Courses Offered by the Mathematics Department
800:002. Elementary Algebra - 0 hrs. First and second degree equations,
operations with polynomials, exponents and radicals. Designed for students
who do not possess sufficient mathematics background to do college work.
Successful completion will satisfy the university's high school mathematics
requirement. Course meeting schedule will be the same as that of a three
credit-hour course.
800:023. Mathematics in Decision Making - 3 hrs. A survey of mathematical
ideas of particular use in analyzing information and in forming and analyzing
hypotheses. Topics include logical statements, probability, statistics,
graphs, interest and matrices.
800:030. Mathematics for Elementary Teachers - 3 hrs. Mathematics as problem
solving, communication, connections, and reasoning with regard to tasks
involving numeration, relationships, estimation, and number sense of whole and
rational numbers, measurement, and geometry and spatial sense. Activities and
models appropriate to elementary school mathematics are used to represent
these topics.
800:037. Technology for Elementary School Mathematics Teachers - 3 hrs.
Solving problems with calculators and computers; investigating LOGO. Using
computers, calculators, and other technology for teaching elementary school
mathematics. (Formerly 810:037.)
800:040. Intermediate Algebra - 4 hrs. Fundamental mathematical concepts;
functions and graphs; solutions of equations; elementary trigonometry; systems
of equations and inequalities; matrices and determinants. Applications.
800:043. Analysis for Business Students - 3 hrs. Analysis of rational
functions. Analysis and interpretation of graphs. Exponential and
logarithmic functions. Linear systems, linear programming, matrices and
determinants. Mathematical induction and conic sections. No credit for
students with credit in 800:046.
800:046. Elementary Analysis. - 4 hrs. Pre-calculus mathematics. Equations
and inequalities. Logarithms, exponential and circular functions. Analytic
trigonometry, analytic geometry, mathematical induction. Applications.
Repeats the credit in 800:043.
800:048. Condensed Calculus - 4 hrs. Survey of analytic geometry and
elementary calculus with emphasis on applications. May not be applied to
Mathematics major or minor. Prerequisite: 800:040 or equivalent.
800:050. Matrices with Applications - 3 hrs. Introduction to matrices,
systems of linear equations, vector spaces and linear mappings, rank and
inverses, determinants, characteristic values and characteristic vectors.
Prerequisite: 800:046. Students with credit in 800:076 should not enroll in
this course without consent of the head of the department.
800:060. Calculus I - 4 hrs. The derivatives and integrals of elementary
functions and their applications. Prerequisite: 800:046 or equivalent.
800:061. Calculus II - 4 hrs. Continuation of 800:060. Prerequisite: C- or
better in 800:060.
800:062. Calculus III - 4 hrs. Continuation of 800:061. Prerequisite: C- or
better in 800:061.
800:072. Introduction to Statistical Methods - 3 hrs. Descriptive statistics
including correlation and curve fitting. Intuitive treatment of probability
and inferential statistics including estimations and hypothesis testing.
Students with credit in 800:172 should not enroll in 800:072.
800:074. Discrete Mathematics - 3 hrs. Introduction to mathematical
reasoning, sets, relations and functions with applications in computer
science. Prerequisites: 800:050 or 800:060; 810:030 or equivalent.
800:076. Linear Algebra for Applications - 3 hrs. Gaussian elimination;
matrix algebra; vector spaces, kernels, and other subspaces; orthogonal
projection; eigenvalues and eigenvectors. Prerequisite: 800:060.
800:080. Mathematics of Finance - 3 hrs. A study of the mathematics of
financial transactions: simple and compound interest, annuities, amortization
of indebtedness, bonds, depreciation, life annuities and death insurance. Of
special interest to actuarial and business students. Prerequisite: a working
knowledge of algebra.
800:092. Introduction to Mathematical Modeling - 3 hrs. The components of
mathematical modeling. The formulation, interpretation and testing of models.
Prerequisite: four years of college preparatory mathematics, or 800:046.
800:111(g). Introduction to Analysis for Elementary Teachers - 3 hrs.
