Course Descriptions
Mth 070Elementary Algebra (4 credits)
This is a basic course covering first-year high school algebra. Credit for enrollment (eligibility) but not toward graduation; satisfies no University or general education requirements. Expected preparation: Passing at the necessary level on the mathematics placement test.
Mth 095
Intermediate Algebra (4 credits)
Topics include problem solving, linear equations,
systems of equations, polynomials and factoring
techniques, rational expressions, radicals and exponents,
quadratic equations. Credit for enrollment
(eligibility) but not toward graduation; satisfies no
University or general education requirements.
Prerequisites: Completion of Mth 70 with a grade
of C- or above within the last year, or passing at the
necessary level on the mathematics placement test
within the last year.
Mth 105
Excursions in Mathematics (4 credits)
Exploration of a variety of modern mathematical
topics. Topics may include the mathematics of
voting systems, graphs and networks, symmetry in
art and nature, population growth, fractals, probability.
Intended for students without a strong algebra/
calculus background, but with a desire to
explore some interesting mathematics.
Prerequisites: Completion of Mth 95 with a grade
of C- or above within the last year, or passing at
the necessary level on the mathematics placement
test within the last year.
Mth 111, 112
Introductory College Mathematics I, II (4, 4 credits)
An integrated treatment of topics from algebra
and trigonometry. These courses serve as additional
preparation for students with insufficient background
who desire to take Mth 251, 252, 253.
Neither Mth 111 nor 112 can be taken for credit
if a grade of C-, P, or above has already been
received for a course which requires either of them
as a prerequisite. Courses must be taken in
sequence. Prerequisites for Mth 111: Completion
of Mth 95 with a grade of C- or above within the
last year, or passing at the necessary level on the
mathematics placement test within the last year
(see Math Department webpage at mth.pdx.edu
for information). Prerequisites for Mth 112:
Completion of Mth 111 with a grade of C- or
above within the last year, or passing at the necessary
level on the mathematics placement test
within the last year.
Mth 191, 192, 193
Mathematics Tutoring (3, 3, 3 credits)
Training in one-to-one and small-group tutoring
over a wide range of mathematical topics. Mth 191:
tutoring in arithmetic and other non-university
courses. Mth 192: tutoring in freshman-level mathematics.
Mth 193: tutoring in sophomore- junior and
senior-level mathematics. Required field work
consists of providing tutoring service in the community
or University. Recommended prerequisite: consent
of instructor.
Mth 199
Special Studies (Credit to be arranged.)
Mth 211, 212, 213
Foundations Of Elementary Mathematics I, II, III (4, 4, 4 credits)
A constructivist approach to fundamental ideas of
mathematics. Courses must be taken in sequence.
Prerequisites for Mth 211: Completion of Mth 95
with a grade of C- or above within the last year,
or passing at the necessary level on the mathematics
placement test within the last year.
Prerequisites for Mth 212, 213: Mth 211.
Mth 241
Calculus for Management and Social Sciences (4)
**This course is no longer offered.**
Mth 251, 252, 253
Calculus I, II, III (4, 4, 4 credits)
Differential and integral calculus of functions of a
single variable, analytic geometry, infinite series,
and applications. Courses must be taken in
sequence. Prerequisites for Mth 251: Completion
of Mth 112 with a grade of C- or above within
the last year, or passing at the necessary level on
the mathematics placement test within the last
year.
Mth 254
Calculus IV (4 credits)
An introduction to differential and integral calculus
of functions of several variables and applications.
Prerequisites: Mth 252, 261.
Mth 256
Applied Differential Equations I (4 credits)
Solution techniques in ordinary differential equations;
applications. Prerequisites: Mth 252, 261.
Mth 261
Introduction to Linear Algebra (4 credits)
Introduction to rudimentary set theory, the algebra
of sets, systems of linear equations, linear transformations,
matrix algebra, vector spaces, and determinants.
Prerequisites: Completion of Mth 112 with a
grade of C- or above within the last year, or passing
at the necessary level on the mathematics placement
test within the last year.
Mth 271
Mathematical Computing (4 credits)
Machine representation of the real number field
and its consequences. Elements of error analysis.
Introduction to the design, analysis, and stability
of algorithms. Well/ill-conditioned problems.
Programming, graphics, numeric and symbolic
computations in MATLAB (a high level programming
environment). Examples and applications in
mathematics, science, and engineering.
Prerequisite: Mth 253, 261.
