Mathematics (Math)
1. Elementary Algebra (3)
Fundamental operations, linear equations, polynomials, factoring, rational
expressions, graphing of linear equations, introduction to inequalities,
quadratic equations, and systems of linear equations. CR/NC grading only.
(See Duplication of Courses)
1AR. Elementary Algebra Laboratory (1)
Prerequisite; concurrently enrolled in Math 1 and assigned to laboratory
after taking placement examination, Laboratory does not count toward baccalaureate
degree. Extra review and practice with skills essential to success in elementary
algebra. CR/NC grading only; not applicable toward baccalaureate degree
requirements.
2R. Elementary Geometry (3)
Prerequisite; elementary algebra. Postulates concerning points, lines, planes.
Definitions. Congruence; properties of triangles. Parallel lines. Properties
of quadrilaterals. Area formulae. Similar figures. Circles. Volumes of certain
solids. CR/NC grading only; not applicable toward baccalaureate degree requirements.
4A. Intermediate Algebra (3)
Prerequisite: elementary algebra and geometry. Radicals, rational exponents,
quadratic equations, simultaneous linear equations, graphing, inequalities,
complex numbers in rectangular form, introduction to exponential and logarithmic
functions, applications. CR/NC grading only; not applicable toward baccalaureate
degree requirements. (See Duplication of Courses. )
4AR. Intermediate Algebra Laboratory (1)
Prerequisite: concurrently enrolled in Math 4R and assigned to laboratory
after taking placement examination. Laboratory does not count toward baccalaureate
degree. Extra review and practice with skills essential to success in intermediate
algebra. CR/NC grading only; not applicable toward baccalaureate degree
requirements.
5. Trigonometry (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Concept of a function, sine and cosine functions, tables
and graphs, other trigonometric functions, identities and equations. Trigonometric
functions of angles, solution of triangles. (See Duplication of Courses.)
6. Precalculus (4)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Basic algebraic properties of real numbers; linear and quadratic
equations and inequalities; functions and graphs; polynomials; exponential
and logarithmic functions; analytic trigonometry and functions; conics;
sequences, and series.
11. Elementary Statistics (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Illustration of statistical concepts: elementary probability
models, sampling, descriptive measures, confidence intervals, testing hypotheses,
chi-square, nonparametric methods, regression. It is recommended that students
with credit in Math 72 or 75 take Math 101.
11L. Elementary Statistics Laboratory (1)
Concurrent enrollment in Math 11. (Not required for Math 11.) Computational
techniques pertinent to elementary statistics with emphasis on calculator
programming and formula derivation.
41. Number Systems (3)
Not open to mathematics majors. Prerequisite: Students must take the ELM
exam; students who do not pass the exam must record a grade of C or better
in a college-taught intermediate algebra course. Designed for elementary
credential candidates. Development of rational number system and its subsystems
from the informal point of view; sets, relations and operations, equivalence
classes; definitions of number systems and operations; algorithms for operations;
prime numbers, divisibility tests; ratios.
43. Elementary Problem Solving (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. The purpose of this course is to develop problem solving
skills using elementary mathematics.
45. What Is Mathematics? (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught intermediate
algebra course. Intended primarily for liberal arts students. Topics: mathematics
and social science, mathematics of shape and growth, statistics, mathematics
of management science and mathematics of computers.
51. Elements of Modern Mathematics (3)
Prerequisite: passing score on the Entry Level Mathematics (ELM) Exam and
intermediate algebra. Logic, set theory, vectors and matrices, linear programming,
permutations and combinations, probability, Markov chains, applications
to business and social sciences.
52. Elementary Linear Algebra (3)
Prerequisite: passing score on the Entry Level Mathematics (ELM) Exam and
intermediate algebra. Elementary properties of matrices, determinants; systems
of linear equations; linear transformations.