Investigating real number systems, relations, functions and their graphs,
systems of equations and inequalities, and their applications. Using physical
models and technology to explore and represent these topics. Prerequisites:
800:030; 800:037.
800:112(g). Introduction to Geometry and Measurement for Elementary Teachers
- 3 hrs. Van Hiele levels of thinking. Investigation of two- and three-
dimensional concepts, rigid transformations, symmetry, and spatial sense.
Prerequisites: 800:030; 800:037.
800:113(g). Topics in Mathematics for Grades K-8 - 3 hrs. Investigation of
ratio, proportion, percent; number theory; data analysis; patterns; and
connections to algebra and geometry. These mathematical topics will be
explored in the context of the K-8 mathematics curriculum. Prerequisites:
800:030; 800:037.
800:114(g). Problem Solving in mathematics for Elementary Teachers - 4 hrs.
Strategies for constructing and communicating a mathematics problem solving
process. Analysis of resources and strategies to generate mathematics tasks
and to create an effective problem solving environment. Problem solving as a
means of constructing mathematics knowledge. Prerequisites: 800:134; at least
one of 800:111, 800:112, 800:113.
800:134. Teaching Mathematics in the Elementary School - 3 hrs. Effective
instructional models and strategies for teaching elementary school
mathematics; will involve selecting and designing mathematical tasks, creating
an environment, and orchestrating discourse. Using and supplementing
mathematics materials within a sound psychological framework for making
instructional decisions. Prerequisite: 800:030.
800:136(g). Metric System and Measurement - 2 hrs. Basic ideas of measurement
(e.g., meaning, standard units, and errors). Experiments for experiences with
metric units for length, area, volume, mass and temperature. Simple
conversion techniques between and within systems. This course is available
only through correspondence. Prerequisite: junior standing or consent of
department.
800:137. Action Research for Elementary School Mathematics Teachers - 1 hr.
Planning, conducting assessments, providing instruction and evaluating
instructional effectiveness for selected mathematics topics in the elementary
curriculum. Prerequisite: 800:134 or 800:190.
800:140(g). Intermediate Mathematical Analysis I - 3 hrs. Algebraic and
topological structure of the reals. Limits and continuity. Theory of
differentiability of functions of a single real variable. Prerequisites:
80:062; 80:076.
800:141(g). Intermediate Mathematical Analysis II - 3 hrs. Riemann
integration. Sequences and series of functions. Introduction to Lebesgue
integration. Prerequisite: 80:140.
800:144(g). Elementary Number Theory - 3 hrs. Topics from prime numbers,
elementary theory of congruence, continued fractions. Diophantine equations.
Fibonacci numbers, Pell's equation, the golden rectangle. Pythagorean triples
and transfinite numbers. Prerequisite: 800:046 or 800:111; junior standing
or consent of department.
800:149(g). Differential Equations - 3 hrs. Elementary theory and
applications of first order differential equations. Introduction to numerical
techniques of solving differential equations. Solutions of nth order linear
differential equations with constant coefficients. Prerequisites: 80:062;
80:076; junior standing.
800:150(g). Partial Differential Equations - 3 hrs. A study of applied
partial differential equations using heat, wave and potential equations as
basis; Fourier series and integrals; Laplace transformations. Prerequisite:
80:149.
800:152(g). Introduction to Probability - 3 hrs. Axioms of probability,
sample spaces having equally likely outcomes, conditional probability and
independence, random variables, expectation, moment generating functions,
jointly distributed random variables, weak law of large numbers, central limit
theorem. Prerequisite: 80:061.
800:154(g). Introduction to Stochastic Processes - 3 hrs. Markov chains,
Poisson processes, continuous time Markov chains, renewal processes, Brownian
motion and stationary processes. Prerequisite: 80:152.
800:155(g). Differential Geometry - 3 hrs. The analytic study of curves and
surfaces in three-dimensional Euclidean space. Prerequisites: 80:062;
80:076.
800:156(g). Introduction to Complex Analysis - 3 hrs. Differentiation and
integration of functions of a single complex variable. Taylor and Laurent
expansions. Conformal mapping. Prerequisites: 80:062; junior standing.