Mth 299
Math Excel (1 credit)
MTH 299
Math Excel (1) -- Fall-Winter-Spring Terms only
Math Excel is an open-ended problem solving course. This course is
offered to give students additional techniques and skills in problem
solving, and is focused on the types of problems that come up in the
first two terms of the calculus sequence. This course is intended to
be a supplement to the MTH 251, MTH 252 courses, and is not a
substitute for any prerequisites. This course cannot be used to
fulfill University mathematics requirements for graduation.
Prerequisite: Concurrent enrollment in MTH 251 or MTH 252.
Mth 299
Head Start Calculus (3 credits) -- Summer Session Only
Head Start Calculus is a focused workshop providing an integrated
treatment of topics from algebra and trigonometry that serves as
additional preparation for students who will be taking the calculus
course sequence (beginning with MTH 251). This workshop-style course
is offered to help refresh students' knowledge of previously learned
material, and may not be used as a replacement for MTH 111 and/or MTH
112, nor can it be used to fulfill University mathematics requirements
for graduation. Prerequisite: MTH 111 and MTH 112; or a full year of
high school pre-calculus or equivalent.
Mth 301, 302, 303
Elements of Modern Mathematics I, II, III (4, 4, 4)
**This sequence is no longer offered**
Mth 311
Advanced Calculus (4 credits)
Properties of the real numbers, introduction to
metric spaces, Euclidean spaces, functions of a real
variable, limits, continuity, the extreme and intermediate
value theorems, sequences. Prerequisite:
Mth 253, 261.
Mth 312, 313
Advanced Multivariate Calculus (4, 4 credits)
Differential and integral calculus of functions of
several variables, the inverse and implicit function
theorems, infinite and power series, differential
forms, line and surface integrals, Green's, Stokes', and Gauss' theorems. Courses must be taken in
sequence. Prerequisite: Mth 254 and Mth 311.
Mth 322
Applied Partial Differential Equations (4 credits)
Introduction to equations of mathematical physics,
in particular, linear and nonlinear advection equation,
wave equation, initial and boundary value
problems, method of characteristics, separation of
variables. Prerequisites: Mth 256.
Mth 324
Vector Analysis (4 credits)
Modern vector methods with applications for students
of mathematics, physics, and engineering.
Prerequisite: Mth 254.
Mth 338
Modern College Geometry (4 credits)
Topics in Euclidean and non-Euclidean geometry.
Prerequisites: Mth 252, 261 .
Mth 343
Applied Linear Algebra (4 credits)
Topics in matrix algebra, determinants, systems of
linear equations, eigenvalues, eigenvectors, and linear
transformations. Selected applications from science,
engineering, computer science, and business.
Prerequisites: Mth 252, 261.
Mth 344
Introduction to Group Theory and Applications (4 credits)
Groups, homomorphisms, factor groups. Selected
applications from geometry, combinatorics, computer
science, chemistry. Prerequisites: Mth 252,
261.
Mth 345
Introduction to Ring and Field Theory (4 credits)
Topics in rings, integral domains, fields, ordered
fields, polynomial rings. The development of the
real number system. Prerequisite: Mth 344.
Mth 346
Number Theory (4 credits)
A presentation of the properties of numbers as
found in the theory of divisibility, congruence,
diophantine equations, continued fractions, and
algebraic numbers. Prerequisites: Mth 252, 261.
Mth 356
Discrete Mathematics (4 credits)
Topics in discrete mathematics, including propositional
logic, sets, relations, inverse functions, divisibility,
induction, recurrences, inclusion-exclusion,
permutations, combinations, graphs, graph coloring,
and applications. Prerequisite: Mth 253.
Recommended: Mth 261.
Mth 399
Introduction to Mathematical Reasoning (4 credits) -- Summer Session Only
The course covers fundamental abstract concepts common to all branches of mathematics. Special emphasis is placed on ability to understand and construct rigorous proofs. This course is specifically intended to help mathematics majors and minors prepare for Mth 344 and Mth 311. Prerequisites: Mth 253 and Mth 261.
Mth 399
SPST: STATS & FINANCIAL MATH (4 credits) -- Summer Session Only
The objectives of the course are to understand and implement
the basic concepts of Statistics and Financial Mathematics into real life
problems.
Prerequisites: Stat 243 or equivalent
Mth 401/501
Research (Credit to be arranged.)
Consent of instructor.
Mth 404/504
Cooperative Education/Internship (Credit to be arranged.)
Mth 405/505
Reading and Conference (Credit to be arranged.)