70. Mathematis for Life Sciences (4)
No credit if taken after Math 72 or 75; one unit of credit if taken after
Math 71. Prerequisite: Students must take the ELM exam; students who do
not pass the exam must record a grade of C or better in a college-taught
intermediate algebra course. Functions and graphs, limits, derivatives,
antiderivatives, differential equations, and partial derivatives with applications
in the Life Sciences.
71. Elementary Mathematical Analysis I (3)
No credit if taken after Math 70, 72, or 75. Prerequisite: Students must
take the ELM exam; students who do not pass the exam must record a grade
of C or better in a college-taught intermediate algebra course. Review of
algebra, real numbers, inequalities, function, graph, finite induction,
limit, differentiation of algebraic functions and applications to extrema,
mean value theorem, I'Hôpital's rule.
72. Elementary Mathematical Analysis II (3)
No credit if taken after Math 75; 2 units of credit if taken after Math
70. Prerequi sites: Math 71 and trigonometry. Analytic geometry and calculus
of polynomials, rational functions, transcendental functions; polar coordinates,
conic sections, integration and applications.
75. Mathematical Analysis I (4)
No credit if taken after Math 72; 2 units of credit if taken after Math
71; 3 units of credit if taken after Math 70. Prerequisite: Students must
take the ELM exam. Additionally,beginning in the fall of 1994, a passing
score on the Precalculus Diagnostic Test or a grade of C or better in Math
6 will be required prior to registration. Inequalities, functions, graphs,
limits, continuity, derivatives, antiderivatives, the definite integral
and applications.
76. Mathematical Analysis II (4)
Prerequisite: Math 72 or 75. Transcendental functions, techniques of integration,
improper integrals, conic sections, polar coordinates, introduction to vectors.
77. Mathematical Analysis III (4)
Prerequisite: Math 76. Three dimensional calculus, partial derivatives,
multiple integrals, infinite series, and applications. (
81. Applied Analysis (4)
Prerequisite: Math 77. Introduction to ordinary linear differential equations;
solutions by power series and Laplace transforms. Solution of systems of
equations. Introduction to Fourier series. Use of the microcomputer as an
exploratory tool. (3 lecture, 2 lab hours) (Computer lab fee, $15)
101. Statistical Methods (4)
Prerequisite: Math 70, 71, or equivalent; no credit if taken after Math
108. Application of statistical procedures to examples from biology, engineering,
and social science; one- and two-sample normal theory methods; chi-square,
analysis of variance, and regression; nonparametric methods. Computerized
statistical packages are used.
102. Sampling Theory and Methods (3)
Prerequisite: one semester of statistics, and Math 70 or 72 or 75. Basic
concepts of sampling; probability sampling, stratification, clusters, single
and multiple-stage designs; estimation procedures, non- sampling errors;
illustrations from agriculture, biology, and social sciences.
103. Linear Statistical Models and Their Application (4)
Prerequisite: Math 101. Elements at matrix algebra. Components of experimental
design. Common linear statistical models including factorial designs, split-plot,
Latin square. Multiple regressional analysis, residual analysis, path diagrams.
Analysis including both continuous and classification variables. Simple,
multiple and partial correlation.
107. Introduction to Probability and Statistics (3)
Prerequisite: Math 77 or concurrently. Basic concepts required for applications
of probability theory; standard discrete and continuous models; random variables;
conditional distributions; limit theorems.
108. Statistics (3)
Prerequisite: Math 107. Criteria used for selecting particular procedures
of data analysis; derivation of commonly used procedures; topics from sampling,
normal theory, nonparametrics, elementary decision theory.
109. Applied Probability (3)
Prerequisite: Math 107. Introduction to stochastic processes and their applications
in science and industry. Markov chains, queues, stationary time series.
110. Symbolic Logic (3)
rerequisite: Math 71 or 75. An informal treatment of the theory of logical
inference, statement calculus, truth-tables, predicate calculus, interpretations
applications.
111. Theory of Sets (3)
Prerequisite: Math 71 or 75. Set theory from an informal axiomatic foundation,
relations and functions, cardinal numbers, ordinal numbers, applications.
