Course Descriptions
All MATH/STAT/OPRS courses offered by the Department of Mathematics are approved to satisfy requirements for the Problem Solving Goal of UNC Charlotte Education.
Undergraduate
MATH 1100. College Algebra and Probability. (3) Prerequisite:
appropriate score on the Mathematics Placement Test or placement
by the department. The basic mathematics course for undergraduates
not majoring in mathematics, engineering, or the physical sciences.
Fundamental concepts of algebra and probability. (Credit may not
be given for both MATH 1100 and 1103; students who received credit
for MATH 1101 between Fall 1987 and Fall 1989 may not take 1100
for credit; students who already have credit for MATH 1120 or
1141 with a grade of C or better may not take 1100 for
credit.) (Fall, Spring, Summer) (Evenings)
MATH 1102. Introduction to Mathematical Thinking. (3) Prerequisite:
appropriate score on the Mathematics Placement Test or placement
by the department. An introduction to mathematical ideas designed
primarily for nonscience students. Topics are drawn from various
branches of mathematics which may include algebra, geometry, number
theory, probability, statistics and graph theory. Computers may
be used. (Fall, Spring)
MATH 1103. Precalculus Mathematics for Science and Engineering.
(3) Prerequisite: appropriate score on the Mathematics Placement
Test or placement by the department. Intended for students who
plan to take MATH 1141. Functions and graphs, linear and quadratic
functions, polynomial and rational functions, exponential and
logarithmic functions, trigonometric identities. (Credit may not
be given for both MATH 1100 and 1103; students who received credit
for MATH 1100 between Fall 1987 and Fall 1989 may not take MATH
1103 for credit; students who already have credit for MATH 1120
or 1141 with a grade of C or better may not take MATH 1103
for credit.) (Fall, Spring, Summer) (Evenings)
MATH 1104. Concepts of Trigonometry. (1) Prerequisite:
appropriate score on the Mathematics Placement Test or placement
by the department. Trigonometric functions and their graphs, trigonometric
identities. (Credit not given for both MATH 1103 and 1104.) (On
demand)
MATH 1105. Finite Mathematics. (3) Prerequisite: appropriate
score on the Mathematics Placement Test or placement by the department.
Review of high school algebra, elementary matrix algebra, systems
of linear equations and inequalities, elementary linear programming;
probability. (On demand)
MATH 1120. Calculus. (3) Prerequisite: appropriate score
on the Mathematics Placement Test; MATH 1100 or 1103; or placement
by the department. Intended for students majoring in fields other
than engineering, mathematics or science. Elements of differential
and integral calculus for polynomial, rational, exponential, logarithmic
and trigonometric functions, with applications to business and
the social and life sciences. (May not be taken for credit if
credit has been received for MATH 1121 or 1141.) (Fall, Spring,
Summer) (Evenings)
MATH 1121. Calculus (ET). (3) Prerequisite: appropriate
score on the Mathematics Placement Test; MATH 1100 or 1103; or
placement by the department. Intended for students majoring in
engineering technology. Elements of differential and integral
calculus for polynomial, rational, exponential, logarathmic and
trigonometric functions, with applications to engineering. May
not be taken for credit if credit has been received for MATH 1120
or 1141. (Fall, Spring, Summer) (Evenings)
MATH 1141. Differential and Integral Calculus I. (4) Prerequisite:
appropriate score on the Mathematics Placement Test; MATH 1103
with a grade of C or better; or placement by the department.
Limits, continuity, differentiation and integration of rational
and trigonometric functions, curve sketching, maxima and minima,
area, applications of the integral. (Fall, Spring, Summer)
(Evenings)
MATH 1142. Differential and Integral Calculus II. (4) Prerequisite:
MATH 1141 with a grade of C or better. Exponential and
logarithmic functions, methods of integration; improper integrals,
L'Hopital's rule, infinite series; conic sections; hyperbolic
functions. (Fall, Spring, Summer) (Evenings)
MATH 1165. Introduction to Discrete Structures. (3) Prerequisite:
CSCI 1100 or 1201 and its lab. Propositions and truth tables,
sets, permutations and combinations, relations and functions,
lattices, and trees. Credit will not be given for both MATH 1165
and 2165. (Fall, Spring, Summer) (Evenings)
MATH 2050. Topics in Mathematics. (2-3) Prerequisite: consent
of the department. Topics in mathematics elected to supplement
regular offerings at the 2000 level. (May or may not count for
a Math core course for the CSCI major.) May be repeated for additional
credit with the approval of the department. (On demand)
MATH 2101. Fundamental Concepts in Mathematics I. (4)
Prerequisite:
consent of the department. An intuitive development of the real
number system with emphasis on the principles of teaching and
learning elementary mathematics; sets and set operations; systems
of numeration; arithmetic operations. Laboratory activities and
practical teaching experience in an elementary classroom. May
not be used to satisfy requirement for a major or minor in Mathematics.
