James Hirstein, Chair
Mathematics is studied both as a tool and for its own sake.
Its usefulness in the sciences--physical, biological, social,
behavioral, and environmental--and in decision making processes
is so established as to make it an indispensable part of many
curricula. Mathematics is chosen as a major area of study by
individuals who find it challenging, fascinating, and beautiful.
It is also appreciated by many who seek primarily to use mathematics
as a tool.
A career in mathematics, except for teaching at the secondary
level, generally requires a graduate degree as preparation.
Careers include teaching, research, and the application of mathematics
to diverse problems in institutions of higher learning, business,
industry, and government.
The Bachelor of Arts, Master of Arts, and Doctor of Philosophy
degrees are offered as well as a Bachelor of Science in Mathematical
Sciences-Computer Science.
High School Preparation: For study of mathematics at the University,
it is recommended that high school preparation include the equivalent
of three years of algebra, plane geometry, trigonometry, and
analytic geometry.
Special Degree Requirements
Refer to graduation requirements listed previously in the catalog.
See index.
Mathematics Requirements for B.A. Degree
with a Major in Mathematical Sciences
To obtain a B.A. degree with a major in Mathematical Sciences,
the required courses are MATH 152, 153, 221, 251 (except for
students in the Mathematics Education option),305 and six additional
3 or 4 credit mathematics courses numbered 300 or above (at
least three of the six must be numbered 400 or above, not including
444 or 445). All mathematics courses counted toward the major
must be passed with a grade of C or better. In addition, if
a special option is desired, the minimum requirements listed
below for that option must be met. Additional courses should
be chosen in consultation with a mathematics advisor.
Requirements for the Special Options
Pure Mathematics Option
MATH 351, 421 and two courses from MATH 422, 451, 452.
Mathematics Education Option
MATH 301, 326, 341, 406, 421, 431; one mathematics course chosen
from 251, 311, 325, 381, 382 or any additional 3 4 credit 400
level mathematics course; and the completion of certification
requirements for teaching in secondary schools to include C&I
430.
Statistics Option
MATH 341, 441, 442. (Additional mathematics and statistics courses
chosen with advisor.)
Combinatorics and Optimization Option
Three courses chosen from MATH 381, 382, 485; and one course
chosen from 341, 414, 471, or CS 332.
Applied Analysis Option
MATH 311, 312, 414 and one of 452 or 471. (MATH 351, and 485
are recommended.)
Major Requirements in Courses Outside
Mathematics
1. Except for the Mathematics Education option, students must
complete the foreign language requirement as specified in 3.a.
under the General Education requirements or two courses chosen
from CS 131, 132, 201, 202, 203, 204, 205.
2. All mathematics majors, except those selecting the mathematics
education option, must complete 18 credits in at most three
sciences selected from astronomy, biology, chemistry, computer
science, economics, forestry, geology, management, microbiology,
and physics. Students selecting the mathematics education option
must complete 12 credits in at most two sciences selected from
astronomy, biology, chemistry, computer science, geology, microbiology
and physics. An alternative to the science requirement is for
the student to present a minor or second major in one of the
schools or departments within the University, or for the student
with a mathematics education option to complete an additional
teaching minor or major.
3. The upper-division writing requirement for Mathematical Sciences
majors consists of:
a. An approved General Education upper-division Writing course
OR
b. A senior thesis, research paper or final project approved
in advance by the Undergraduate Committee in the Department
of Mathematical Sciences.
Requirements for a B.S. Degree with
a Combined Major in Mathematical Sciences-Computer Science
The purpose of this combined program is to provide a thorough
background in both allied disciplines and to inculcate a deeper
understanding of their goals and methods. A student must complete
60 credits in the two disciplines: 30 of these credits in mathematical
sciences courses and 30 of these credits in computer science
courses. A minimum grade of "C" is required in all
courses which follow.
The mathematical sciences requirements are: 152-153,
221, 251, 305 (or 225), and twelve credits of MATH electives
selected from courses numbered above 305.
The computer science requirements are: 131-132, 231-232,
331, 332, 335, and nine credits of CS electives selected from
courses numbered 300 and above.
The combined nine additional credits of computer science electives
and twelve additional credits of mathematical sciences electives
must include at least three 3- or 4-credit courses numbered
400 or above, with at least one chosen from each department
(not including MATH 406, 444, 445, and CS 487).