114. Discrete Structures (3)
Prerequisite: Math 76. Counting techniques, matrix algebra, graphs, trees
and networks, recurrence relations and generating functions, applied modern
algebra.
116. Theory of Numbers (3)
Prerequisite: Math 72 or 75. Divisibility, greatest common divisor, Euler's
function, continued fractions, congruences, quadratic residues, Diophantine
equations, different forms of the Prime Number Theorem, Mobius inversion
formula.
118. Graph Theory (3)
Prerequisite: Math 77. Trees, connectivity, Euler and Hamilton paths, matchings,
chromatic problems, planar graphs, independence, directed graphs, networks.
121. Numerical Analysis I (3)
Prerequisites: Math 77 and working knowledge of C, Fortran, or Pascal. Zeros
of nonlinear equations, interpolation, quadrature, systems of equations,
numerical ordinary differential equations, and eigenvalues. Use of numerical
software libraries.
122. Numerical Analysis II (3)
Prerequisite: Math 121. Advanced topics from numerical linear algebra, function
approximation, fast Fourier transforms, and numerical partial differential
equations. Use of numerical software libraries.
123. Topics in Applied Mathematics (3)
Prerequisite: Math 77. Vector spaces and linear transformations, eigenvalues
and eigen functions. Special types of linear and nonlinear differential
equations; solution by series. Fourier transforms. Special functions, including
gamma, hypergeometric, Legendre, Bessel, Laguerre, and Hermite functions.
Introduction to partial differential equations.
124. Applied Matrix Analysis (3)
Prerequisite: Math 77. Matrix algebra, systems of equations, eigenvalues,
eigenvectors, diagonalizations, functions of ma-trices with applications
to differential equations, optimization, and Markov chains.
128. Complex Analysis (3)
Prerequisite: Math 77. Analytic functions of a complex variable, contour
integration, series, singularities of analytic functions, the residue theorems,
conformal mappings; applications to engineering and physics.
131. Game Theory and Linear Programming (3)
Prerequisites: Math 72 and permission of instructor; or Math 76. Introduction
to linear programming, problem formulation, adaptation of the Dantzig simplex
algorithm to linear programming problems, duality theory, transportation
problems. Games of chance, strategy, minimax theorem for two-person zero-sum
games, relationship to linear programming.
132. Mathematical Methods of Operations Research (3)
Prerequisite: Math 131 or permission of instructor. Simplex method, parametric
programming, goal programming, dynamic programming, integer programming,
nonlinear programming, and network models, with applications.
132L. Mathematical Methods of Operations Research (1)
Concurrent enrollment in Math 132. (Not required for Math 132.) Use of computers
in setting up and solving problems in operations research.
136. Coding Theory (3)
Prerequisite: Math 114. Mathematical properties of error correcting codes;
information rate, error. detecting and error correcting capacities, encoding
and decoding algorithms. Linear, cyclic, Hamming, BCH, and Golay codes.
143. History of Mathematics (4)
Prerequisite: Math 72 or 75. History of the development of mathematical
concepts in algebra, geometry, number theory, analytical geometry, and calculus
from ancient times through modern times. Theorems with historical significance
will be studied as they relate to the development of modern mathematics.
145. Problem Solving (3)
Prerequisite: at least ine 100-200 series mathematics course. A study of
formulation of problems into mathematical form; analysis of methods of attack
such as specialization, generalization, analogy, induction, recursion, etc.
applied to a variety of non-routine problems. Topics will be handled through
student presentation.
151. Principles of Algebra (4)
Prerequisite: Math 76. Groups, cyclic groups, normal subgroups; rings,integral
domains and polynomials; fields.
152. Linear Algebra (4)
Prerequisite: Math 151. Linear transformations, matrices, determinants,
linear functionals, bilinear forms, quadratic forms, orthogonal and unitary
transformations, selected applications of linear algebra.
153T. Topics in Algebra (3)
Prerequisite: Math 151. Topics may include such algebraic theories as Galois
Theory, permutation groups, modules, lattices, etc.