(Fall, Spring) (Evenings)
MATH 2102. Fundamental Concepts in Mathematics II. (4)
Prerequisite: MATH 2101 with a grade of C or better. Mathematical
systems; the study of metric and non-metric geometry; relations,
functions and their graphs. Activities and applications related
to elementary school mathematics goals. Practical teaching experience
in an elementary classroom. May not be used to satisfy requirement
for a major or minor in Mathematics. (Fall, Spring) (Evenings)
MATH 2103. Problem Solving in Mathematics Using Computers and
Calculators in the Classroom. (3) Prerequisite: MATH 2101
with a grade of C or better. Calculators in the mathematics
curriculum; microcomputer hardware and courseware in mathematics;
LOGO; probability; data collection, analysis, and interpretation.
May not be used to satisfy requirement for a major or minor in
Mathematics. (Fall, Spring, Summer) (Evenings)
MATH 2121. Introduction to Probability. (3) Prerequisite:
MATH 1100 or 1103. Discrete sample spaces, probability, conditional
probability, independent events, random variables, mean, variance,
joint probability functions, independent random variables, covariance,
correlation, binomial distribution. (On demand)
MATH 2141. Differential and Integral Calculus III. (3)
Prerequisite: MATH 1142 with a grade of C or better. Polar
coordinates, parametric equations, vectors in two and three dimensions,
quadric surfaces, partial derivatives, multiple integrals, line
integrals. (Fall, Spring, Summer) (Evenings)
MATH 2164. Matrices and Linear Algebra. (3) Prerequisite:
MATH 1120 or 1141 with a grade of C or better or consent
of the department. Matrix algebra, systems of linear equations,
vector spaces, linear transformations, determinants, inner products,
eigenvalues. (Fall, Spring, Summer) (Evenings)
MATH 2165. Discrete Structures. (3) Prerequisite: MATH
2164. A study of discrete mathematical structures including groups,
lattices, Boolean functions, graphs and trees with applications
to computer science. Credit will not be given for both MATH 1165
and 2165. (On demand)
MATH 2171. Differential Equations. (3) Prerequisite: MATH
1142 with a grade of C or better. An introduction to ordinary
differential equations including first order equations, general
theory of linear equations, series solutions, special solutions,
special equations such as Bessel's equation, and applications
to physical and geometric problems. (Fall, Spring, Summer)
(Evenings)
MATH 3050. Selected Topics in Mathematics. (2-3) Prerequisite:
consent of the department. Topics selected to supplement regular
offerings at the 3000 level in mathematics or statistics. May
be repeated for credit with the approval of the department. (On
demand)
MATH 3116. Graph Theory. (3) Prerequisite: MATH 2164 or
2165 or consent of the department. Graphs as mathematical models.
Planarity, colorability, connectivity, trees. Applications and
algorithms for networks, matching problems and areas of computer
science. (Fall) (Alternate years)
MATH 3122. Probability and Statistics I. (3) Prerequisite:
MATH 2141 with a grade of C or better. Sample spaces, random
variables, moment generating functions, some standard distributions,
multivariate distributions, laws of large numbers, limit theorems.
(Fall) (Evenings)
MATH 3123. Probability and Statistics II. (3) Prerequisite:
MATH/STAT 3122. Estimation, bias, consistency, efficiency, maximum
likelihood estimates, sufficient statistics, testing, the power
function, chi-square test, Kolmogorov-Smirnov test. Credit for mathematics
major not given for both MATH 3125 and MATH/STAT 3123. (Spring)
(Evenings)
MATH 3125. Statistical Techniques. (3) Prerequisite: consent
of the department. Probability models, random variables, large
sample statistics, inferential statistics, analysis of variance
and experimental design. Credit for mathematics major not given
for both MATH 3125 and MATH/STAT 3123. (Spring) (Evenings)
MATH 3141. Advanced Calculus of One Variable. (3) Prerequisites:
MATH 2141 and 2164 with grades of C or better. Topology
of the real line; continuity, uniform continuity, differentiability,
integration, sequences and series of functions. (Fall) (Evenings)
MATH 3142. Advanced Calculus of Several Variables. (3)
Prerequisite: MATH 3141. Continuity and differentiability of functions
of several variables, inverse and implicit function theorems,
integration, Fubini's theorem, change of variables, the classical
integral theorems of Gauss, Green and Stokes and their generalizations.
