Mathematics
Course Descriptions and Syllabi
Undergraduate Course Descriptions and Syllabi
The Mathematics Department offers a variety of entry-level courses. The prerequisite
for each is a minimum of two years of high school algebra and one year of high school
geometry. In addition, prerequisites for MATH 1730-Precalculus and MATH 1910-Calculus
I include trigonometry. For certain pairs of courses, e.g., 1710 and 1730, credit
is not given for both. The entry-level course for students planning to major in Engineering,
Mathematics, Physics, or other technical areas, but who lack the necessary preparation
for Calculus, is MATH 1730-Precalculus Mathematics. The prerequisites for this course
are 2 years of high school algebra, one year of high school geometry, and at least
12 weeks of high school trigonometry (or equivalent).
NOTE: All mathematics prerequisite courses must be completed with a grade of "C" or better.
In addition, students cannot receive credit for a 1000-level mathematics course if
that course is a prerequisite for any mathematics course that has been completed with
a grade of "C" or better.
NOTE: The u designation before a course listing indicates that the course meets Tennessee Tech General Education requirements.
NOTE: Graduate courses are listed below the undergraduate courses.
NOTE: Please consult our Course Offerings Page when planning a schedule of coursework.
uMATH 1010. Math for General Studies. Lec. 3. Credit 3. Syllabus for MATH 1010
Mathematics as applied to real-life problems selected from such topics as preference
schemes for voting, fair division and apportionment methods, routing and scheduling
problems, analysis of graphs, growth and symmetry, and counting problems.
MATH (CSC, PHYS) 1020. First-Year Connections. Rec. 2. Credit 1. Syllabus for MATH 1020
This course is intended as a bridge course for students entering Tennessee Tech from
high school. The course is designed to strengthen the student’s connection to Tennessee
Tech, the College of Arts and Sciences, and the appropriate department (CSC, MATH,
or PHYS) by focusing on the enhancement of skills needed for academic success. This
course engages the student in meaningful academic and non-academic out-of-the-classroom
activities, as learning occurs both in and out of the classroom. It emphasizes critical
thinking, the formation of academic and social goals and support groups, and time-management
and study skills.
uMATH 1410. Number Concepts for Teachers. Lec. 3. Credit 3. Syllabus for MATH 1410
Prerequisite: Admission is restricted to students majoring in Elementary Education.
Introduction to sets and operations on sets, properties and operations on whole numbers,
and integers, rational and real numbers.
MATH 1420. Geometry Concepts for Teachers. Lec. 3. Credit 3. Syllabus for MATH 1420
Prerequisite: C or better in MATH 1410. Admission is restricted to students majoring
in Elementary Education. Introduction to elements of probability and statistics and
basic concepts of Euclidean Geometry including congruence, similarity, measurements,
areas, and volumes.
uMATH 1530. Introductory Statistics. Lec. 3. Credit 3. Syllabus for MATH 1530
Descriptive statistics including measures of central location and variation, frequency
distributions, histograms, and frequency polygons. Probability relating to elementary
sample spaces, events, conditional probability, discrete and continuous type random
variables, mathematical expectation, and the normal probability distribution. Inferential
statistics relating to the confidence intervals and hypothesis tests related to the
mean and proportion.
uMATH 1710. Pre-Calculus Algebra. Lec. 3. Credit 3. Syllabus for MATH 1710
Review of algebra; relations and functions and their graphs, including polynomial
and rational functions; conic sections; inequalities; arithmetic, and geometric sequences
and series. Credit will not be given for both MATH 1710 and MATH 1130 or for MATH
1710 and MATH 1730.
uMATH 1720. Pre-Calculus Trigonometry. Lec. 3. Credit 3. Syllabus for MATH 1720
Circular functions and radian measure, graphs of the trigonometric functions, trigonometric
identities, and equations, the inverse trigonometric functions, polar coordinates.