800:157(g). Statistical Quality Control - 3 hrs. Exploratory data analysis,
Shewhart control charts and their variations, process capability analysis,
CUSUM charts, EWMA charts, sampling inspection by attributes and by variables,
continuous sampling plans, application of design of experiments in quality
engineering. Prerequisite: 80:152.
800:158(g). Topics in Actuarial Science - 3 hrs. Topics may include
mathematics of life contingencies, risk theory, survival analysis,
construction of actuarial tables, demography, graduation. May be repeated on
a different topic. Prerequisite: consent of instructor.
800:160(g). Modern Algebra I - 3 hrs. An introduction to the study of
algebraic systems. Includes: groups, rings, fields, homomorphisms and
isomorphisms. Prerequisites: 80:061; 80:076.
800:161(g). Linear Algebra I - 3 hrs. Vector spaces, linear transformations,
determinants, eigenvalues and eigenvectors, canonical forms, inner product
spaces. Prerequisite: 80:160.
800:162(g). Modern Algebra II - 3 hrs. A continuation of 80:160. Includes
groups with operators, modules over rings, Sylow theorems, composition series,
semi-simple and simple rings, field theory and introduction to Galois theory.
Prerequisite: 80:160.
800:165(g). Introduction to Modern Geometries - 3 hrs. Historical survey of
Euclidean geometry and an examination of its modern formulation. Introduction
to transformational geometry. Elements of hyperbolic non-Euclidean geometry
and its models in the Euclidean plane and space. Prerequisite: 80:060.
800:167(g). Topology I - 3 hrs. An introductory study of metric spaces,
completeness, topological spaces, continuous functions, compactness,
connectedness, separability, product and quotient spaces. Prerequisite:
80:140.
800:168(g). Topology II - 3 hrs. A continuation of 80:167. Two- and n-
dimensional manifolds, orientable manifolds, the fundamental group of a space,
free groups, covering spaces, application to geometry and knot theory.
Prerequisites: 80:160 and 80:167.
800:169(g). Mathematical Logic - 3 hrs. An introduction to the semantics and
syntax of the propositional and predicate calculus. Applications to
electrical networks and the analysis of formal mathematical theories.
Prerequisites: 80:060; junior standing.
800:172(g). Statistical Methods - 3 hrs. Descriptive statistics including
graphical representation, central tendency and variation, correlation and
regression. Elementary probability. Problems of estimation and hypothesis
testing from an intuitive approach. Use of statistical packages such as SAS
or SPSS. Students with credit in 800:072 or 800:174 may not enroll in
800:172. Prerequisite: junior standing or consent of department.
800:173. Probability and Statistics - 3 hrs. Descriptive statistics and
graphical representations; basic concepts of probability and distributions;
random variables; expectations; sampling theory; tests of statistical
significance. Calculus is employed in developing and applying these ideas.
Specific attention devoted to the use of technology in motivating and
explaining concepts and techniques. Emphasis on applications appropriate for
secondary school probability/statistics courses. Prerequisite: 80:061.
800:174(g). Introduction to Mathematical Statistics - 3 hrs. Sampling
distribution theory, point and interval estimation, Bayesian estimation,
statistical hypotheses including likelihood ratio tests and chi-square tests,
selected nonparametric methods. Prerequisites: 80:062; 80:152.
800:175(g). Regression Analysis - 3 hrs. Regression analysis, analysis of
variance, time series methods. Prerequisite: 80:174.
800:176(g). Numerical Analysis I - 3 hrs. Theory and application of standard
numerical techniques dealing with nonlinear equations, systems of linear
equations, interpolation and approximation, numerical differentiation and
integration. Prerequisites: 80:061; 80:076; 81:031, 81:032, or 81:033, or
equivalent.
800:177(g). Linear and Non-Linear Programming - 3 hrs. Linear, non-linear,
integer, and dynamic programming. Prerequisites: 800:061; 800:050 or
800:076; 810:031, 810:032, 810:034, or 810:035 or equivalent.