(Spring) (Evenings)
MATH 3146. Introduction to Complex Analysis. (3) Prerequisite:
MATH 2141 with a grade of C or better. Analytic functions,
complex integration, calculus of residues, conformal mapping.
(Spring) (Alternate years)
MATH 3163. Introduction to Modern Algebra. (W) (3) Prerequisite:
MATH 1141 with a grade of C or better or consent of the
department. Examples and elementary properties of basic algebraic
structures, especially groups. The course emphasizes the writing
of proofs of elementary theorems. (Fall, Spring) (Evenings)
MATH 3166. Combinatorics. (3) Prerequisites: MATH 2164
or 2165. Combinatorial modeling, generating functions, recurrence
relations, inclusion-exclusion principle and problems from recreational
mathematics. (Spring) (Alternate years)
MATH 3171. Applied Mathematics. (3) Prerequisites: MATH
2141 and 2171 with grades of C or better. Separation of
variables techniques for the classical partial differential equations
of mathematical physics; Fourier series; Sturm-Liouville theory.
(Fall) (Evenings)
MATH 3176. Numerical Analysis. (3) Prerequisites: CSCI
1100 or 1201 and its lab, MATH 2141 and 2171. Numerical solution
of initial value and boundary value problems in ordinary differential
equations, direct and iterative methods of solving systems of
equations. Selected problems will be programmed for computer solution.
(Spring) (Alternate years)
MATH 3181. Fundamental Concepts of Geometry. (3) Prerequisite:
MATH 2164. Foundations of geometry, transformations, comparison
of Euclidean and non Euclidean geometries. (Fall, Spring)
(Evenings)
MATH 3183. Intuitive Topology. (3) Prerequisite: MATH 2141.
Introduction to combinatorial topology; topology of Euclidean
space, winding number, homotopy, fundamental group. (On demand)
MATH 3551. Mathematics Cooperative Education Experience. (0)
Prerequisites: Sophomore standing, a 3.0 GPA in MATH/STAT/OPRS
courses and consent of the Department of Mathematics. The student
will be employed in a manner that affords him/her the opportunity
of using and enhancing mathematical knowledge and skills through
practical experience. After completing MATH 3551, the student
must take MATH 3652. MATH 3551 may be repeated with consent of
the department. (On demand)
MATH 3652. Mathematics Cooperative Education Seminar. (1)
Prerequisite: MATH 3551. The student will give an exposition of
his/her work experience in MATH 3551. An exposition of underlying
theoretical concepts and related ideas may also be required. (On
demand)
MATH 3688. Mathematics Awareness Seminar. (0) Prerequisite:
junior standing. Visiting speakers, discussion of job opportunities
and of selected topics in mathematics. (Fall)
MATH 3689. Mathematics Project Seminar. (1) Prerequisite:
senior standing. Oral presentation by the student on an area of
mathematics or a mathematical problem. (Fall, Spring)
MATH 3691. Seminar. (1-6) Prerequisite: consent of the department.
Readings, study and discussion designed to develop the student's
ability to study independently and to present results properly.
(On demand)
MATH 3790. Junior Honors Seminar. (3) Prerequisite: consent
of the department. May be repeated once for additional credit
with approval of the department. (On demand)
MATH 3791. Senior Honors Tutorial. (3) Prerequisite: consent
of the department. Individual tutorials in which the student will
pursue independent study and research in any area of mathematics
under the direction of one or more faculty members. The project
of the student will be planned to culminate in a research paper
of original or expository nature. May be repeated for additional
credit with the approval of the department. (On demand)
MATH 4000. Topics in Foundations or History of Mathematics.