Applications involving triangles, vectors in the plane and complex numbers. Credit
will not be given for both MATH 1720 and MATH 1730.
uMATH 1730. Pre-Calculus Mathematics. Lec. 5. Credit 5. Syllabus for MATH 1730
Prerequisites: Two years of high school algebra, one year of high school geometry,
and 12 weeks of trigonometry. Review of algebra and trigonometry; relations and functions
and their graphs, including polynomial and rational functions; conic sections; inequalities;
polar coordinates; complex numbers; and advanced topics in algebra. Credit will not
be given for both MATH 1730 and any of MATH 1710 and MATH 1720.
uMATH 1830. Applied Calculus. Lec. 3. Credit 3. Syllabus for MATH 1830
Prerequisites: ACT mathematics score of 25 or above and three years of high school
mathematics, including algebra and geometry; or, special permission of the Mathematics
Department; or, C or better in MATH 1130 or MATH 1710 or equivalent. A survey of limits,
continuity, and the differential and integral calculus with applications in business,
economics and the life sciences.
uMATH 1831. Further Topics in Applied Calculus. Lec. 1. Credit 1. Syllabus for MATH 1831
Corequisite: MATH 1830. Includes systems of linear equations, linear programming,
exponential and logarithmic equations, partial differentiation, separable and linear
differential equations. This course is designed to enhance students’ understanding
of calculus and its applications to Economics.
uMATH 1845. Technical Calculus. Lec. 3. Credit 3. Syllabus for MATH 1845
Prerequisites: ACT mathematics score of at least 25 and four years of high school
mathematics, including algebra, geometry, trigonometry, and advanced or pre-calculus
mathematics; or, special permission of the Mathematics Department; or, C or better
in MATH 1730; or, C or better in MATH 1710 and 1720 or equivalent. A survey of differential
and integral calculus of functions of a single variable including transcendental functions.
MATH 1904. Extended Calculus 1A. Lec. 4. Credit 4. Syllabus for MATH 1904
Prerequisites: ACT mathematics score of 27 or above and four years of high school mathematics including algebra, geometry, trigonometry, and advanced or pre-calculus mathematics; or special permission of the Mathematics Department; or C or better in MATH 1730; or C or better in MATH 1720 and MATH 1710; or equivalent.
MATH 1906. Extended Calculus 1B. Lec. 3. Credit 3. Syllabus for MATH 1906
Prerequisites: C or better in MATH 1904 (Extended Calculus A)
uMATH 1910. Calculus I. Lec. 4. Credit 4. Syllabus for MATH 1910
Prerequisites: ACT mathematics score of 27 or above and four years of high school
mathematics, including algebra, geometry, trigonometry, and advanced or pre-calculus
mathematics, or special permission of the Mathematics Department; or C or better in
MATH 1730; or C or better in MATH 1720 and MATH 1710 or equivalent. Limits, continuity,
derivatives and integrals of functions of one variable. Applications of differentiation
and introduction to the definite integral.
MATH 1911. Calculus I Honors Seminar. Lab. 1. Credit 0. Syllabus for MATH 1911
Co-requisite: Concurrent enrollment in MATH 1910. An ACT score of 30 or higher is
also recommended. Selected topics to add depth to the understanding of the material
in MATH 1910. Honors students can receive honors credit for MATH 1910 by successfully
completing both MATH 1910 and MATH 1911.
MATH 1920. Calculus II. Lec. 4. Credit 4. Syllabus for MATH 1920
Prerequisite: C or better in MATH 1910; or equivalent AP credit for MATH 1910. Integration
techniques, applications of the definite integral, polar coordinates, parametric equations,
sequences, and series.
MATH 1921. Calculus II Honors Seminar. Lab. 1. Credit 0. Syllabus for MATH 1921
Prerequisite: MATH 1911 or permission of the instructor. (A grade of "A" in MATH 1910
is recommended for students not taking 1911).
