Course
Descriptions
Mathematics
(MTH)
Course
Schedules
MTH 520 Optimization Theory
3(3-0)
The theory of and computer methods in classical and modern
optimization, using linear programming. Prerequisites:
knowledge of FORTRAN, MTH 223, MTH 233 or permission of
instructor.
MTH 521 Theory of Numbers
3(3-0)
Properties of integers, congruencies, greatest common divisors and prime
factorization, applications of number theory to computer science and
cryptology. Prerequisite: MTH 332 or permission of instructor.
MTH 523 Modern Algebra I
3(3-0) F, Sp
Groups, rings, integral domains, fields, and fundamental
homomorphism theorems. Prerequisite: MTH 332 or graduate
status.
MTH 525 Modern Algebra II
3(3-0)
Vector spaces, subspaces, bases and dimensions; linear
transformations, their algebra, their representation by
matrices, and linear functionals; eigenvalues, triangulable
and diagonalizable transformations; inner product spaces.
Prerequisite: MTH 523.
MTH 532 Advanced Calculus I
3(3-0) F
Rigorous development of calculus for functions of one
variable. Sequences, limits, continuity, differentiation,
integration, exponential and logarithmic functions, arc
length, series. Prerequisites: MTH 233 and MTH 332, or graduate
status.
MTH 533 Advanced Calculus II
3(3-0) Sp
Continuation of MTH 532. Rigorous development of calculus for
functions of several variables. Limits, continuity,
differentiation, and integration. Prerequisite: MTH 532.
MTH 539 Mathematical
Foundation of Actuarial Science 3(3-0) Sp
Develop a knowledge of fundamental mathematical tools for
quantitatively assessing risk. The application of these tools
to problems encountered in actuarial science is emphasized.
Does not count toward graduate degree. CR/NC only.
Prerequisites: FIN 257 and STA 584.
MTH 545 Introduction to
Point-Set Topology 3(3-0)
Development of elementary point-set topology. Sets, functions,
metric spaces, topological spaces, quotient surfaces,
compactness, and connectedness. Prerequisite: MTH 332 or
graduate status.
MTH 551 Number Systems for
Elementary Teachers 3(3-0)
Continuation of MTH 151. Integers, real numbers,
mathematical sentences, number theory, mathematical systems.
Credit will not apply toward master’s
degree in mathematics. Prerequisites: MTH 107, MTH 152.
MTH 554 Probability and
Statistics for Elementary and Middle School Teachers 3(3-0)
Examines experimental probability and statistics suitable for
elementary and middle school. Data gathering, organizing and
presenting. Credit will not apply toward Master’s degree in
mathematics. Prerequisites: MTH 107, MTH 551.
MTH 556 Microcomputers for
Elementary Mathematics Teachers 3(3-0)
Develops the use of microcomputers in elementary education
with particular emphasis on mathematical applications.
Computer literacy and BASIC Programming are included. Open
only to those students pursing a B S. in Education, Elementary
Emphasis. Prerequisite: MTH 107 and MTH 251 or equivalent.
MTH 565 Using Graphics
Calculators in Mathematics Education 1(1-0)
Course is designed for secondary mathematics education majors
and minors. Emphasis will be on the classroom use of graphics
calculators to teach mathematics. Prerequisites: MTH 132 with
MTH 223 as a corequisite.
MTH 566 Microcomputers for
Secondary Mathematics Teachers 3(3-0)
Examines microcomputer use in secondary education with
particular emphasis on mathematical applications. Open only to
those students pursuing a B.S. in Ed., Secondary Emphasis.
Prerequisite: MTH 223 or equivalent.
MTH 570 Mathematical Logic
3(3-0)
Logical connectives, truth tables, quantifiers, models,
logical truth. Incompleteness and undecidability of elementary
number theory. Prerequisite: MTH 332.
MTH 573 History of Mathematics
3(3-0) F, Sp
History of arithmetic, algebra, geometry, calculus.
Prerequisites: MTH 332 or MTH 341 or graduate status.
MTH 578 Combinatorics I 3(3-0)
Construction of mathematical models, combinatorics and graph
theory. Prerequisite: MTH 523.