161. Principles of Geometry (3)
Prerequisite: Math 77. The classical elliptic, parabolic, and hyperbolic
geometries developed on a framework of incidence, order and separation,
congruence; coordinatization. Theory of parallels for parabolic and hyperbolic
geometries. Selected topics of modern Euclidean geometry.
165. Differential Geometry (3)
Prerequisite: Math 77. Study of geometry in Euclidean space by means of
calculus, including theory of curves and surfaces, curvature, theory of
surfaces, and intrinsic geometry on a surface.
167. Catastrophe Theory (3)
Prerequisite: Math 77. Structural stability, morphogenesis and Thorn's classification
of the seven elementary catastrophes with applications to the physical,
biological and social sciences.
168. Geometric Topology (3)
Prerequisite: Math 77. Topology of surfaces the Euler characteristic, homeomorphism:
the fundamental group, Vector fields on surfaces, knot theory and introduction
to differentiable manifolds.
171. Intermediate Mathematical Analysis I (4)
Prerequisite: Math 77. Sets, real numbers as a complete ordered field, its
usual topology, functions of a real variable, limits, continuity, uniform
continuity, differentiability, generalized mean value theorem, Riemann integrals,
series of functions, uniform convergence, and Fourier series of integrable
functions.
172. Intermediate Mathematical Analysis II (4)
Prerequisite: Math 171A. Differentiation of functions of several variables,
applications of partial differentiation, functions of bounded variation,
rectifiable curves, theory of Riemann-Stieltjes integration, multiple integrals
and line integrals, improper Riemann-Stieltjes integrals. Inverse and implicit
function theorems.
173T. Topics in Real Analysis (3)
Prerequisite: Math 172. Topics will vary according to needs and interests
of students. May include elementary measure theory. Fourier series and integrals;
Dirac delta function and elementary distribution theory.
181. Differential Equations (3)
Prerequisite: Math 81 or 123. Definition and classification of differential
equations; general, particular, and singular solutions; existence theorems;
theory and technique of solving certain differential equations: phase plane
analysis, elementary stability theory; applications.
182. Partial Differential Equations (3)
Prerequisites: Math 81 or 123, and 171A. Classical methods for solving partial
differential equations including separation of variables, Green's functions,
the Riemann-Volterra method and Cauchy's problem for elliptic, parabolic,
and hyperbolic equations; applications to theoretical physics.
190. Independent Study (1-3; max see reference)
See Academic Placement -- Independent Study.
191T. Proseminar (1-3; max total 9)
Prerequisite: permission of instructor. Presentation of advanced topics
in mathematics in the field of the student's interest.
(See Course Numbering System.)
Mathematics (Math)
202. Fundamental Concepts of Mathematics (3)
Prerequisites: Math 151, 161 and 171A. Fundamental notions regarding number
theory, number systems, algebra of number fields; functions.
210. Foundations of Mathematics (3)
Prerequisite: Math 110 or 151. Formal introduction to theories of inference,
first order theories, completeness metatheorems, consistency metatheorems,
decision problems.
216. Topics in Number Theory (3; max total 6)
Prerequisite: Math 116. An investigation of topics having either historical
or current research interest in the field of number theory.
221. Advanced Numerical Analysis (3)
Prerequisite: Math 121. Linear equations and matrices; parabolic, hyperbolic,
and elliptic differential equations; constructive function theory.
223. Principles and Techniques of Applied Mathematics (3)
Prerequisite: Math 123. Linear spaces and spectral theory of operators.
224. Optimization Methods (3)
Prerequisite: Math 123. Techniques for optimizing static and dynamic systems,
calculus of variations, Hamiltonian canonical form, maximum principle, with
applications.
228. Functions of a Complex Variable (3)
Prerequisite: Math 128, 171B. Representation theorems of Weierstrass and
Mittag-Leffler, normal families, conformal mapping and Riemann mapping theorem,
analytic continuation, Dirichlet problem.