Co-requisite: Concurrent enrollment in MATH 1920. Selected topics to add depth to
the understanding of the material in MATH 1920. Honors students can receive honors
credit for MATH 1920 by successfully completing both MATH 1920 and MATH 1921.
MATH 2010. Introduction to Linear Algebra. Lec. 3. Credit 3. Syllabus for MATH 2010
Prerequisite: C or better in MATH 1910. Systems of linear equations, matrix algebra,
inverses, matrix factorizations, determinants, vector spaces and dimension, rank,
linear transformations, eigenvalues, and eigenvectors, inner product, orthogonal projections.
MATH 2110. Calculus III. Lec. 4. Credit 4. Syllabus for MATH 2110
Prerequisite: C or better in MATH 1920; or equivalent AP credit for MATH 1910 and
MATH 1920. Analytic geometry and vectors, differential calculus of functions of several
variables, multiple integration, and topics from vector calculus.
MATH 2120. Differential Equations. Lec. 3. Credit 3. Syllabus for MATH 2120
Prerequisite: C or better in MATH 1920. First order equations, linear equations of
higher order, power series solutions (including Frobenius method), Laplace transforms,
other topics. It is recommended but not required that students take MATH 2010 before
taking MATH 2120.
MATH 2610. Discrete Structures. Lec. 3. Credit 3. Syllabus for MATH 2610
Prerequisite: C or better in MATH 1920. Topics to be chosen from algebra of sets and
relations, functions, algebras, graphs and digraphs, monoids and machines, groups
and subgroups, computer arithmetic, binary codes, logic, and languages.
MATH 3000. Selected Topics in Mathematics. Lec. 1. Credit 1.
Prerequisite: C or better in MATH 1920 and consent of instructor. Lectures on and
discussion of topics from upper level mathematics to be selected by the instructor
in a setting with less structure than in a traditional class.
MATH 3070-3080. Statistical Methods I-II. Lec. 3-3. Credit 3-3. Syllabus for MATH 3070, Syllabus for MATH 3080
Prerequisite: MATH 3070: ACT mathematics score greater than or equal to 19; or C or
better in MATH 1130 or MATH 1710 or equivalent. MATH 3080: C or better in MATH 3070.
Introduction to parametric statistical methods with some non-parametric alternatives,
sampling, probability, Type I and Type II error, sample size estimation, confidence
interval estimation, test of hypotheses using normal, Student's t, Snedecor's F, Chi-square
and the binomial distributions, linear regression, analysis of variance, and data
analysis utilizing statistical software.
MATH 3400. Introduction to Concepts of Mathematics. Lec. 2. Rec. 2. Credit 3. Syllabus for MATH 3400
Prerequisite: C or better in MATH 1920. A rigorous treatment of elements of logic
and set theory including propositional calculus (statements, connectives, conditionals,
and negation), quantifiers, sets and operations on sets, mappings, equivalence relations,
and mathematical induction. Students are expected to work in an abstract setting using
precise definitions and formal proofs.
MATH 3430. College Geometry. Lec. 3. Credit 3. Syllabus for MATH 3430
Prerequisite: C or better in MATH 3400. A rigorous development of geometry from first
concepts using the metric approach. Topics include constructions and hyperbolic geometry.
MATH 3470. Introductory Probability and Statistics. Lec. 3. Credit 3. Syllabus for MATH 3470
Prerequisite: C or better in MATH 1920. Probability, random variables, discrete and
continuous distributions and their simulation, elementary sampling theory, and estimation
with an overall emphasis on simulation of random processes (Not allowed for mathematics
majors after having taken MATH 4480.)
MATH 3670. Theory and Applications of Random Signals. Lec. 2. Credit 2. Syllabus for MATH 3670
Introduction to randomization, unconditional and conditional probability, independence,
and concepts of random variables. Distributions and density functions, moments and
moment generating functions, univariate and multivariate random variables, random
process concepts, spectral characteristics of random processes, and linear systems
with random inputs.