MTH 586 Operations Research I
3(3-0)
Mathematical theory and applications of mathematical
programming. Linear programming duality, integer programming,
mixed integer programming, and dynamic programming.
Prerequisites: MTH 133/137, knowledge of FORTRAN.
MTH 587 Operations Research II
3(3-0)
Continuation of MTH 586. Theory and application of stochastic
models in operations research. Inventory models, queuing
theory, Markov chains, stochastic programming. Prerequisites: STA 382, MTH 586, or equivalent.
MTH 591 Seminar in the
Solution of Putnam Problems 1-3(Spec)
Problem-solving techniques demonstrated through solutions of
the Putnam Examination problems. Designed particularly for
those students interested in participating in the Putnam
Examination. Prerequisite: MTH 233 and permission of instructor.
MTH 594 Seminar in Higher
Mathematics 3(3-0)
Class presentation of results of independent study, and final
comprehensive
written report in an approved subject. Prerequisite: one year
of calculus and permission of instructor.
MTH 595 Special Topics in
Mathematics Education 1-6(Spec)
Subject matter not included in regular mathematics education
course. May be taken for credit more than once, total credit
not to exceed 6 hours. Does not count as one of two 400- or
500-level courses required on mathematics major. May not be
counted toward a major or minor in mathematics except for
students pursuing a B.S. in Ed. degree. Prerequisite:
permission of instructor.
MTH 596 Special Topics in
Mathematics 1-6(Spec)
Subject matter not included in regular course. May be taken
for credit more than once, total credit not to exceed 6
hours. Prerequisite: permission of instructor.
MTH 597 Independent Study
1-6(Spec) F, Sp
Open to students with permission of instructor. May be taken
for credit more than once, total credit not to exceed 6
hours.
MTH 619 Continuing
Registration for Final Research Project 1(1-0)
A
non-credit course intended for students who have completed all
program credits but still need to use university resources to
complete their degree requirements.
MTH
623
The Theory of Groups 3(3-0)
Introductory topics from classical theory of groups including
mappings on groups, structure theorems for groups.
Prerequisite: MTH 523 or permission of instructor.
MTH 625 Theory of Associative
Rings 3(3-0)
Theory of rings and ideals, including isomorphism theorems,
unique factorization domains, and fields. Prerequisites: any
two of MTH 523, MTH 525, and MTH 623, or permission of instructor.
MTH 632 Introduction to Real
Analysis and Its Applications 3(3-0)
Development of integration theory with introduction to
Lebesgue measure and integral on the real line. Elementary
theory of normed spaces, bounded linear operators and linear
functionals with applications. Prerequisite: MTH 532 or
permission of instructor.
MTH 633 Real Variables 3(3-0)
A study of functional analysis. Consideration of Banach
spaces, metric spaces, and compact spaces. General measure and
integration theory. Prerequisite: MTH 632 or permission of
instructor.
MTH 634 Fourier Analysis
3(3-0)
Study of Fourier Series, convergence, summability, Fourier
Transforms, distributions. Applications of fast Fourier
Transform to Heat and Wave Equation. Signal Processing,
Fourier Optics. Prerequisite: MTH 532.
MTH 636 Introduction to
Complex Variables 3(3-0)
Complex numbers, analytic functions, elementary functions,
Cauchy's theorem, Integral formula, Taylor and Laurent series,
residue theorem and its applications, Rouche's theorem.
Prerequisite: MTH 532.
MTH 637 Complex Variable
Theory 3(3-0)
Conformal mapping, Mobius transformations, harmonic functions,
Dirichlet problem, entire and meromorphic functions, analytic
continuation, Reimann surfaces, applications of complex
analysis. Prerequisite: MTH 636.
MTH 638 Theoretical Numerical
Analysis 3(3-0)
Numerical linear algebra with applications in linear and
nonlinear systems. Interpolation and approximation and their
applications to numerical differentiation, numerical
integration, and differential equations. Prerequisite: MTH
532, corequisite 533.
MTH 641 Topics in Geometry
3(3-0)
Advanced topics in geometry, foundations, non-Euclidean
geometry. Prerequisite: MTH 341.