(2-3) (2-3G) Prerequisite: consent of the department. Topics
in the foundations or the history of mathematics selected to supplement
regular course offerings in this area of mathematics. May be repeated
for credit with approval of the department. Credit for the M.A.
degree in mathematics requires approval of the department. (On
demand)
MATH 4020. Topics in Probability and Statistics. (2-3) (2-3G)
Prerequisite: consent of the department. Topics in probability
and statistics selected to supplement regular course offerings
in this area of mathematics. May be repeated for credit with the
approval of the department. Credit for the M.A. degree in mathematics
requires approval of the department. (On demand)
MATH 4040. Topics in Analysis. (2-3) (2-3G) Prerequisite:
consent of the department. Topics in analysis selected to supplement
regular course offerings in this area of mathematics. May be repeated
for credit with the approval of the department. Credit for the
M.A. degree in mathematics requires approval of the department.
(On demand)
MATH 4060. Topics in Algebra. (2-3) (2-3G) Prerequisite:
consent of the department. Topics in algebra selected to supplement
regular course offerings in this area of mathematics. May be repeated
for credit with the approval of the department. Credit for the
M.A. degree in mathematics requires approval of the department.
(On demand)
MATH 4070. Topics in Applied Mathematics. (2-3) (2-3G)
Prerequisite:
consent of the department. Topics in applied mathematics selected
to supplement regular course offerings in this area of mathematics.
May be repeated for credit with the approval of the department.
Credit for the M.A. degree in mathematics requires approval of
the department. (On demand)
MATH 4080. Topics in Geometry and Topology. (3) (3G)
Prerequisite:
consent of the department. Topics in geometry or topology selected
as to supplement regular course offerings in this area of mathematics.
May be repeated for credit with approval of the department. Credit
for M.A. degree in mathematics requires approval of the department.
(On demand)
MATH 4109. History of Mathematical Thought. (3) (3G) Prerequisite:
consent of the department. A study of the development of mathematics
in its historical setting from the earliest beginnings to modern
times. Not approved for the M.A. in mathematics degree. (Fall)
(Evenings)
MATH 4161. Number Theory. (3) (3G) Prerequisite: MATH 3163
with a grade of C or better or consent of the department.
A study of the elements of classical number theory including divisibility,
congruences, diophantine equations, prime numbers and their distribution,
quadratic reciprocity, number-theoretic functions, and famous unsolved
problems. Not approved for the M.A. in mathematics degree. (Spring)
(Alternate years)
MATH 4163. Modern Algebra. (3) (3G) Prerequisite: MATH
3163 or consent of the department. Groups, rings, integral domains,
fields. (Fall) (Alternate years)
MATH 4164. Abstract Linear Algebra. (3) (3G) Prerequisite:
MATH 3163 and 2164 or consent of the department. Vector spaces
over arbitrary fields, linear transformations, canonical forms,
multilinear algebra. (Spring) (Alternate years)
MATH 4181. Introduction to Topology. (3) (3G) Prerequisite:
MATH 2164. Topics from set theory and point set topology such
as cardinality, order, topological spaces, metric spaces, separation
axioms, compactness and connectedness. (Fall) (Alternate years)
MATH 4691. Seminar. (1-6) (1-6G) Prerequisite: consent of
the department. Individual or group investigation and exposition
of selected topics in mathematics. (On demand)
MATH 4692. Seminar. (1-6) (1-6G) Prerequisite: consent of
the department. A continuation of MATH 4691. (On demand)
MATH 6004. Topics in Analysis. (3G) Prerequisite: MATH
6101 or consent of department. Topics in analysis selected so
as to complement regular course offerings in this area of mathematics.
May be repeated for credit with the consent of department. (On
demand)
MATH 6008. Topics in Geometry and Topology. (3G) Prerequisite:
consent of department. Topics selected from Euclidean geometry,
non-Euclidean geometry, projective geometry, differential geometry,
pointset topology, algebraic topology. May be repeated for credit
with approval of department. (On demand)
MATH 6100. Foundations of Mathematics. (3G) Prerequisite:
consent of department. Logic, sets and axiomatic systems. (Fall,
Summer) (Alternate years)
MATH 6101. Foundations of Real Analysis. (3G) Prerequisite:
MATH 6100 or consent of department. Axiomatic and historical development
of the real and complex numbers; rigorous development of limits
and continuity of functions, intermediate and extreme value theorems.