Consent of instructor.
Mth 407/507
Seminar (Credit to be arranged.)
Consent of instructor.
Mth 410/510
Selected Topics (Credit to be arranged.)
Consent of instructor.
Mth 411/511, 412/512, 413/513
Introduction to Real Analysis I, II, III (3, 3, 3 credits)
Sequences and series of functions; Lebesgue measure
and integration; the Stone-Weierstrass and
Baire category theorems; Fourier Series; elements
of functional analysis. Courses must be taken in
sequence. Prerequisite: Mth 312.
Mth 420/520
Introduction to Complexity Theory (3)
**This course is no longer offered**
Mth 421/521, 422/522, 423/523
Theory of Ordinary Differential Equations I, II, III (3, 3, 3 credits)
Vector fields and phase flows in the plane.
Geometric and algebraic properties of linear systems.
Existence, uniqueness, and continuity theorems
for systems. Additional topics. Courses must
be taken in sequence. Prerequisite: Mth 312.
Mth 424/524, 425/525
Elementary Differential Geometry and Tensor Analysis I, II (3, 3 credits)
Differential geometry of curves and surfaces; elementary
Riemannian geometry; tensors and their
algebra; elements of tensor analysis; applications
from mechanics and field theory. Courses must be
taken in sequence. Prerequisite: Either Mth 256
or 421.
Mth 427/527, 428/528
Partial Differential Equations I, II (3, 3 credits)
Solution techniques, qualitative analysis and
applications: separation of variables, eigenfunction
expansion, Sturm-Liouville problems, Green's
functions, Fourier transform solutions, finite difference
and finite element methods. Courses must
be taken in sequence. Prerequisites: Mth 256,
Mth 253/254. Prior knowledge of PDEs (Mth
322) is recommended, but not required.
Mth 430/530
Topics in Mathematical Modeling (3 credits)
Basic introduction to mathematical model building
starting with prototype, model purpose definition,
and model validation. Models will be chosen
from life, the physical and social sciences.
Applications chosen from differential equations,
linear programming, group theory, probability or
other fields. Prerequisites: Consent of instructor
and either Mth 256 or 421/521. With approval,
this course may be repeated for credit.
Mth 431/531, 432/532, 433/533
Topics in Geometry I, II, III (3, 3, 3 credits)
Topics selected from projective geometry, non-
Euclidean geometry, algebraic geometry, convexity,
differential geometry, foundations of geometry,
combinatorial topology. With departmental
approval, this sequence may be repeated for credit.
Prerequisite: Mth 311, 338, or 344.
Mth 434/534, 435/535, 436/536
Set Theory and Topology I, II, III (3, 3, 3 credits)
Cardinal and ordinal numbers. The axiom of
choice and equivalent formulations. Introduction
to general topology with the notions of interior,
closure, topological space, continuity, and homeomorphism.
Construction techniques and properties
of point-set topology, especially connectedness,
compactness, and separation. Additional
topics. Courses must be taken in sequence.
Prerequisite: Mth 311.
Mth 440/540
Boolean Algebra (4)
**This course is no longer offered**
Mth 441/541, 442/542, 443/543
Introduction to Abstract Algebra I, II, III (3, 3, 3 credits)
Groups and rings with homomorphism theorems,
vector spaces, modules, algebraic theory of fields
and Galois theory, lattices, algebras. Prerequisite:
Mth 344. Courses must be taken in sequence.
Mth 444/544, 445/545
Advanced Linear/Multilinear Algebra I, II (3, 3 credits)
A second course in linear algebra. Products, quotients,
and duals of vector spaces. Multilinear
maps, tensor products, exterior algebra. Minimal
and characteristic polynomials, canonical forms.
Finite dimensional spectral theory. With departmental
approval, this sequence may be repeated
for credit. Courses must be taken in sequence.
Prerequisite: Mth 344.
Mth 449/549
Topics in Advanced Number Theory (3 credits)
A study of advanced topics selected from the areas
of algebraic or analytic theory. With departmental
approval, this course may be repeated for credit.
Prerequisite: Mth 346.
Mth 451/551, 452/552, 453/553
Numerical Calculus I, II, III (3, 3, 3 credits)
Computer arithmetic. Solution of nonlinear equations.
Interpolation. Numerical integration and
differentiation. Solution of linear equation systems.
Eigenvalue problem, least square, chebyshev,
trigonometric and rational function approximation.
Numerical solution of differential equations.