800:178(g). Numerical Analysis II - 3 hrs. Theory and application of
numerical techniques for solution of ordinary and partial differential
equations. Advanced topics from interpolation, approximation, numerical linear
algebra. Prerequisite: 80:176.
800:180(g). History of Mathematics: To the Calculus - 3 hrs. A survey of the
mathematical activities of mankind to the advent of the calculus in the 17th
century. The motives, influences, and methods affecting the development of
algebra, geometry, and number theory in Mesopotamian, Egyptian, Greek,
Islamic, and eastern civilizations. Prerequisite: junior standing or consent
of instructor.
800:181(g). Philosophy of Mathematics - 3 hrs. Consideration of views on
foundations of mathematics and such topics as the role and possible
limitations of mathematics in scientific investigation; the significance of
logical constructs in mathematics. Prerequisites: A Humanities course, plus
one semester of calculus and at least one additional mathematics course;
junior standing or consent of instructor.
800:182(g). Introduction to Set Theory - 3 hrs. An overview of Cantor's set
theory. Informal introduction to the axioms of set theory. General relations
and functions. Order relations. The axiom of choice, Zorn's lemma, and well-
ordering. Ordinal and cardinal numbers and their arithmetics. The Cantor-
Schroeder-Bernstein theorem. Prerequisite: 80:160 or 80:165 or 80:169.
800:184(g). Introduction to Automata Theory - 3 hrs. Finite automata and
their decision problems: perspectives from finite-state machines, neural
networks, and regular sets. Introduction to Turing machines, computability,
and the halting problem. Prerequisites: 80:061 and at least one 100-level
mathematics course.
800:185(g). History of Mathematics: From the Calculus to the 21st Century -
3 hrs. A survey of the mathematical activities of mankind from the development
of calculus in the 17th century. The rise of analysis, and the development of
modern algebra, non-Euclidean geometries, and the general axiomatic method in
the 19th century. Set theory, topology, mathematical logic, and other
integrating developments in 20th century mathematics. Prerequisites: 80:061;
junior standing or consent of instructor.
800:187(g). Formal Languages - 3 hrs. Natural languages and formal languages;
a brief comparison. Grammars and their generated languages. The Chomsky
hierarchy and corresponding automata theories. Operations on languages. Some
solvable and unsolvable problems. Prerequisites: 80:061 and at least one
100-level mathematics course.
800:188. The Teaching of Middle School/Junior High Mathematics - 3 hrs.
Teaching strategies for grades 5 to 8; roles of content and methods;
participation in a middle school/junior high teaching situation.
Prerequisites: 200:018; 200:040; 6 hours of 100-level courses in Mathematics.
800:189(g). Geometric Transformations - 3 hrs. Isometries and similarity
transformations in the Euclidean plane and Euclidean space. Preservation
properties of isometries. Existence and classification of isometries in the
Euclidean plane. Applications to concepts and problems in geometry, physics
and modern algebra, and to the analysis of congruence and similarity.
Prerequisites: 80:076 and 80:165.
800:190. The Teaching of Secondary Mathematics - 3 hrs. Teaching strategies
for grades 7-12; roles of content and methods; participation in a secondary
teaching situation. Prerequisites: 200:018; 200:040; 250:050; 800:160;
800:165; 800:188.
800:191(g). Contemporary Mathematics Curricula - 1-2 hrs. Study and
evaluation of innovative curriculum materials. The course will focus on early
elementary, middle grades, or high school curriculum. May be repeated for a
different curriculum level with the consent of the department. Prerequisite:
800:134 or 800:188 or 800:190.
800:192. Mathematics for Elementary Students with Special Needs - 1 hr.
Assessing, designing and providing appropriate mathematical tasks for students
with special needs. Prerequisite: 800:134 or 800:190.
800:193(g). Linear Algebra II - 3 hrs. Inner product spaces, Gram-Schmidt
orthonormalization, unitary operators and their matrices, bilinear forms,
Hermitian forms, normed linear vector spaces. Prerequisite: 800:161.