MATH 3810. Complex Variables. Lec. 3. Credit 3. Syllabus for MATH 3810
Prerequisite: C or better in MATH 2110. Complex numbers, calculus of complex variables,
analytic functions, Cauchy's Theorem, series, the Residue Theorem, and applications.
MATH 3910. Independent Study. Credit 1-3.
Prerequisite: Consent of instructor. Readings and study under the supervision of a
qualified staff member.
MATH 4010-4020 (5010-5020). Modern Algebra I-II. Lec. 3-3. Credit 3-3. Syllabus for MATH 4010-4020, 5010-5020
Prerequisite: MATH 4010 - C or better in MATH 2010 and C or better in MATH 3400; MATH
4020 - C or better in MATH 4010. Groups and subgroups including cyclic, abelian, finite;
permutation groups; group homomorphisms; cosets and Lagrange's Theorem; normal subgroups
and factor groups. Rings including integral domains, unique factorization domains
and Euclidean domains, ideals and factor rings, ring homomorphisms, fields and their
extensions, geometric constructions.
MATH 4050 (5050). Number Theory. Lec. 3. Credit 3. Syllabus for MATH 4050-5050
Prerequisite: C or better in MATH 3400 or consent of instructor. Properties of integers,
division algorithms, prime numbers, diophantine equations, and congruences.
MATH 4060 (5060). Topics in Cryptography. Lec. 3. Credit 3. Syllabus for MATH 4060-5060
Prerequisite: C or better in MATH 2010 and C or better in either MATH 3400 or CSC
2700. Fundamental concepts of cryptography presented with mathematical background
(including groups, fields, elements of number theory, probability and statistics).
Special attention will be given to the RSA algorithm, Elliptic Curve Cryptography,
the ElGamal public key cryptosystem, Diffie-Hellman key exchange and pseudo random
number generators.
MATH 4110-4120 (5110-5120). Advanced Calculus I-II. Lec. 2-2. Rec. 2-2. Credit 3-3. Syllabus for MATH 4110-4120, 5110-5120
Prerequisite: MATH 4110 (5110): C or better in MATH 3400 or consent of instructor;
MATH 4120 (5120): C or better in MATH 4110 (5110). Rigorous treatment of functions
of one and several variables, improper integrals, sequences, infinite series, uniform
convergence, and applications. Students are expected to improve their ability to work
in an abstract setting using precise definitions and formal proofs and to present
their work in class.
MATH 4210-4220 (5210-5220). Numerical Analysis I-II. Lec. 3-3. Credit 3-3. Syllabus for MATH 4210-4220, 5210-5220
Prerequisite: MATH 4210 (5210): C or better in MATH 1920; MATH 4220 (5220): C or better
in MATH 2120 or consent of instructor. Iterative methods for nonlinear equations,
computational error analysis, convergence of iterative techniques, interpolation,
numerical differentiation and integration, approximate solutions of initial-value
problems, boundary-value problems, and nonlinear systems, and direct and iterative
methods for linear systems.
MATH 4250-4260 (5250-5260). Advanced Ordinary Differential Equations I-II. Lec. 3-3. Credit 3-3. Syllabus for MATH 4250-4260-5250-5260
Prerequisite: MATH 4250 (5250): C or better in MATH 2110 and MATH 2120; MATH 4260
(5260): C or better in MATH 4250 (5250). Systems of ordinary differential equations,
matrix methods, approximate solutions, stability theory, basic theory of nonlinear
equations and differential systems, trajectories, phase space stability, and construction
of liapunov functions.
MATH 4310-4320 (5310-5320). Introduction to Topology I-II. Lec. 3-3. Credit 3-3. Syllabus for MATH 4310-4320, 5310-5320
Prerequisite: MATH 4310 (5310): C or better in MATH 3400; MATH 4320 (5320): C or better
in MATH 4310 (5310). Topological spaces, continuity, connectedness, compactness, separation
axioms, function spaces, and fundamental groups.