Prerequisites: knowledge of FORTRAN or
PASCAL, Mth 253, 261 for Mth 451/551, Mth 451/551 for Mth 452/552, Mth 322 for Mth 453/553.
Mth 456/556
Topics in Combinatorics (3 credits)
Course Description: Selected topics from: permutations, combinations, partitions, generating functions, inclusion/exclusion, recursion, Polya counting, block designs, orthogonal polynomials, and error-correcting codes. With departmental approval may be repeated for credit.
Prerequisite: MTH 356 or CS 251.
Mth 457/557, 458/558
The Mathematical Theory of Games (3,3 credits)
Introduction to mathematical game theory and
game theoretic analysis. Topics include: combinatorial
and strategic games, Perfect Competition,
Zermelo's Algorithm, Payoffs, cooperative and
non-cooperative games, bargaining, mixed strategies,
Nash Equilibrium, repeated games and finite
automata, common knowledge and incomplete
information, the prisoner's dilemma. Selected
applications to economics, biology, computer science,
and political science. Prerequisite: Mth 261
or Stat 243.
Mth 461/561, 462/562
Graph Theory I, II (3, 3 credits)
Topics in graph theory, including connectivity,
matchings, graph algorithms, network flows,
graph matrices, isomorphisms, Eulerian and
Hamiltonian graphs, spanning trees, decompositions,
shortest paths, the matrix-tree theorem, colorings
of graphs, planarity and embeddings,
Kuratowski's theorem, matroids, and selected
applications. Courses must be taken in sequence.
Prerequisites: Mth 261, 356.
Mth 470/570, 471/571, 472/572
Complex Analysis and Boundary Value Problems I, II, III (3, 3, 3 credits)
Fundamental concepts of complex variables, partial
differential equations and boundary value
problems using Fourier series. Prerequisites: Mth
254 and either 256 or 421.
Mth 477/577, 478/578
Mathematical Control Theory I, II (3, 3 credits)
Mathematical foundations of linear time invariant
control systems. Controllability, observability, stabilizability,
feedback. Elements of the calculus of
variations and optimal control. Dynamic programming.
Pontryagin maximum principle.
Applications. Prerequisites: Mth 256.
Expected preparation: Mth 253, 254.
Mth 480/580
Systems Analysis: Calculus of Variations (3 credits)
Basic problems of the calculus of variations. Euler
equations. Lagrange conditions. Lagrange multipliers.
Lagrange equations. Hamilton's equations.
Application to mechanical and electrical systems.
Prerequisite: Mth 256 or 422/522.
Mth 481/581
Topics in Probability for Mathematics Teachers (3, 2-3 credits)
Introduction to probability as a modeling technique
in mathematics and methods of teaching probability.
Use of probability in decision making and inference.
Simulation of experiments. Methods of enumeration.
Laws of probability. Special probability
distributions. Computer-assisted analysis. With
departmental approval may be repeated for credit.
Prerequisite: at least two upper-division courses
approved for math major credit. Enrollment is
limited to pre-service and in-service mathematics
teachers or permission of instructor.
Mth 482/582
Topics in Statistics for Mathematics Teachers (3, 2-3 credits)
Introduction to methods of statistical analysis and
methods for teaching statistics. Descriptive statistics,
organization of data, sampling techniques, sampling
distributions, methods of statistical inference, estimation,
hypothesis testing, regression, and correlation.
Computer-assisted analysis. With departmental
approval may be repeated for credit. Prerequisite:
at least two upper-division courses approved for math major credit. Enrollment is limited to preservice
and in-service mathematics teachers or permission
of instructor.
Mth 483/583
Topics in Geometry for Mathematics Teachers (3, 2-3 credits)
Selected topics in geometry for mathematics teachers.
With departmental approval may be repeated
for credit. Prerequisite: at least two upper-division
courses approved for major credit.
Mth 484/584
Topics in Algebra for Mathematics Teachers (3, 2-3 credits)
Selected topics in algebra for mathematics teachers.
With departmental approval may be repeated
for credit. Prerequisite: at least two upper-division
courses approved for major credit.
Mth 485/585
Topics in Analysis for Mathematics Teachers (3, 2-3 credits)
Selected topics in analysis for mathematics teachers.
With departmental approval may be repeated for
credit. Prerequisite: at least two upper-division
courses approved for major credit.
Mth 486/586
Topics in The History of Mathematics (3, 2-3 credits)
Selected topics in the historical development of
mathematics. With departmental approval, this
course may be repeated for credit. Prerequisite: at
least two upper-division courses approved for
major credit.