Other requirements are: PHYS 221N-222N, either CHEM 334,
FOR 220, and either COMM 111A or COMM 242.
Each student plans a program in consultation with a mathematical
sciences and a computer science advisor. Students planning to
attend graduate school in he mathematical sciences or computer
science should consult with their respective advisors.
Suggested Curricula:
Applied Math-Scientific Programming: MATH 311, 312, 414, and
one course chosen from MATH 341, 351, 451, 452, 471. Three courses
chosen from CS 344, 445, 486, "Scientific Computation".
Combinatorics and Optimization-Artificial Intelligence: MATH
381, 382, and two courses chosen from MATH 325, 341, 414, 485.
Three courses chosen from CS 344, 455, 456, 457 "Machine
Learning".
Statistics-Machine Learning: MATH 341, 441, and two courses
chosen from MATH 325, 382, 442, 485. Three courses chosen from
CS 365, 455, 456, 486, "Machine Learning".
Algebra-Analysis: MATH 351, 421, and two courses chosen from
MATH 326, 422, 451, 452. CS 344, 441, and one other course.
Suggested Course of Study
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First Year
MATH 152 153 Calculus I, II
ENEX 101 Composition
Computer programming language
Electives and General Education
Total....................................................................................................................
Second Year
MATH 221 Linear Algebra
MATH 251 Calculus III
MATH 305 Introduction to Abstract Math
Electives and General Education
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Requirements for a Minor
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To earn a minor in mathematics the student must earn 23 credits
in mathematics including at least three 3 or 4 credit courses
at the 300 level or above. All courses counted toward the minor
must be passed with a grade of C or better.
Mathematics Education Minor: For a teaching minor endorsement
in the field of mathematics, a student must complete MATH 152
153, 221, 301, 305, 326, 341, and 431. Students also must complete
C&I 430, gain admission to Teacher Education and Student
Teaching and meet the requirements for certification as a secondary
teacher (see the School of Education section of this catalog).
All courses counted toward the minor must be passed with a letter
grade of C or better.
Courses
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U = for undergraduate credit only, UG = for undergraduate or
graduate credit, G = for graduate credit. R after the credit
indicates the course may be repeated for credit to the maximum
indicated after the R.
Unless the student has prior written approval by the Mathematical
Sciences Department, credit is not allowed for MATH 100 if credit
has been or is being earned in any mathematics course numbered
above 100. Unless the student has prior written approval of
the Mathematical Sciences Department, credit is not allowed
for any mathematics course that is a prerequisite for a mathematics
course for which credit has already been earned. Students receiving
transfer or Advanced Placement credit for MATH 241 may take
MATH 117 for credit.
See the College of Technology section for Introductory Algebra,
MAT 005.
U 100 Intermediate Algebra 5 cr. Offered autumn and spring.
Prereq., MAT 005 or appropriate placement score. Topics include
linear equations and systems of linear equations, inequalities,
applications and graphing; polynomials; rational expressions
and equations; radicals, rational exponents and complex numbers;
quadratic equations; introduction to exponential and logarithmic
functions.
U 107 Contemporary Mathematics 3 cr. Offered every term.
Prereq., MATH 100 or appropriate placement score. An introduction
to mathematical ideas and their impact on society. Intended
for students wishing to satisfy the general education mathematics
requirement.
U 109 Numbers as News 3 cr. Offered spring. Prereq.,
MATH 100 or appropriate placement score. An exploration of mathematics
and statistics as used in the popular media. For students in
the School of Journalism only.
U 117 Probability and Linear Mathematics 3 cr. Offered
every term. Prereq., MATH 100 or appropriate placement score.
Systems of linear equations and matrix algebra. Introduction
to probability with emphasis on models and probabilistic reasoning.
Examples of applications of the material in many fields.
U 121 Precalculus 4 cr. Offered autumn and spring. Prereq.,
MATH 100 or appropriate placement score or three years of college
preparatory mathematics. Properties of algebraic functions of
one variable and their graphs, conic sections, trigonometric
functions and inverses, trigonometric identities, exponential
and logarithmic functions, and polar coordinates. Credit not
allowed for both MATH 121 and MAT 120.
U 130 Mathematics for Elementary Teachers 5 cr. Offered
autumn and spring. Prereq., MATH 100 or appropriate placement
score. Open only to elementary education majors. Topics include
problem solving, sets and logic, functions, whole numbers, integers,
rational numbers, real numbers, number theory, probability and
statistics.