MATH 4350 (5350). Introductory Combinatorics. Lec. 3. Credit 3. Syllabus for MATH 4350-5350
Prerequisite: C or better in MATH 3400 or consent of instructor. Topics to be covered
include permutations, combinations, multisets, partitions, recurrence relations, generating
functions, and the principle of inclusion-exclusion.
MATH 4360 (5360). Graph Theory. Lec. 3. Credit 3. Syllabus for MATH 4360-5360
Prerequisite: C or better in MATH 3400 or consent of instructor. Fundamental concepts
of undirected and directed graphs, trees, connectivity, traversability, colorability,
network flows, and matching theory.
MATH 4410 (5410). Differential Geometry. Lec. 3. Credit 3. Syllabus for MATH 4410-5410
Prerequisites: C or better in MATH 2110, 2010 and 3400. Geometry of curves and surfaces
in three dimensional space. Calculus on surfaces, curvature and Riemannian geometry.
MATH 4470-4480 (5470-5480). Probability and Statistics I-II. Lec. 3-3. Credit 3-3. Syllabus for MATH 4470-4480, 5470-5480
Prerequisite: MATH 4470: C or better in MATH 2110; MATH 4480: C or better in MATH
4470. Mathematical foundations of elementary statistical methods, application and
theory, probability in discrete and continuous distributions, correlation and regression,
sampling distributions, and significance tests.
MATH 4510 (5510). Advanced Mathematics for Engineers. Lec. 3. Credit 3. Syllabus for MATH 4510-5510
Prerequisites: C or better in MATH 2110 and MATH 2120. Fourier series, Sturm-Liouville
problems, orthogonal functions, Legendre polynomials, Bessel functions, separable
partial differential equations (e.g. heat, wave and Laplace equations), and other
topics.
MATH 4530-4540 (5530-5540). Linear Algebra I-II. Lec. 3. Credit 3. Syllabus for MATH 4530-4540, 5530-5540
Prerequisites: MATH 4530 (5530): C or better in MATH 2010 and MATH 3400; MATH 4540
(5540): C or better in MATH 4530 (5530). A theoretical study of vector spaces, bases
and dimension, subspaces, linear transformations, dual spaces, eigenvalues and eigenvectors,
inner product spaces, spectral theory, duality, and quadratic and bilinear forms.
MATH 4550/5550-4560/5560. Mathematics of Investment I-II. Lec. 3. Cr. 3. Syllabus for MATH 4550/5550, 4560/5560
MATH 4550/5550: Prerequisite: C or better in MATH 1920 or consent of instructor. Topics
include examination of annuities, loans, bonds and other securities, portfolio, immunization,
interest rate swaps.
MATH 4560/5560: Prerequisite: C or better in both MATH 4550/5550 and MATH 4470/5470,
or consent of instructor. Topics include derivative securities, mathematical models
of financial risk management, and corporate finance.
MATH 4610 (5610). History of Mathematics I. Lec. 3. Credit 3. Syllabus for MATH 4610-5610
Prerequisite: C or better in MATH 3400. The development of mathematics and its relation
to the development of civilization prior to the beginnings of calculus.
MATH 4620 (5620). History of Mathematics II. Lec. 3. Credit 3. Syllabus for MATH 4620-5620
Prerequisite: C or better in MATH 3400. History of mathematics from the beginnings
of calculus through the modern times.
MATH 4710 (5710). Vector Analysis. Lec. 3. Credit 3. Syllabus for MATH 4710-5710
Prerequisite: C or better in MATH 2110. The algebra and the differential and integral
calculus of vectors, and applications to geometry and mechanics.
MATH 4750 (5750). Category Theory of Sets. Lec. 3. Credit 3. Syllabus for MATH 4750-5750
Prerequisite: C or better in MATH 3400 (or consent of instructor for MATH 5750). Abstract
sets and mappings, categories, sums, universal property, monomorphisms and parts,
finite inverse limits, colimits, epimorphisms, the Axiom of Choice, mapping sets and
exponentials, covariant and contravariant functoriality of function spaces, Cantor's
diagonal argument, power sets, variable sets, models of additional variation, and
selected applications.