Mth 487/587
*Topics in Combinatorial Analysis (3, 2-3 credits) (*Please note the title of this course is in the process of being changed to "Discrete Mathematics for Teachers".)
"Discrete Mathematics for Teachers" will focus on preparing math teachers for teaching Discrete Mathematics at the high school level. Prerequisite: at least two upper-division
courses approved for major credit. (A new Combinatorics course is in the process of being created to replace the former "Topics in Combinatorial Analysis".)
Mth 488/588
Topics in Technology for Mathematics Teachers (3, 1-3 credits)
Hands-on experience in the study of the role of
computer software and calculators in the teaching
and learning of mathematics. With departmental
approval may be repeated for credit. Prerequisite:
at least two upper-division courses approved for
major credit.
Mth 490/590
Computing in Mathematics for Middle School Teachers (3 credits)
A study of the role of computing in mathematics
with emphasis on the use of modern technology.
Not approved for major credit. Available for graduate
credit toward the graduate certificate program
in middle school mathematics. Prerequisites:
Mth 112, 212, 213.
Mth 491/591
Experimental Probability and Statistics for Middle School Teachers (3 credits)
A study of probability and statistics through laboratory
experiments, simulations, and applications.
Not approved for major credit. Available for graduate
credit toward the graduate certificate program
in middle school mathematics. Prerequisites:
Mth 112, 212, 213.
Mth 492/592
Problem Solving for Middle School Teachers (3 credits)
Examination and application of problem-solving
techniques and strategies. Problems are drawn
from various areas of mathematics. Not approved
for major credit. Available for graduate credit
toward the graduate certificate program in middle
school mathematics. Prerequisites:
Mth 112, 212, 213.
Mth 493/593
Geometry for Middle School Teachers (3 credits)
Selected topics from informal geometry, both twoand
three-dimensional. Not approved for major
credit. Available for graduate credit toward the
graduate certificate program in middle school
mathematics. Prerequisites:
Mth 112, 212, 213.
Mth 494/594
Arithmetic and Algebraic Structures for Middle School Teachers (3 credits)
The study of the real number system and its subsystems
will lead to the introduction of more general
algebraic structures and their applications.
Not approved for major credit. Available for graduate
credit toward the graduate certificate program
in middle school mathematics. Prerequisites:
Mth 112, 212, 213.
Mth 495/595
Historical Topics in Mathematics for Middle School Teachers (3 credits)
A survey of the historical development of topics in
mathematics from ancient to modern times, with
special emphasis on topics in arithmetic, algebra
and informal geometry. Not approved for major
credit. Available for graduate credit toward the
graduate certificate program in middle school
mathematics. Prerequisites: Mth 493/593,
494/594.
Mth 496/596
Concepts of Calculus for Middle School Teachers (3 credits)
An introduction to the limit concept and its role
in defining the derivative, the integral and infinite
series. Applications to middle school mathematics.
Not approved for major credit. Available
for graduate credit toward the graduate certificate
program in middle school mathematics.
Prerequisites:
Mth 112, 212, 213.
Mth 503
Thesis (Credit to be arranged.)
Mth 601
Research (Credit to be arranged.)
Mth 603
Thesis (Credit to be arranged.)
Mth 604
Cooperative Education/Internship (Credit to be arranged.)
Mth 605
Reading and Conference (Credit to be arranged.)
Mth 607
Seminar (Credit to be arranged.)
Mth 610
Selected Topics (Credit to be arranged.)
Mth 611, 612, 613
Theory of Functions of a Real Variable I, II, III (3, 3, 3 credits)
**This sequence is no longer offered**
Mth 614, 615, 616
Modern Analysis I, II, III (3, 3, 3 credits)
Topics from nonlinear analysis, harmonic analysis,
analytic functions, ordered vector spaces, analysis
on Lie groups, and operator theory.
Recommended prerequisite: Mth 412/512.
Mth 617, 618, 619
Functional Analysis I, II, III (3, 3, 3 credits)
Hilbert and Banach spaces, the Hahn-Banach,
open mapping, and closed graph theorems.
Compact, self-adjoint, normal, and Fredholm
operators. Locally convex spaces, weak topologies,
duality. Banach- and C* -algebras, spectral theory.
Courses must be taken in sequence.
Recommended prerequisite: Mth 412/512.