(Fall) (Alternate years)
MATH 6102. Calculus from an Advanced Viewpoint. (3G)
Prerequisite:
MATH 6101 or its equivalent. A continuation of MATH 6101. A rigorous
approach to differentiation and integration of functions of one
real variable. (Spring) (Alternate years)
MATH 6103. Computer Techniques and Numerical Methods. (3G)
Prerequisite: MATH 6101 or consent of department. Computer systems,
programming, and the computer solution of numerical problems.
(Summer) (Alternate years)
MATH 6104. Programming in BASIC and LOGO. (3G) Prerequisite:
consent of department. Introduction to BASIC and LOGO with emphasis
on designing and developing programs to enhance instruction in
problem solving. Students will develop a specific curriculum project
using acquired programming concepts and techniques. (Yearly)
MATH 6105. Problem Solving in Discrete Mathematics. (3G)
Prerequisite: consent of department. Propositional and predicate
calculus, counting techniques, partially ordered sets, lattices,
graphs and trees. (Alternate years)
MATH 6106. Modern Algebra. (3G) Prerequisite: MATH 3163
or its equivalent or consent of department. Topics chosen from
group theory, rings and ideals, integral domains, fields and elementary
Galois theory. (Summer) (Alternate years)
MATH 6107. Linear Algebra. (3G) Prerequisite: MATH 2164
or its equivalent or consent of department. Systems of linear
equations, matrices, vector spaces, linear transformations, determinants,
canonical forms of matrices, inner products. (Summer) (Alternate
years)
MATH 6118. Non-Euclidean Geometry. (3G) Prerequisite: consent
of department. History of Euclid's Fifth Postulate and attempts
to prove it; work of Gauss, Bolyai, Lobachevsky and others; systematic
development of hyperbolic geometry; relative consistency of hyperbolic
geometry; relative consistency of hyperbolic and Euclidean geometries.
(Alternate years)
MATH 6171. Advanced Applied Mathematics I. (3G) Prerequisites:
MATH 2141 and 2171 with grades of C or better, or consent
of department. Power series solutions of ordinary differential
equations, vector calculus, line and surface integrals, partial
differential equations and Fourier integrals. (Fall) (Evenings)
MATH 6172. Advanced Applied Mathematics II. (3G) Prerequisites:
MATH 2141 and 2171 with grades of C or better or consent
of department. Complex analysis; probability and statistics. (Spring)
(Evenings)
MATH 6609. Seminar. (1-2-3G) Prerequisite: consent of department.
A series of regularly scheduled meetings in which each student
will present one or more topics selected by the instructor. May
be repeated for credit with the consent of department. (On
demand)
Advanced Graduate Only
MATH 7028. Topics in Probability. (3G) Prerequisite: MATH
7120 and 7121, or consent of department. Topics of current interest
in probability and advanced topics in probability. May be repeated
for credit with the consent of the department. (On demand)
MATH 7050. Topics in Mathematics. (2-3G) Prerequisite: consent
of department. Topics chosen from such fields as algebra, topology,
analysis, applied mathematics, differential geometry, mathematical
physics, graph theory, probability, statistics. May be repeated
for credit as topics vary and with the approval of department.
(On demand)
MATH 7065. Topics in Applied Algebra and Algebraic Structures.
(3G) Prerequisite: consent of the department. Current topics
in Applied Algebra and Algebraic Structure. (On demand)
MATH 7070. Topics in Numerical Analysis. (3G) Prerequisite:
consent of the department. Topics of current interest in numerical
analysis. May be repeated for credit with the consent of the department.
(On demand)
MATH 7071. Topics in Differential Equations. (3G) Prerequisite:
consent of the department. Topics of current interest in ODE,
PDE, dynamical systems, inverse problems and related subjects.
May be repeated for credit with the consent of the department.