U 131 Mathematics for Elementary Teachers 4 cr. Offered
autumn and spring. Prereq., 130. Topics include introductory
geometry, geometric constructions, congruence, similarity, measurement,
coordinate geometry and an introduction to computer geometry.
U 150 Applied Calculus 4 cr. Offered autumn and spring.
Prereq., MATH 121 or appropriate placement score. Introductory
course surveying the principal ideas of differential and integral
calculus with emphasis on applications and computer software.
Mathematical modeling in discrete and continuous settings. Intended
primarily for students who do not plan to take higher calculus.
U 152 Calculus I 4 cr. Offered autumn and spring. Prereq.,
MATH 121 or equiv. or appropriate placement score. Differential
calculus, including limits, continuous functions, Intermediate
Value Theorem, tangents, linear approximation, inverse functions,
implicit differentiation, extreme values and the Mean Value
Theorem. Integral Calculus including antiderivatives, definite
integrals, and the Fundamental Theorem of Calculus.
U 153 Calculus II 4 cr. Offered autumn and spring. Prereq.,
MATH 152. Techniques of Integration. Area computations. Improper
integrals. Infinite series and various convergence tests. Power
series. Taylor's Formula. Polar coordinates. Parametric curves.
U 158 Applied Differential Equations 3 cr. Offered spring.
Prereq., MATH 150 or 152. Solution of ordinary differential
equations and systems with emphasis on applications, numerical
methods and computer software.
U 221 Linear Algebra 4 cr. Offered autumn and spring.
Prereq., MATH 153. Vectors in the plane and space, systems of
linear equations and Gauss Jordan elimination, matrices, determinants,
eigenvalues and eigenvectors, vector spaces, linear transformations.
Calculators and/or computers used where appropriate.
U 225 Discrete Mathematics 3 cr. Offered autumn. Prereq.,
MATH 152. Mathematical concepts used in computer science with
an emphasis on mathematical reasoning and proof techniques.
Elementary logic, sets, functions and relations, combinatorics,
mathematical induction, recursion and algorithms. Mathematics
majors should take 305 instead of 225.
U 231 Topics in Geometry 3 cr. Offered spring. Prereq.,
MATH 131 or consent of instr. Geometry topics for teaching grades
6-12 mathematics. Intended primarily for students in elementary
education who plan to teach middle school mathematics.
U 241 Statistics 4 cr. Offered autumn and spring. Prereq.,
MATH 117 or consent of instr. Introduction to major ideas of
statistical inference. Emphasis is on statistical reasoning
and uses of statistics.
U 251 Calculus III 4 cr. Offered autumn and spring. Prereq.,
MATH 153. Calculus of functions of several variables; differentiation
and elementary integration. Vectors in the plane and space.
U 294 Seminar Variable cr. (R 9) Offered autumn and spring.
Prereq., consent of instr. Guidance in special work for advanced
students.
U 295 Special Topics Variable cr. (R 9) Offered autumn and
spring. Prereq., consent of instr. Experimental offerings of
visiting professors, experimental offerings of new courses,
or one time offerings of current topics.
U 296 Independent Study Variable cr. (R 9) Offered autumn
and spring. Prereq., consent of instr. Guidance of an individual
student in doing independent study on material
not offered in a regular course.
UG 301 Mathematics with Technology for Teachers 3 cr. Offered
autumn. Prereq., MATH 221. Discrete and continuous mathematical
models from a variety of disciplines using appropriate technology.
U 305 Introduction to Abstract Mathematics 3 cr. Offered
autumn and spring. Prereq., MATH 153. Designed to prepare students
for upper division proof based
mathematics courses. Topics include proof techniques, logic,
sets, relations, functions and axiomatic methods.
UG 311 Ordinary Differential Equations and Systems 3 cr.
Offered autumn. Prereq., MATH 251. Ordinary differential equations.
Systems of linear differential equations from a matrix viewpoint.
Series solutions. Existence and uniqueness for initial value
problems. Numerical methods. Stability and selected topics.
UG 312 Partial Differential Equations 3 cr. Offered spring.
Prereq., MATH 311. Fourier series, Sturm Liouville and boundary
value problems. Partial differential equations: Cauchy problems
and the method of characteristics, separation of variables and
Laplace transform methods. Numerical methods and selected topics.