Mth 621, 622, 623
Advanced Differential Equations I, II, III (3, 3, 3 credits)
Advanced theory of dynamial systems and partial
differential equations including the basics of partial
differential equations, boundary value problems for
elliptic equations, the Cauchy problem, and parabolic
equations. Topics selected from Hamiltonian
systems, waves and shocks, variational methods,
control theory. Recommended prerequisite: Mth
423/523 or 472/572.
Mth 624, 625, 626
Advanced Differential Geometry I, II, III (3, 3, 3 credits)
Topics selected from differentiable manifolds, differential
forms, DeRham cohomology, Lie groups,
fibre bundles, the Riemannian metric, affine and
Riemannian connections, parallel translations,
holonomy, geodesics, curvature, isometric embeddings
and hypersurfaces, the Second Fundamental
Form, complete Riemannian manifolds and the
Hopf-Rinow theorem, spaces of constant curvature,
variations of arc length, and the Morse Index
theorem. Recommended prerequisite: Mth
425/525.
Mth 634, 635, 636
Algebraic Topology I, II, III (3, 3, 3 credits)
Topics from singular and simplicial homology and
cohomology theories, fundamental group and
covering spaces, CW complexes and elements of
homotopy theory, algebraic theory of manifolds,
introduction to differential topology and vector
bundles, applications. Courses must be taken in
sequence. Recommended prerequisites: Mth
435/535 and 444/544.
Mth 637, 638, 639
Geometric Topology I, II, III (3, 3, 3 credits)
Topics from geometric and piecewise linear topology,
knots and 3-manifolds and gauge theories,
geometric structures and geometrization of manifolds,
applications to differential topology, vector
bundles and to mathematical physics.
Recommended prerequisite: Mth 436/536.
Mth 641, 642, 643
Modern Algebra I, II, III (3, 3, 3 credits)
Topics from groups, semigroups, rings, fields,
algebras, and homological algebra. Recommended
prerequisite: Mth 443/543 or both 442/542 and
445/545.
Mth 651, 652, 653
Advanced Numerical Analysis I, II, III (3, 3, 3 credits)
An advanced study of numerical methods with
emphasis on theory, economy of computation, and
the solution of pathological problems. Topics will
typically be chosen from: evaluation of functions,
roots of equations, quadrature, ordinary and partial
differential equations, integral equations, eigenvalues,
construction of approximating functions,
orthonomalizing codes, and treatment of singularities.
Courses must be taken in sequence.
Recommended prerequisite: Mth 453/553.
Mth 661, 662, 663
Algebraic Graph Theory I, II, III (3, 3, 3 credits)
Topics selected from algebraic and spectral graph
theory, including automorphism groups, transitivity,
primitivity, homomorphisms, generalized polygons,
designs, projective planes, cores, fractional
colorings and cliques, spectral decomposition,
eigenvalue interlacing, strongly-regular and distance-
regular graphs, line graphs, root systems, graph laplacians, graph polynomials, and graphtheoretic
link invariants. Courses must be taken in
sequence. Prerequisite Mth 462/562.
Mth 667, 668, 669
Stochastic Processes and Probability Theory I, II, III (3, 3, 3 credits)
Sets, spaces, and measures. Probability distributions.
Random variables. Dependence. Limit theorems.
Birth and death processes and Markov processes.
Mathematical statistics, hypothesis testing,
and sequential analysis. Selected applications.
Courses must be taken in sequence.
Recommended prerequisite: Mth 411/511,
Stat 463/563.
Mth 690
Introduction to Research in Mathematics Education (3 credits)
Topics in the history of mathematics education
including an examination of the current research
trends in mathematics education.
Mth 691
Curriculum in Mathematics Education (3 credits)
An analysis of curriculum development and
assessment efforts in mathematics education
both past and present.
Mth 692
Research Methodology and Design (3 credits)
An examination of quantitative and qualitative
research methodologies and their applications to
the design of research in mathematics education.
Mth 693
Research on the Learning of Mathematics (3 credits)
An analysis of the mathematics education
research on the learning of mathematics, including
topics from K-16 mathematics.
Mth 694
Research on the Teaching of Mathematics (3 credits)
An analysis of the research on the teaching of
mathematics, including issues from levels K-16.
Mth 695
Topics in Research in Mathematics Education (3 credits)
A special topics seminar devoted to exploring
particular issues in more depth................................................................................................................................................................................................................................................................................