MATH 4850 (5850). Computational Algebraic Geometry I. Lec. 3. Credit 3. Syllabus for MATH 4850-5850
Prerequisites: C or better in MATH 2010 and C or better in MATH 3400 or equivalent
(or consent of instructor for MATH 5850). Additional recommended prerequisite: MATH
3510 or any other 4000/5000-level mathematics course in which proofs are required.
Affine varieties and polynomial ideals, Groebner bases, elimination theory, Hilbert’s
Nullstellensatz, Zariski closure, and decomposition into irreducible varieties.
MATH 4860 (5860). Computational Algebraic Geometry II. Lec. 3. Credit 3. Syllabus for MATH 4860-5860
Prerequisite: C or better in MATH 4850 (5850). Polynomial and rational functions on
a variety, projective varieties, the dimension of a variety, selected applications
in robotics, automatic theorem proving, and invariant theory of finite groups.
MATH 4910-4920 (5910-5920). Directed Readings. Credit 1-3.
Prerequisite: Consent of instructor. These courses provide an opportunity for individual
reading and study under the supervision of a qualified staff member.
MATH 4950 (5950). Topics in Mathematics. Lec. 3. Credit 3.
Prerequisite: Consent of instructor. A formal course in any area where there is no
other course offering. May be taken more than once provided that the topic is different.
MATH 4970. Senior Seminar. Lec. 1. Credit 1. Syllabus for MATH 4970
Prerequisite: Senior standing. Preparation of papers at an advanced level in mathematics
to be presented both in writing and orally.
MATH 4991, 4992, 4993. Mathematical Research. Credit 1, 2, 3. Syllabus for MATH 4991, Syllabus for MATH 4992, Syllabus for MATH 4993
Prerequisite: C or better in MATH 1920 and consent of instructor. This course introduces
students to the process of performing research. By reading papers the students will
learn how to define open and significant problems, set up a research plan and, if
applicable, define relevant experiments. Students will be required to give presentations
on either their own or other people's research. These courses can be taken for credit
more than once.
GRADUATE COURSE Descriptions and Syllabi
MATH 6001. Communicating Mathematics I. Lec. 3. Cr. 3. Syllabus for MATH 6001
This course provides mathematics graduate teaching assistants with practical training
in the teaching of mathematics.
MATH 6002. Communicating Mathematics II. Lec. 3. Cr. 3 Syllabus for MATH 6002
This course provides practical training in the writing, typesetting, and oral presentation
of mathematics.
MATH 6010-20. Functional Analysis I-II. Lec. 3. Cr. 3. Syllabus for MATH 6010-6020
Prerequisite: MATH 6010: C or better in MATH 4120(5120) or consent of instructor;
MATH 6020: C or better in MATH 6010. Metric spaces, normed and Banach spaces, inner
product and Hilbert spaces. Fundamental theorems for normed and Banach spaces and
their applications. Linear operators on normed and Hilbert spaces.
MATH 6070-80. Applied Linear Statistical Methods I-II. Lec. 3. Cr. 3. Syllabus for MATH 6070-6080
Prerequisite: MATH 6070: Consent of instructor; MATH 6080: B or better in MATH 6070.
These two courses cover simple linear regression, multiple regression, diagnostic
measures, prediction and estimation, polynomial regression, qualitative regression,
nonlinear regression, and logistic regression.
MATH 6110-20. Abstract Algebra I-II. Lec. 3. Cr. 3. Syllabus for MATH 6110-6120
Prerequisite: MATH 6110: C or better in MATH 4010(5010) or consent of instructor;
MATH 6120: C or better in MATH 4020(5020) and C or better in MATH 6110, or consent
of instructor. An extensive treatment of groups, semigroups, integral domains, rings
and ideals, fields, and Galois fields.