(On demand)
MATH 7120. Probability Theory I. (3G) Prerequisites: MATH
7143 and MATH/STAT 3122 or consent of department. Topics include
probability spaces, probability measures, sigma-algebras, characteristic
functions, sequences of random variables, law of large numbers,
general forms of the Central Limit Theorem. (Fall) (Alternate
years)
MATH 7121. Probability Theory II. (3G) Prerequisite: MATH
7120. A continuation of MATH 7120. (On demand)
MATH 7125. Stochastic Processes I. (3G) Prerequisites:
MATH/STAT 3122 or MATH 7143 or consent of department. Basic ideas
in the study of stochastic processes. Topics will be selected
from: discrete and continuous time Markov processes, stationary
and renewal processes, applications to queuing theory, reliability
theory, stochastic differential equations, time-series analysis,
filtering and stochastic control theory. (On demand)
MATH 7126. Stochastic Processes II. (3G) Prerequisite:
MATH 7125. A continuation of MATH 7125. (On demand)
MATH 7141. Complex Analysis I. (3G) Prerequisite: MATH
5143 or consent of department. Holomorphic functions, complex
integration, residues, entire and meromorphic functions, conformal
mapping, harmonic functions. (Spring) (Alternate years)
MATH 7142. Complex Analysis II. (3G) Prerequisite: MATH
7141. A continuation of MATH 7141. (On demand)
MATH 7143. Real Analysis I. (3G) Prerequisite: MATH 5144
or consent of department. Lebesgue integration on the real line,
Lp spaces, introduction to general measure and integration theory.
(Fall)
MATH 7144. Real Analysis II. (3G) Prerequisite: MATH 7143.
A continuation of MATH 7143. (Spring)
MATH 7147. Applied Functional Analysis. (3G) Prerequisite:
MATH 5144. Introduction to functional analysis and its applications
to such areas as linear and nonlinear differential equations,
integral equations, and control theory. Topics chosen from Banach
spaces, operators, the HahnBanach, open mapping and closed graph
theorems, Sobolev spaces, spectral theory, operators in Hilbert
space. (Summer) (On Demand)
MATH 7148. Functional Analysis. (3G) Prerequisite: MATH
7144 or consent of the department. Material selected from: spectral
theory, spectral theory of differential operators, groups and
semigroups of operators, nonlinear functional analysis, asymptotic
analysis, integral equations, Fourier analysis, distributions,
and Sobolev spaces. (Fall)(Alternate years)
MATH 7163. Modern Algebra I. (3G) Prerequisite: MATH 4163
and 4164 or consent of department. Topics will be selected from
Galois theory, commutative algebra, modules, ring theory, homological
algebra. (Fall) (Alternate years)
MATH 7164. Modern Algebra II. (3G) Prerequisite: MATH 7163.
A continuation of MATH 7163. (On demand)
MATH 7172. Partial Differential Equations. (3G) Prerequisite:
MATH 7144 or consent of department. Harmonic functions, mean-value
theorem, maximum principle, Green's representation for the solution
of the Dirichlet problem for Laplace's equation; Poisson's equations
and the Poisson formula; statement and proof of the existence
theorem for general second-order elliptic operators, generalized
maximum principles; Sobolev spaces. Evolution equations involving
elliptic operators, such as the heat or wave equations, may also
be introduced. (Spring) (Alternate years)
MATH 7173. Evolution Equations. (3G) Prerequisite: MATH
7144 and 7172 or consent of the department. Semigroups of operators
and their generators, examples of semigroups. The heat equation,
examples of elliptic operators that generate semigroups, Hille-Yosida
theory, analytic semigroups; examples, fractional powers of operators.
(On demand)
MATH 7174. Linear and Non-linear Waves. (3G) Prerequisite:
MATH 7144 or consent of the department. Hyperbolic waves, characteristics,
Riemann invariants, conservation laws, weak solutions, shock structure.
Burger's equation, gas dynamics, dispersive waves, group velocity,
water waves, non-linear optics. (On demand)
MATH 7175. Inverse Problems. (3G) Prerequisite: MATH 7144
and MATH 5174 or consent of the department. Ill-posed problems
and numerical methods for them. Applications of inverse problems
to real processes. One dimensional inverse problems. Multi-dimensional
inverse problems: uniqueness and numerical methods. Inverse scattering
problems. (On demand)
MATH 7176. Advanced Numerical Analysis. (3G) Prerequisites:
MATH 2164, 2171 and 5176. A selection of topics from such areas
as iterative methods of solving linear and non-linear systems
of equations, approximation theory, splines, and finite element
methods for partial differential equations. (Spring) (Alternate
years)
MATH 7177. Applied Optimal Control. (3G) Prerequisites:
MATH 5143 or consent of department. Examples of control systems
and optimization problems, optimal control of discrete-time systems,
solutions of the general discrete-time optimization problem, optimal
control of continuous-time systems, the calculus of variations,
solution of the general continuous optimization problem, applications
of the Pontryagin Maximum Principle, Dynamic programming, and
Bang-bang control. Controllability and differential games may also
be introduced. (Spring) (Alternate years)
MATH 7178. Computational Methods for Fluid Dynamics. (3G)
Prerequisite:
CSCI 1100 or 1201 and 1201L, MATH 2141, 2171, 5174 and 5176 or
consent of the department. Topics on various numerical techniques
for the solution of incompressible and compressible flows. Finite
difference, finite element and spectral methods, and shock capturing
and fitting methods. Multi-grid method and acceleration techniques.