The following 800-level in-service courses have limited
application toward advanced degrees:
Mth 801
Research (Credit to be arranged)
Mth 802
Independent Study (Credit to be arranged)
Mth 804
Cooperative Education/Internship (Credit to be arranged)
Mth 805
Reading and Conference (Credit to be arranged)
Mth 806
Special Problems/Projects (Credit to be arranged)
Mth 807
Seminar (Credit to be arranged)
Mth 808
Workshop (Credit to be arranged)
Mth 809
Practicum (Credit to be arranged)
Mth 810
Selected Topics (Credit to be arranged.)
Stat 105
Elementary Data Analysis (4 credits)
A course in exploration of data analysis and basic
statistical topics. May include descriptive statistics,
graphical and tabular summaries, computer software,
confidence intervals, correlation and regression.
Prerequisites: Completion of Mth 95 with a
grade of C- or above within the last year, or passing
at the necessary level on the mathematics
placement test within the last year.
Stat 199
Special Studies (Credit to be arranged)
Stat 243, 244
Introduction to Probability and Statistics I, II (4, 4 credits)
A basic course in statistical analysis including presentation
of data probability, probability distributions,
sampling distributions, estimation, tests of
significance, experimental design and analysis of
variance, regression and correlation, nonparametric
statistics, selected topics, applications, and use
of statistical computer packages. A broad nontechnical
survey designed primarily for non-math students
who need to utilize the subject in their own
fields. Not approved for major credit. Courses
must be taken in sequence. Prerequisites for Stat
243: Completion of Mth 95 with a grade of C- or
above within the last year, or passing at the necessary
level on the mathematics placement test
within the last year.
Stat 366
Introduction to Experimental Design (4 credits)
Nonparametric statistics, multiple regression,
topics in experimental design analysis of variance,
factorial designs, analysis of covariance,
other designs. Prerequisite: Stat 244.
Stat 399
Special Studies (Credit to be arranged)
Stat 401/501
Research (Credit to be arranged)
Consent of instructor.
Stat 404/504
Cooperative Education/Internship (Credit to be arranged)
Stat 405/505
Reading and Conference (Credit to be arranged)
Consent of instructor.
Stat 407/507
Seminar (Credit to be arranged)
Consent of instructor.
Stat 410/510
Selected Topics (Credit to be arranged)
Consent of instructor.
Stat 451/551, 452/552
Applied Statistics for Engineers and Scientists I, II (4, 3 credits)
An introduction to techniques of applied probability,
statistics, and data analysis. Stat 451/551:
sample spaces, probability and counting measures,
discrete and continuous probability models, sampling
theory, and computer applications. Stat
452/552: point and interval estimation, hypothesis
testing, regression, correlation, experimental
design, analysis of variance, multivariable experiments,
nonparametrics, statistical quality control,
and computer applications. Prerequisite: Mth 253
or Mth 254.
Stat 461, 462, 463
Introduction to Mathematical Statistics I, II, III (3, 3, 3 credits)
Theory of probability, distributions of random
variables, central limit theorem, sampling distributions,
point and interval estimation, tests of
hypotheses, analysis of variance. Courses must
be taken in sequence. Prerequisite: Mth 256.
Stat 464/564
Applied Regression Analysis (3 credits)
Basic concepts of regression analysis, matrix
approach to linear regression selecting the “best”
regression equation, and multiple regression.
Computational algorithms and computer software
regression packages. Applications in science, engineering,
and business. Prerequisites: Mth 261 and
either Stat 451/551 or 461/561.
Stat 465/565, 466/566
Experimental Design: Theory and Methods (3, 3 credits)
A theoretical and applied treatment of experimental
design; analysis of variance, fixed effect models,
random effects models, checking model adequacy;
block designs, Latin squares, related designs;
incomplete designs; factorial designs, confounding
two-level designs, split-plot designs; fractional factorial
designs; nested designs; relation to regression
analysis; analysis of covariance. All sections will
illustrate real world applications with computer
usage. Prerequisite: Stat 464/564.
Stat 467/567, 468/568
Applied Probability I, II (3, 3 credits)
Basic concepts of probability, conditional probability,
conditional expectation, discrete-time Markov
chains, branching processes, Poisson processes, continuous-
time Markov chains, birth and death processes,
queues and inventory, renewal processes.
Courses must be taken in sequence. Prerequisite:
Stat 461/561 or Stat 451/551.
Stat 470/570
Statistical Consulting (Credit to be arranged)
Introduction to techniques and methods of statistical
consulting. Faculty supervised consulting
sessions with clients on appropriate projects
brought to the Statistics Consulting Laboratory.