MTH 645 Topology 3(3-0)
A continuation of MTH 545. Topics include fundamental groups,
product spaces, covering spaces, and homology. Prerequisite:
MTH 523, MTH 545.
MTH 651 Basic Ideas and
Procedures in Elementary School Arithmetic 3(3-0)
Mathematical concepts, fundamental processes, and mensuration
formulas. Prerequisite: successful completion of the
Elementary Teachers Proficiency Tests.
MTH 652 The Teaching of
Measurement 3(3-0)
The history, concepts, and learning of measurement systems.
The metric system and laboratory activities are emphasized.
Prerequisite: teaching experience or permission of instructor.
MTH 656 Teaching &
Learning Mathematics with Technology 3(3-0)
Use of instructional technology for teaching and learning
mathematics and an introduction to related research literature
in mathematics and mathematics education. Prerequisites: MTH
566; or permission of instructor.
MTH 658 Workshop in Teaching
Mathematics 1-6(Spec)
Preparing materials and investigating methods for teaching
mathematics in grades K-12. May be repeated, total credit not
to exceed 6 hours. Prerequisite: permission of the instructor.
MTH 660 Laboratory:
Construction and Use of Teaching Aids in Mathematics 2(1-2)
Multisensory aids produced and demonstrated. Devices and
models constructed.
MTH 661 The Teaching of Middle
School Mathematics 3(3-0)
Objectives of mathematics instruction in the middle school.
Prerequisite: minor in mathematics or teaching experience in
middle or senior high school mathematics.
MTH 666 Seminar: Problems in the
Teaching and Supervision of Secondary Mathematics 3(3-0)
Current practices and significant research in secondary school
mathematics.
MTH 671 Introduction to the
Axiomatic Method 3(3-0)
Study of the foundations of mathematics. Axiomatic set theory,
ordinal and cardinal arithmetic. The axiom of choice and
continuum hypothesis. Prerequisites: MTH 521, MTH 523, or MTH 532, or
permission of instructor.
MTH 673 History of Advanced
Mathematics 3(3-0)
History of the development of modern mathematics from 1700
into the 20th century. Prerequisites: MTH 525 and MTH 532.
MTH 678 Combinatorics II
3(3-0)
Finite geometries, combinatorial designs, strongly regular
graphs, and error correcting codes. Prerequisites: MTH 578 and
corequisite MTH 525.
MTH 692 Graduate Seminar in
Mathematics Education 1-4(Spec)
Seminars will focus on current issues in mathematics
education. May be taken for credit more than once, total
credit not to exceed four hours. 3 credits needed before
it counts as elective on any graduate degree in mathematics.
Prerequisites: admission to graduate program in mathematics,
or permission of instructor.
MTH 693 Graduate Seminar in
Mathematics and Its Applications 1-4(Spec) F, Sp
One hour seminars in subfields of mathematics and its
applications; 3 credits needed before it counts as
elective on graduate degrees in mathematics. Prerequisites: graduate standing in mathematics and permission of instructor.
MTH 694 Practicum in
Mathematics 3(3-0)
To be taken during the last semester in the M.A. program.
Experience in mathematics applications is gained by engaging
in supervised consulting work in industry whenever possible.
Prerequisites: MTH 623 and permission of instructor.
MTH 695 Special Topics in
Mathematics Education 1-6(Spec)
Consideration of subject matter not included in regular
course. May be taken for credit more than once, total credit
not to exceed 6 hours. Prerequisite: permission of instructor.
MTH 696 Special Topics in
Mathematics 1-6(Spec)
Consideration of subject matter not included in regular
course. May be taken for credit more than once, total credit
not to exceed 6 hours. Prerequisite: permission of instructor.
MTH 697 Independent Study
1-9(Spec) F, Sp
Open to graduate students in mathematics with permission of
instructor. May be taken for credit more than once, total
credit not to exceed 9 hours.