UG 325 Discrete Mathematics 3 cr. Offered spring. Prereq.,
MATH 152 and 225 or 305. Continuation of 225 and topics from
graph theory, Boolean algebras, automata theory, coding theory,
computability and formal languages.
UG 326 Elementary Number Theory 3 cr. Offered spring. Prereq.,
MATH 225or 305. Congruences, Diophantine equations, properties
of primes, quadratic residues, continued fractions, algebraic
numbers.
UG 341 Introduction to Probability and Statistics 3 cr.
Offered autumn and spring. Prereq., MATH 153. Probability, probability
models and simulation, random variables, density functions,
special distributions, and a brief survey of estimation and
hypothesis testing. Computer use integrated throughout.
UG 351 Advanced Calculus 4 cr. Offered autumn even-numbered
years. Prereq., MATH 251, 305. Rigorous development of the theory
of functions of several variables. Differentiability, Taylor's
theorem, inverse and implicit function theorems, multiple integration,
differential forms and Stokes' theorem.
UG 381 Discrete Optimization 3 cr. Offered spring. Prereq.,
MATH 153 (221or 225 recommended). Intended for non mathematics
majors as well as mathematics majors. Introduction to discrete
optimization and modeling techniques with applications. Topics
from combinatorics and graph theory, including enumeration,
graph algorithms, matching problems and networks.
UG 382 Linear Optimization 3 cr. Offered autumn. Prereq.,
MATH 153 (221 recommended). Coreq., MATH 388 recommended. Intended
for non mathematics majors as well as majors. Introduction to
linear programming and modeling techniques with applications.
Topics include the simplex method, duality, sensitivity analysis
and network models.
UG 388 Linear Optimization Laboratory 1 cr. Offered autumn.
Coreq., MATH 382. Introduction to linear optimization software.
U 394 Seminar Variable cr. (R 9) Offered autumn and
spring. Prereq., consent of instr. Guidance in special work
for advanced students.
U 395 Special Topics Variable cr. (R 9) Offered autumn
and spring. Prereq., consent of instr. Experimental offerings
of visiting professors, experimental offerings of new courses,
or one time offerings of current topics.
U 396 Independent Study Variable cr. (R 9) Offered autumn
and spring. Prereq., consent of instr. Guidance of an individual
student in doing independent study on material not offered in
a regular course.
U 398 Cooperative Education Experience Variable cr. (R
9) Offered autumn and spring. Prereq., consent of instructor.
Extended classroom experience which provides practical application
of classroom learning during placements off campus. Prior approval
must be obtained from the faculty supervisor and the Center
for Work-Based Learning.
UG 406 History of Mathematics 3 cr. Offered spring. Prereq.,
MATH 305. Historical study of the development of mathematics
from the Egyptian and Babylonian eras to the 20th century.
UG 414 Deterministic Models 3 cr. Offered autumn. Prereq.,
MATH 158 or 311 or consent of instr. Linear and nonlinear difference
and differential equations: stability, phase plane analysis,
oscillatory behavior, limit cycles, and chaos. Eigenvalues and
eigenfunctions. Emphasis on models in biology.
UG 421 Abstract Algebra I 4 cr. Offered autumn. Prereq.,
MATH 305. An introduction to modern ideas of algebra through
the study of groups, rings, and fields.
UG 422 Abstract Algebra II 4 cr. Offered spring. Prereq.,
MATH 421. Continues the investigation of groups, rings, and
fields begun in MATH 421. Further topics include vector spaces
and field extensions.
UG 431 Euclidean and Non Euclidean Geometry 3 cr. Offered
autumn. Prereq., MATH 305; MATH 231 recommended. Euclidean geometry
from a rigorous, axiomatic viewpoint and Non Euclidean geometries
chosen from Lobachevskian, projective, finite and Riemannian.
UG 441 Mathematical Statistics 3 cr. Offered autumn.
Prereq., MATH 251 and 341 or consent of instr. An introduction
to probability, random variables and their probability distributions,
estimation and hypothesis testing. This course is the foundation
on which more advanced statistics courses build.
UG 442 Mathematical Statistics 3 cr. Offered spring.
Prereq., MATH 441. Continuation of 441.