251. Abstract Algebra I (3)
Prerequisite: undergraduate abstract algebra. Groups, rings, integral domains,
and fields.
252. Abstract Algebra II (3)
Prerequisite: Math 251. Rings and ideals, modules, linear and multilinear
algebras, representations.
263. Point Set Topology (3)
Prerequisite: Math 172. Basic concepts of point set topology, set theory,
topological spaces, continuous functions; connectiv-ity, compactness and
separation properties of spaces. Topics selected from function spaces, metrization,
dimension theory.
265. Differential Geometry (3)
Prerequisites: Math 165, 172. Study of geometry of curves and surfaces in
Euclidean space; including an introduction to Riemannian geometry and theory
of manifolds.
271. Real Variables (3)
Prerequisite: Math 172. Theory of sets; cardinals; ordinals; function spaces,
linear spaces; measure theory; modern theory of integration and differentiation.
272. Functional Analysis (3)
Prerequisite: Math 271. The Lebesgue-Stieltjes integral and its generalizations,
integral equations, Hilbert and Banach spaces, linear transformations (bounded
and unbounded).
290. Independent Study (1-3; max see reference)
See Academic Placement -- Independent Study.
291. Seminar (3)
Prerequisite: graduate standing. Presentation of current mathematical research
in field of student's interest.
298. Research Project in Mathematics (3)
Prerequisite: graduate standing. Independent investigation of advanced character
as the culminating requirement for the master's degree. Approved for SP
grading.
(See Course Numbering System.)
Mathematics (Math)
302. Topics in Mathematics for Teachers (3; max total 6 if topic
not repeated)
Computer Science (C Sci)
10. Introduction to BASIC Programming (1)
Prerequisite: elementary algebra. Introduction to structured programming
techniques using the programming language BASIC. Topics include input/output,
branching, looping, subroutines, and computer graphics. No prior experience
required.
20. Introduction to Computer Programming (4)
Prerequisite; ELM Exam, intermediate algebra and trigonometry. Introduction
to programming in FORTRAN with emphasis on program design, debugging and
documentation. Elementary applications and structured programming for algorithm
development. (3 lecture, 2 lab hours)
40. Computer Programming I (4)
Prerequisites: ELM exam, intermediate algebra, and trigonometry. Introduction
to problem solving, algorithm development, procedural and data abstraction;
program design, coding, debugging, testing, and documentation; programming
language Pascal. No credit if taken after C Sci 20. (3 lecture, 2 lab hours)
41. Computer Programming II (4)
Prerequisite: C Sci 40. Programming methodology, program correctness. Review
of data types. Data structures: linear and nonlinear structures, files.
Implementation of data structures. Recursion. Searching and sorting. (3
lecture, 2 lab hours)
112. Assembly Language Programming (4)
Prerequisite: C Sci 41. Boolean algebra, combinational logic, elementary
digital circuits. A comparison of several assembly languages with an in-depth
study of the organization of a particular computer. (3 lecture, 2 lab hours)
115. Data Structures (3)
Prerequisites: C Sci 41. Review of basic data structures. Graph, search
paths, and spanning trees. Algorithm design and analysis of sorting, merging,
and searching. Memory management, hashing, dynamic storage allocation. Integration
of data structures into system design.
117. Programming Languages (3)
Prerequisites: C Sci 41 and 112. Examination of general concepts and paradigms
of programming languages; scope and binding rules. A study oftwo or more
of the following languages: ADA, ALGOL, APL, PL/1, MODULA II, PROLOG, SNOBOL.
124. Introduction to File Processing (3)
Prerequisite: C Sci 115. Definition of file components, access methods,
and file operations. Algorithms for efficient implementation of data structures;
characteristics of bulk storage media for mainframe and microcomputers.
Introduction to database management systems. (Spring semester)
126. Database Systems (3)
Prerequisite: C Sci 115. Database concepts; hierarchical, relational, and
network models. Data normalization, data description languages, data manipulation
languages, and query design. (Fall semester)
134. Compiler Design (3)
Prerequisites: C Sci 112, 115, 119. Syntax and semantics of programming
languages. Lexical analysis, parsing techniques, parser generator, SLR and
LALR parsing. Introduction to symbol table organization and semantic routines.
