, also, when a student and instructor agree on a subject
matter, content, and credit hours. |
Prerequisite: Independent Study form must be completed
and submitted to the Registrar.
Variable Credit; 1 to 6 credit hours. |
|
MACS701. GRADUATE THESIS - MASTER OF SCIENCE (I,II) |
| Preparation of the master's thesis under the supervision of the
graduate student's advisory committee. |
6 semester hours upon completion of thesis.
Required for all candidates for the degree of Master of Science. |
|
MACS703. GRADUATE THESIS - DOCTOR OF PHILOSOPHY (I,II,S) |
| Preparation of the doctor's thesis under the supervision of the
graduate student's advisory committee. |
| 30 semester hours upon completion of thesis. |
|
MACS705. GRADUATE RESEARCH CREDIT - MASTER OF SCIENCE (I,II,S) |
| Research credit hours required for completion of the degree of
Master of Science - thesis. Research must be carried out under the direct
supervision of the graduate student's faculty advisor. |
|
MACS706. GRADUATE RESEARCH CREDIT - DOCTOR OF PHILOSOPHY (I,II,S) |
| Research credit hours required for completion of the degree of Doctor
of Philosophy. Research must be carried out under the direct supervision of
the graduate student's faculty advisor. |