MATH 6150. Mathematical Modeling. Lec. 3. Cr. 3. Syllabus for MATH 6150
Prerequisite: Consent of instructor. Applications of mathematics to real world problems
with emphasis on problem definition, research, solution, and written report presentation.
MATH 6170-80. Experimental Design I-II. Lec.3. Cr. 3. Syllabus for MATH 6170-6180
Prerequisite: MATH 6170: Consent of instructor; MATH 6180: C or better in MATH 6170.
Introduction to basic concepts of experimental design, fundamental assumptions in
analysis of variance, multiple comparison tests, complete randomized design, general
linear model approach to ANOVA, various experimental designs, incomplete block designs,
factorial experiments, fractional factorial experiments, response surface methods,
repeated measure designs.
MATH 6210-20. Topology I-II. Lec. 3. Cr. 3. Syllabus for MATH 6210-6220
Prerequisite: MATH 6210: C or better in MATH 4320 (5320) or consent of instructor;
MATH 6220: C or better in MATH 6210. Topics in point-set topology, homotopy theory,
triangulated spaces, homology theory, other topics in topology.
MATH 6240-50. Representations and Characters of Groups I -II. Lec. 3. Cr. 3. Syllabus for MATH 6240-6250
Prerequisite: MATH 6240: C or better in MATH 4010/5010 while C or better in MATH 4530/5530
is recommended, or consent of instructor; MATH 6250: C or better in MATH 6240. FG-modules,
reducibility, group algebras, FG-homomorphisms, Maschke’s Theorem, Schur’s Lemma,
irreducible modules, characters, inner products of characters, character tables, orthogonality
relations. Normal subgroups and lifted characters, tensor products, restriction to
a subgroup, induced modules and characters, Frobenius reciprocity relation, applications
to group theory such as real representations, groups of order pq, p-groups, characters
of GL(2,q), symmetric groups, Burnside’s Theorem, and molecular vibrations
MATH 6270. Mathematical Statistics. Lec. 3. Cr. 3. Syllabus for MATH 6270
Prerequisite: Consent of instructor. Statistical hypothesis, uniform most powerful
tests, sufficient statistics, completeness, Rao-Cramer inequality, sequential probability
ratio test, analysis of variance, multiple comparisons, nonparametric techniques.
MATH 6310-20. Complex Analysis I-II. Lec. 3. Cr. 3. Syllabus for MATH 6310-6320
Prerequisite: MATH 6310: C or better in MATH 4120 (5120) or consent of instructor;
MATH 6320: C or better in MATH 6310. Complex numbers, calculus of complex variables,
analytic function. Cauchy's Theorem and complex integration, power series including
Taylor's and Laurent's, residue theory with applications, conformal mapping with physical
applications.
MATH 6370-80. Probability Theory and Stochastic Processes I-II. Lec. 3. Cr. 3. Syllabus for MATH 6370-6380
Prerequisite: MATH 6370: C or better in MATH 4480(5480) or consent of instructor;
MATH 6380: C or better in MATH 6370. Probability theory of sets, random variable distribution
and characteristic functions, convergence, limits and law of large numbers, convolutions,
compound distribution, recurrent events, random walk models, Markov chains, homogeneous,
nonhomogeneous, and queuing processes.
MATH 6410-20. Real Analysis I-II. Lec. 3. Cr. 3. Syllabus for MATH 6410-6420
Prerequisite: MATH 6410: C or better in MATH 4120(5120) or consent of instructor;
MATH 6420: C or better in MATH 6410. Theory of Lebesgue measure and integration, Lp
spaces. Integration in locally compact space.
MATH (CSC) 6450. Advanced Theory of Computation. Lec. 3. Cr. 3. Syllabus for MATH 6450
Prerequisite: Consent of the instructor (previous coursework involving proofs and
some programming experience are needed). A rigorous treatment of the theory of computation.