Compiler generators. (Spring semester)
136. Compiler Construction (3)
Prerequisite: C Sci 134. Advanced topics in compiler design. Type checking.
Run-time storage management. Intermediate code generation. Interpreters.
Error recovery techniques. Code generation and optimization. (Spring semester)
144. Operating Systems and Computer Architecture I (3)
Prerequisites: C Sci 112, 115. Review o1 system architecture. Dynamic
procedure activation. Process management'-interrupt hardware, process control
blocks, concurrent processes, semaphores, monitors, deadlock. Storage management
-- real and virtual. Processor management-job and processor scheduling,
multiprocessing.
146. Operating Systems and Computer Architecture II (3)
Prerequisites: C Sci 113A, 144. Auxiliary storage management, disk scheduling,
file and database systems. Performance measuring, monitoring and evaluation,
analytic modeling. Networks, security and case studies.
148. Systems Programming (3)
Prerequisites: C Sci 113A, 144. Topics include implementation of operating
system components and modification of existing systems. Device drivers,
memory management, communication networks, and file systems will be examined.
Projects will be emphasized.
154. Simulation (3)
Prerequisites: C Sci 41, 60; Math 75. Simulation as a tool for the study
of complex systems in computer science, statistics and operations research.
Generating random variables. Review of principles behind and examples of
simulation languages.
164. Artificial Intelligence Programming (3)
Prerequisite: C Sci 117. Introduction to functional programming and applicative
languages via LISP. Production systems. Knowledge-based systems. Examples
from: game playing, theorem proving, language processing. Introduction to
logic programming and declarative languages via PROLOG. Introduction to
expert systems. (Fall semester)
166. Principles of Artificial Intelligence (3)
Prerequisite: C Sci 164. Automated reasoning including nonmonotonic logic.
Topics from: robot planning, natural language processing, perception (computer
vision, speech), learning.
172. Computer Graphics (4)
Prerequisites: Math 76, C Sci 41. Hardware devices, raster graphics, device
in dependence, graphic data structure and representations, interactive techniques,
and algorithms for the display of two- and three-dimensional objects, graphic
transformations, graphics standards, modeling, animation, and scientific
visualization. (3 lecture, 2 lab hours)
174. Design and Analysis of Algorithms (3)
Prerequisites: C Sci 115, 119. Models of computation and measures of complexity,
algorithms for sorting and searching, set representation and manipulation,
branch and bound, integer and polynomial arithmetic, pattern-matching algorithms,
parsing algorithms, graph algorithms, NP-complete problems. (Spring semester)
186. Automata Theory and Formal Languages (3)
Prerequisite: C Sci 119. Introduction to formal language theory. Regular
grammars, context-free grammars, context-sensitive grammars, unrestricted
grammars; properties of context-free languages, push-down automata.
188. Theory of Computation (3)
Prerequisite: C Sci 186. Compatibility, effective procedures, algorithms;
finite-state and infinite machines; Turing machines, recursive functions,
limitations of effective compatibility, the halting problem, the debugging
problem, computable and noncomputable real numbers. (Former Math 113 and
C Sci 113A and C Sci 184)
190. Independent Study in Computer Science (1-3)
191T. Proseminar (1-3)
Prerequisite: permission of instructor. Presentation of selected topics
in computer science.
194. Cooperative Education (1-4; max total 8)
Prerequisites: courses appropriate to the work experience; approval by major
department cooperative education coordinator. Integration of work experience
with academic program, individually planned through coordinator. CR/NC grading
only.
198. Project (3)
Prerequisite: senior standing in computer science or permission of instructor
and approved subject. See Criteria for Thesis and Project. Study of a problem
under the supervision of a faculty member. Presentation by the student in
a seminar setting and a final report are required. Satisfies the senior
major requirement for the B.S. in Computer Science.