800:194. Senior Mathematics Seminar - 1 hr. Do research and write a paper
exploring a specific theme, topic, or problem in mathematics, culminating with
an oral presentation to the class. Prerequisite: senior standing.
800:195. Undergraduate Research in Mathematics - 3 hrs. Research on a
selected topic in mathematics with faculty supervision. Presentation of a
written paper at a departmental seminar. Prerequisite: completion of the
core of Plan A, B, or C with a minimum GPA of 3.00.
800:196(g). Applied Multivariate Statistical Analysis - 3 hrs. Multivariate
normal distribution, tests of significance with multivariate data,
discrimination and classification, clustering, principal components, canonical
correlations, use of statistical computer packages. Prerequisites: 80:076 and
80:174.
800:198. Independent Study.
800:201. Mathematical Analysis I - 3 hrs. The real numbers. Topology of
Cartesian spaces. Continuous functions. Differentiation in Cartesian spaces.
Prerequisite: 80:140.
800:202. Mathematical Analysis II - 3 hrs. Riemann-Stieltjes and Lebesgue
integrals. Integration in Cartesian spaces. Improper and infinite integrals.
Infinite series. Prerequisite: 80:201.
800:203. Complex Analysis I - 3 hrs. Analyticity. Differentiation and
integration of functions of one complex variable. Power series, Laurent
series. Calculus of residues. Prerequisites: 80:140; 80:156.
800:204. Complex Analysis II - 3 hrs. Analytic continuation. Harmonic
functions. Entire functions. Conformal mapping. Selected applications.
Prerequisite: 80:203.
800:210. Theory of Numbers - 3 hrs. A mathematical study of the integers:
induction, divisibility, prime numbers, congruences, quadratic reciprocity,
multiplicative functions.
800:211. Teaching Algebra in the Middle Grades - 2 hrs. Examine the
literature and students' thinking related to algebraic concepts. Curriculum
issues, teaching strategies and implications of technology. Prerequisite:
800:215 or consent of department.
800:213. Selected Topics in Mathematics for the Middle Grades - 2 hrs.
Investigation of a mathematical topic(s), such as geometry, data analysis,
probability, or number sense. The examination of a major mathematical idea
will include implications of research literature, and examination of relevant
curriculum materials. The course may be repeated once on a different topic
with consent of department. Prerequisite: consent of department.
800:214. Mathematical Problem Solving in the Middle Grades - 1 hr. Solving
problems from a variety of mathematical topics such as linear programming,
geometry, and probability. Analyzing problem solving techniques and teaching
strategies. Investigating issues related to implementing a problem solving
approach in the classroom.
800:215. Teaching Rational Numbers - 2 hrs. Examination of the literature,
problems and issues related to teaching fractions, decimals, ratios,
proportion, and percent in grades 4-8. Exploration of innovative strategies
for developing concepts, skills, and proportional reasoning. Implications of
research and reform recommendations for the curriculum.
800:220. New Developments in Middle Grades Mathematics - 3 hrs. Investigation
of current recommendations for goals, content, instructional strategies, and
curriculum of mathematics programs in grades 4-8. In-depth examination of
selected content and implementation of a problem-solving approach to
instruction. Focus on application to classroom practice and planning for
change for a selected topic.
800:221. Mathematics Literacy in an Information Age - 2 hrs. Examination of
applications and contributions of mathematics to other disciplines, the
workplace, personal lives, and society. Investigation of shifting conceptions
of mathematics and mathematics literacy in today's world. Diverse uses of
mathematics will be illustrated. Prerequisites: 800:220; 800:236; 800:238.
800:222. Issues and Problems in Teaching Mathematics in the Middle Grades - 2
hrs. Issues and problems related to current reform in mathematics, including
planning curriculum, assessing student learning, managing instruction, and
providing for individual needs. Examination of related literature.
Prerequisite: 800:220.
800:235. Problems in Teaching Elementary School Mathematics - 2 hrs. Course
content usually generated by participants. Typical topics are problems
dealing with: individualizing instruction, assessing growth, major concepts
and skills in the elementary mathematics program. Prerequisite: consent of
department.