MTH 698 Plan B Project
1-2(Spec)
Plan B paper is normally an expository paper or research
project on an area or problem related to but in addition to
material covered in a course, written under the direction of
graduate faculty. Each Plan B project is 1 credit hour. May
be taken for credit more than once. Total credit not to exceed
2 hours. CR/NC only. Prerequisites: permission of advisor.
MTH 725 Topics in Algebra
3(3-0)
Advanced topics in abstract algebra. Designed to add breadth
to the student's abstract algebra background and to open
possible research areas. Prerequisites: MTH 625.
MTH 732 Functional Analysis
3(3-0)
Fundamentals of topological vector spaces, normed spaces,
Banach and Hilbert spaces, functional on such spaces,
operators on Banach and Hilbert spaces, spectral theorems,
Banach algebras. Prerequisites: MTH 632 and MTH 636.
MTH 734 Partial Differential
Equations and Applications 3(3-0)
Solutions of partial differential equations by analytic and
numerical techniques using standard methods, including Fourier
series and Laplace transforms, perturbation, finite elements
and finite differences. Prerequisites: MTH 334 and MTH 636.
MTH 761 Methods for Teaching
College Mathematics 3(3-0)
Methods in teaching undergraduate mathematics education
including use of technology, cooperative learning, inquiry,
and guided discovery. Students will create activities and
debate issues surrounding undergraduate instruction.
Prerequisites: completion of 30 hours of coursework required
for the Doctoral program and at least one semester of teaching
experience at the post secondary level (this may include a
teaching assistantship).
MTH 762 Research in Collegiate
Mathematics Education 3(3-0)
Introduction to the research literature in collegiate
mathematics education including learning theories for
mathematics, literature search strategies, issues in
mathematics education, and writing about and debating such
issues. Prerequisites: completion of 30 hours of coursework
required for the Doctoral program and at least one semester of
teaching experience at the post secondary level (this may
include a teaching assistantship); MTH 761.
MTH 764 Qualitative Research
Methods in Mathematics Education 3(3-0)
Introduction to the qualitative research in mathematics
education including research design, development of protocols,
fieldwork, collecting and analyzing data and techniques for
interviewing. Prerequisites: MTH 762; or permission of
instructor.
MTH 766 Internship: College
Teaching 3-6(Spec)
Teaching of undergraduate mathematics or statistics courses
200 level or above. Students will conduct their teaching
internship under the supervision of a graduate faculty member.
CR/NC only. Prerequisites: MTH 761; successful completion of
all qualifying examinations.
MTH 767 Seminar in Collegiate
Mathematics Education I 3(3-0)
Use of a review of literature to focus research questions and
to develop a research proposal. Each student develops a
proposal for his/her dissertation research. This course
requires a concurrent enrollment in MTH 692. Prerequisites:
MTH 764; EDU 660
MTH 768 Seminar in Collegiate
Mathematics Education II 3(3-0)
Design and execution of a pilot study of student’s proposed
dissertation research. This course requires a concurrent
enrollment in MTH 692. Prerequisites: MTH 767
MTH 778 Topics in
Combinatorics 3(3-0)
Advanced topics in combinatorics. Designed to add breadth to
the student's combinatorial background and to open possible
research areas. Prerequisites: MTH 678
.
MTH 796 Special Topics in
Mathematics 1-6(Spec)
Consideration of subject matter not included in regular
courses. May be taken for credit more than once; total credit
not to exceed 6 hours. Prerequisites: completion of 30 hours
of coursework required for the Doctoral program.
MTH 797 Independent Study
1-9(Spec) F, Sp
Open to doctoral students in mathematics who have completed 30
hours of coursework required toward the Doctoral program, with
permission of the instructor. May be taken for credit more
than once; total credit not to exceed 9 hours.
MTH 798 Thesis 1-6(Spec)
CR/NC only.
MTH 898 Dissertation
1-30(Spec)
Doctoral Dissertation Research. CR/NC only. Prerequisites:
permission of
Department.
Unspecified content or variable credit courses. See
additional information on page 43 of this Bulletin regarding
these types of courses. The following courses offered through
the department are of unspecified content or variable credit:
MTH 591, 594, 595, 596, 597, 651, 658, 692, 693, 695, 696,
697, 698, 796, 797.
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