Topics such as: computable functions, the Church-Turing thesis, complexity theory,
and P vs NP.
MATH (CSC) 6460. Computational Methods for Graphics and Modeling. Lec. 3. Cr. 3. Syllabus for MATH 6460
Prerequisite: Consent of the instructor (previous coursework involving proofs and
some programming experience are needed). Mathematical methods for graphics and modeling.
Topics such as: 3-D transformations, ray tracing, rendering, image processing, and
compression.
MATH 6470. Environmental Statistics. Lec. 3. Cr. 3. Syllabus for MATH 6470
Prerequisite: MATH 6070 or MATH 6170 or their equivalents. This course covers statistical
analysis used in environmental modeling. Topics include finite population parameter
estimation, spatial sampling techniques, animal population size estimation, variogram
estimation, kriging, logistic regression, and survival analysis. Familiarity with
computers is necessary. Also necessary is a background in calculus including differentiation
and integration of transcendental functions and series.
MATH 6510. Finite Difference Solutions of Partial Differential Equations. Lec. 3. Cr. 3. Syllabus for MATH 6510
Prerequisite: C or better in MATH 4510(5510) or consent of instructor. Approximate
solutions of boundary and initial value problems using the finite difference method.
Elliptic, parabolic, and hyperbolic PDE's. Numerical differentiation. Solution methods
for linear systems.
MATH 6520. Finite Element Solutions of Partial Differential Equations. Lec. 3. Cr. 3. Syllabus for MATH 6520
Prerequisite: C or better in MATH 4510 (5510) or consent of instructor. Mathematical
foundations of the finite element method. Approximate solutions of PDE's. Polynomial
interpolation. Variational techniques. Numerical integration. Solution methods for
linear systems. Isoparametric technique.
MATH 6530. Integral Equations and Applications. Lec. 3. Cr. 3. Syllabus for MATH 6530
Prerequisite: Consent of instructor. Volterra and Fredholm equations. Green's functions,
Hilbert-Schmidt and Fredholm theories. Neumann series, iterative methods.
MATH 6540. Calculus of Variations and Applications. Lec. 3. Cr. 3. Syllabus for MATH 6540
Prerequisite: Consent of instructor. Euler equation, constraints, Lagrange multipliers,
Ritz method, applications.
MATH 6610. Operational Mathematics. Lec. 3. Cr. 3. Syllabus for MATH 6610
Prerequisite: Consent of instructor. Integral transforms (Laplace, Fourier) inversion
and convolution theorems, applications.
MATH 6700. Graph Theory. Lec. 3. Cr. 3. Syllabus for MATH 6700
Prerequisite: C or better in Math 3400 or consent of instructor. Fundamental concepts
of undirected and directed graphs, trees, connectivity, traversability, colorability,
network flows, matchings and coverings, Ramsey theory, and graph minors.
MATH 6810. Partial Differential Equations. Lec. 3. Cr. 3. Syllabus for MATH 6810
Prerequisite: Consent of instructor. First and second order PDE's, wave, heat, and
Laplace's equations, applications to boundary and eigenvalue problems of mathematics,
physics, and engineering.
MATH 6900. Mathematics Seminar. Lec. 1. Cr. 0-1.
MATH 6910-20. Special Topics in Mathematics. Cr. 1-3.
Prerequisite: Consent of instructor. Individual study of advanced mathematical topics
in fields of interest under the supervision of a qualified staff member.
MATH 6990. Research and Thesis. Cr. 3,6.
MATH 6991. Research and Independent Study. Cr. 1-3. Syllabus for MATH 6991
Prerequisite: Consent of instructor. The purpose of this course is to foster research
and independent study at the graduate level in mathematics or statistics. Students
will independently study a chosen area of mathematics, explore open and significant
problems, draw conclusions, and, if applicable, participate in problem solving via
consulting. Students will be required to give presentations on their own investigations
and conclusions.