Mathematics (Math)
1. Elementary Algebra (3)
Transition from arithmetic to the symbolism and generalization of algebra;
fundamental operations, equations, formulas. (See Duplication of Courses)
2. Plane Geometry (3)
Prerequisite: elementary algebra. Points, lines, angles, triangles, polygons,
circles; axioms, theorems; proofs and constructions. (Former Math 28)
4. Intermediate Algebra (3)
Prerequisite: elementary algebra and geometry. Sets, functions, graphs,
quadratic equations, inequalities, simultaneous equations, matrices and
determinants, mathematical induction, binomial theorem, progressions, exponents
and logarithms. (See Duplication of Courses ) (Former Math 29)
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.)
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.
20. Introductory Computer Programming (3)
Prerequisites: intermediate algebra and trigonometry. Introduction to FORTRAN
programming and flow charts with applications to matrix algebra, integration,
series and linear programming.
41. Number Systems I (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.
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.
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.
113. Theory of Computation (3)
Prerequisite: Math 20. Computability, effective procedures, algorithms;
finite-state and infinite machines; Turing machines, recursive functions;
limitations of effective computability, the halting problem, the debugging
problem; computable and noncomputable real numbers.
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.
120. Structures of Programming Languages (3)
Prerequisite: working knowledge of FORTRAN or COBOL and Math 72 or 75. Formal
definition of programming language; global properties of algorithmic languages;
list processing, string manipulation, data description, simulation languages;
language structure in FORTRAN, ALGOL.
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.
141. Number Systems II (3)
Not open to students with credit in Math 151 or 171. Prerequisite: Math
41 or 71. Especially recommended for prospective teachers. and minors. Development
of the real number system and its subsystems from the formal point of view.
Mathematical induction and definition by recursion. Axiomatic development
of the various number systems and their interrelation.
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.
162. Projective Geometry (3)
Prerequisite: Math 77. Synthetic and analytic projective geometry; axioms;
duality; perspective and projective correspondence; harmonic sets; coordinalization;
projective collineations and correlations; polarities and conics; groups
of projective, affine and Euclidean transformations
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.
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)