Data and/or statistical problems, from within
and outside the University, are provided by clients
and interdisciplinary guest lecturers. Introduction
to and proficiency with various
statistical computing packages as data analytic
tools. A community-based learning course.
Stat 503
Thesis (Credit to be arranged)
Stat 543
Survey of Statistical Methods (4 credits)
An introductory, discipline-neutral course in statistical analysis to prepare graduate students for research methods courses in other departments. Topics include descriptive statistics, confidence intervals, hypothesis tests, regression and correlation, analysis of variance, chi-squared tests, and use of statistical software.
Stat 561, 562, 563
Mathematical Statistics I, II, III (3, 3, 3 credits)
Taught at a higher level than Stat 461, 462, 463. Provides a solid foundation in the theory and methods of statistical inference. Topics include conditional distributions, functions of random variables, sampling distributions, order statistics, convergence in distribution and convergence in probability, central limit theorem, sufficiency, point estimation, confidence intervals, and testing of statistical hypotheses, most powerful tests, likelihood ratio tests, categorical data analysis, regression, nonparametric methods, and Bayesian inference. Prerequisites: Stat 462 or equivalent.
Stat 571
Applied Multivariate Statistical Analysis (3 credits)
Introduction to techniques and methods of multivariate
statistical analysis. Deals with vector-valued
data generated on individual experimental
units. Applies the methods of vector analysis
and matrix algebra to statistical problems of estimation
and hypothesis testing, based primarily
on the multivariate normal distribution. Computing
to be an integral part of the course. Calculations
will be done using a software package
such as SAS or SPSS. Recommended prerequisites: Stat 244,
Mth 254 and 261.
Stat 573
Computer Intensive Methods in Statistics (3 credits)
Resampling methods in statistics using empirical
data, programming with statistical software,
review materials (sampling distributions,
hypothesis testing, confidence interval construction,
and design of experiments), resampling
version of review materials, and applications.
Recommended prerequisites: Stat 452/552 or 466/566.
Stat 576
Sampling Theory and Methods (3 credits)
Introduction to the theory and methodology of
random sampling. Includes stratified, cluster,
systematic, and multi-stage sampling. Applications
include sampling design and analysis, as
well as sample weighting and sampling with
unequal probabilities. Recommended prerequisite: Stat 451/551
Stat 577
Categorical Data Analysis (4 credits)
Topics include cross-tabulation statistics for
matched samples, and methods to assess confounding
and interaction via stratified tables.
Students explore logistic regression in some
detail, and relate results back to those found
with stratified analyses. Topics for logistic regression
will include: parameter interpretation, statistical
adjustment, variable selection techniques,
and model fit assessment. Statistical software is
used. Recommended prerequisite: Stat 452/552.
Stat 578
Survival Analysis (3 credits)
Time-to-event data subject to random and/or
deliberate censoring. Specialized models and
procedures that accommodate censoring are presented.
Parametric models and methods, including
accelerated failure time models, the Kaplan-
Meier estimate of survival, Cox proportionate
hazards model, the extended Cox model, and
frailty models. Software package such as S-PLUS
is used. Recommended prerequisite: Stat 452/552.
Stat 601
Research (Credit to be arranged)
Stat 603
Dissertation (Credit to be arranged)
Stat 604
Cooperative Education/Internship (Credit to be arranged)
Stat 605
Reading and Conference (Credit to be arranged)
Stat 607
Seminar (Credit to be arranged)
Stat 610
Selected Topics (Credit to be arranged.)
Stat 661, 662, 663
Advanced Mathematical Statistics I, II, III (3, 3, 3 credits)
Theory of estimation; tests of statistical hypotheses.
Single and multi-parameter cases. Robustness.
Classical notions, including lower bound
theory, sufficiency, and maximum likelihood
estimation. The Neyman-Pearson construction,
likelihood ratio tests, robust analogues. Recommended prerequisites:
Mth 511, Stat 563.
Stat 664, 665, 666
Theory of Linear Models I, II, III (3, 3, 3 credits)
Multivariate normal distribution; moments and
characteristic functions; noncentral Chi-square
and noncentral F distributions; distribution of
quadratic forms; estimation and distribution of
estimators; principles of maximum likelihood
and least squares; confidence regions and tests of
hypotheses; regression models; Wishart distribution;
Hotelling's T2 statistic. Courses must be
taken in sequence. Recommended prerequisite: Stat 463/563.