800:236. Mathematics for Middle School Teachers I - 3 hrs. An integrated,
historical, cultural study of the development and structure of quantity, data,
and chance. Focus on mathematical ways of knowing and verification.
800:237. Technology in Middle Grades Mathematics - 2 hrs. Uses of technology
in teaching and learning mathematics. Examination of research related to
incorporating technology in the teaching of mathematics.
800:238. Mathematics for the Middle Grades Teacher II - 3 hrs. An integrated,
historical, cultural study of the development and structure of patterns,
functions, relationships and shapes. Focus on ways of knowing and
verification. Prerequisite: 800:236.
800:240. Theory of Rings and Modules - 3 hrs. Ring theory from factorization
in commutative rings, rings of quotients, localization, rings of polynomials
and formal power series, and elements of Galois theory. Module theory from
exact sequences, free modules, projective and injective modules, tensor
products, modules over principal ideal domains, and algebras. Prerequisite:
80:162.
800:245. Topics in Algebra - 3 hrs. Topics from groups, noncommutative rings
and algebras, introduction to homological algebra, introduction to Lie
algebras, and linear algebras. Prerequisite: 80:162 or consent of
instructor.
800:246. Topics in the History of Mathematics - 3 hrs. Topics from the
history of algebra, analysis, arithmetic, geometry, number theory,
probability, and topology as they appear in the development of Mesopotamian,
Greek, Islamic, Indian, Chinese and western civilizations. Prerequisite:
80:180 or 80:185.
800:263. Topics in Mathematical Logic and Set Theory - 3 hrs. Topics from:
the predicate calculus and first-order mathematical theories; the Gdel
completeness and incompleteness theorems; algebraic and many-valued logic;
Boolean algebras, lattices, representation theorems, and models in set theory
and mathematical logic; independence of the axioms of set theory (including
the axiom of choice and the continuum hypothesis). Prerequisite: 80:169 or
80:182.
800:265. Geometric Symmetry - 3 hrs. Symmetry groups in the Euclidean plane
and the geometric significance of normality. Finite and discrete symmetry
groups in the plane: the rosette, frieze, and wallpaper groups. Applications
to the analysis of Escher-type designs and the ornamental designs of the
Alhambra. Finite symmetry groups in Euclidean space. Prerequisite: 80:189.
800:266. Topics in Geometry - 3 hrs. Topics from: geometric convexity, non-
Euclidean geometries, the Banach-Tarski paradox, inversions and mappings of
the Euclidean sphere, geometric inequalities, the history of geometry,
differentiable manifolds. May be repeated on a different topic with the
consent of instructor. Prerequisite: consent of instructor.
800:273. Topics in Probability and Statistics - 3 hrs. Topics chosen from
correlation and regression analysis, analysis of variance and co-variance,
non-parametric methods, order statistics. Prerequisite: consent of
instructor.
800:289. Seminar: Mathematical Connections Laboratory - 3 hrs.
800:290. Problems and Issues in Teaching Junior High School Mathematics - 3
hrs. Course content decided by participants and instructor. Both mathematics
content and methodology of the junior high school considered. Prerequisite:
consent of department.
800:291. Problems and Issues in Teaching High School Mathematics - 3 hrs.
Course content decided by participants and instructor. Both mathematics
content and methodology of the senior high school considered. Prerequisite:
consent of department.
800:292. Teaching Students with Learning Problems in Mathematics - 2 hrs.
Identification, characteristics, and needs of students with learning problems
together with coordinated work with appropriate students. Prerequisite:
800:134 or 800:190.
800:293. The Secondary School Mathematics Curriculum - 3 hrs. Comparison of
current secondary curriculum with national standards, implementation,
assessment, and the role of technology.
800:295. Teaching Gifted and Talented Students in Mathematics - 2 hrs.
Identification, characteristics, and needs of gifted and talented students in
mathematics together with coordinated work with appropriate students.
Prerequisite: 800:134 or 800:190.
800:299. Research