(On demand)
MATH 7179. Advanced Finite Difference Methods. (3G) Prerequisite:
consent of the department. Accuracy analysis and design of high
order schemes, stability theory of schemes with variable coefficients,
stability theory of schemes for initial-boundary value problems,
convergence theory for nonlinear cases. (On demand)
MATH 7181. Topology I. (3G) Prerequisite: consent of department.
Topological spaces, continuous functions, connectedness, compactness,
and metrizability, and further topics from point-set, geometric
or algebraic topology. (On demand)
MATH 7182. Topology II. (3G) Prerequisite: MATH 7181. A
continuation of MATH 7181. (On demand)
MATH 7184. Differential Geometry I. (3G) Prerequisite:
consent of the department. Manifolds, differential structures,
tangent bundles, embeddings, immersions, inverse function theorem,
Morse-Sard theorem, transversality, Borsuk-Ulam theorem, vector
bundles, Euler characteristics, Morse theory, Stokes theorem,
Gauss-Bonnet theorem, Whitney embedding theorem. (On demand)
MATH 7185. Differential Geometry II. (3G) Prerequisite:
consent of the department. Differentiable manifolds, differential
forms, critical points, local and global theory of curves, local
and global theory of surfaces, connections, Geodeusics, curvature,
spaces of constant curvature, Lie groups and Lie algebras. (On
demand)
MATH 7273. Advanced Finite Element Analysis. (3G) Prerequisite:
MATH 5172 and 5174 or consent of the department. Selection of
topics from such areas of finite element analysis as convergence
theorems (Ciarlet), hierarchical basis functions, the h-p method,
adaptive grid techniques and solution methods for nonlinear equations.
(Fall)(Alternate years)
MATH 7275. Dynamical Systems I. (3G) Prerequisites: MATH
5143 and MATH 5173. Cycles and separatrix cycles, Poincaré
first return map: diffeomorphisms, Poincaré-Bendixson Theory,
flows on the two-torus; structural stability, genericity, Peixoto's
theorem; singularities of planar systems. Degenerate singularities,
Hopf bifurcation, saddle-node bifurcation, center bifurcation.
(On demand)
MATH 7276. Dynamical Systems II. (3G) Prerequisite: MATH
7275 or consent of the department. Method of averaging, Melnikov
functions, hyperbolic structure, symbolic dynamics, homocline
and heteroclinic orbits, global bifurcations, infinite dimensional
dynamical systems, inertial manifolds, Lyapunov exponents and
dimension of attractors, codimension-two bifurcations, Duffing's
equation, Lorenz equations, finite dimensional systems of dimension
at least three. (On demand)
MATH 7277. Bifurcation Theory. (3G) Prerequisite: MATH
7275 or consent of the department. Implicit function theorem,
manifolds and transversality, Newton polygons, Lyapunov center
theorem, variational methods, Ljusternik-Schnirelman theory, mountain-pass
theorem, bifurcations with one-dimensional null-spaces, Morse
theory and global bifurcations, geometric theory of partial differential
equations. (On demand)
MATH 7691. Research Seminar. (1-3G) Prerequisite: consent
of department. A seminar in which independent study may be pursued
by the student or a group of students under the direction of a
professor. (On demand)
MATH 7692. Research Seminar. (1-3G) Prerequisite: consent
of department. A continuation of MATH 7691. (On demand)
MATH 7893. Thesis. (0-3G) Prerequisite: consent of department.
Subject to the approval of the department Graduate Committee,
the thesis may be original work, work of an expository nature,
or the mathematical formulation and solution of a particular industrial
or business problem suggested by the career interest of the student.
The thesis must be defended in an oral presentation. May be repeated
for credit with the consent of department. (Fall, Spring, Summer)
MATH 7994. Doctoral Resarch and Reading. (0-9G) Prerequisite:
consent of the department. May be repeated with consent of the
department. (On demand)
Undergraduate/Available for Graduate Credit
Graduate Only
[UNCC CATALOG] [UNC Charlotte]
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