UG 444 Statistical Methods 3 cr. Offered autumn. Prereq.,
one year of college mathematics including MATH 117 or equiv.
course in probability or consent of instr. May not be counted
toward a major in mathematics. Intended primarily for non mathematics
majors who will be analyzing data. Graphical and numerical summaries
of data, elementary sampling, designing experiments, probability
as a model for random phenomena and as a tool for making statistical
inferences, random variables, basic ideas of inference and hypothesis
testing.
UG 445 Statistical Methods 3 cr. Offered spring. Prereq.,
MATH 444. Continuation of MATH 444. May not be counted toward
a major in mathematics. Multiple regression, experimental design,
analysis of variance, other statistical models..
UG 447 Computer Data Analysis 1 cr. Offered autumn. Coreq.,
MATH 444 or consent of instr. An introduction to software for
doing statistical analyses. Intended primarily for students
in MATH 444.
UG 448 Computer Data Analysis 1 cr. Offered spring. Coreq.,
MATH 445 or consent of instr. Continuation of Math 447. Intended
primarily for students in MATH 445.
UG 451 Introduction to Real Analysis 4 cr. Offered autumn
odd-numbered years. Prereq., MATH 251, 305. Theory of metric
spaces and point set topology, Riemann Stieltjes integral, sequences
and series of functions. Stone Weierstrass theorem, theorem
of Arzela Ascoli, introduction to Lebesgue integration.
UG 452 Complex Variables 4 cr. Offered spring. Prereq.,
MATH 251, 305. Analytic functions, complex integration, singularities
and application to contour integration, harmonic functions,
spaces of analytic functions.
U 460 Math Club Seminar 1 cr. (R-6) Offered every semester.
Prereq., consent of instr. Discussion seminar focused on current
and historical topics and issues of interest to students in
mathematics.
UG 471 Numerical Analysis 4 cr. Offered intermittently.
Prereq., MATH 305, 311, one computer language. Error analysis;
approximation and interpolation, numerical solution of linear
and non linear equations, numerical integration of ordinary
and partial differential equations.
UG 485 Graph Theory 3 cr. Offered spring. Prereq., MATH
325, or MATH 305 and 381, or consent of instr. Theory and applications
of graphs. Topics chosen from trees, matchings, connectivity,
coloring, planarity, Ramsey theory, random graphs, combinatorial
designs and matroid theory.
U 494 Seminar Variable cr. (R 9) Offered autumn and spring.
Prereq., consent of instr. Guidance in special work for advanced
students.
UG 495 Special Topics Variable cr. (R 9) Offered autumn
and spring. Prereq., consent of instr. Experimental offerings
of visiting professors, experimental offerings of new courses,
or one time offerings of current topics.
U 496 Independent Study Variable cr. (R 9) Offered autumn
and spring. Prereq., consent of instr. Guidance of an individual
student in doing independent study on material not offered in
a regular course
U 498 Cooperative Education Experience Variable cr. (R
9) Offered autumn and spring. Prereq., consent of instr. Extended
classroom experience which provides practical application of
classroom learning during placements off campus. Prior approval
must be obtained from the faculty supervisor and the Center
for Work-Based Learning.
U 499 Senior Thesis Variable cr. (R 12) Offered autumn
and spring. Prereq., consent of instr. Senior thesis for mathematics
majors and/or Watkins Scholars.
G 500 Current Mathematical Curricula 3 cr. Offered intermittently.
Prereq., undergraduate major or minor in mathematics. Analysis
of contemporary materials for secondary school mathematics:
the goals, the mathematical content, alternative methodologies,
and curriculum evaluation.
G 501 Technology in Mathematics for Teachers 3 cr Offered
intermittently. Prereq., undergraduate mathematics major or
minor. Technology usage--when it is appropriate and when it
is not. Experience is provided with scientific calculators,
graphing utilities, computers, and identification of exemplary
software.
G 504 Topics in Math Education Variable cr. (R-12) Offered
intermittently. Prereq., teacher certification. Topics of current
interest which may include calculus, number theory, probability
and statistics, geometry, or algebra, at a level suitable for
teachers.
G 510 Problem Solving for Teachers 3 cr. Offered intermittently
in summer. Prereq., undergraduate major or minor in mathematics.
Strategies for problem solving, problem posing in a variety
of situations, modeling and applications. Problems are selected
from various areas of mathematics.
G 511 Advanced Mathematical Methods 3 cr. Offered autumn
odd-numbered years. Prereq., MATH 311 312 or 414.. Methods in
applied mathematics related to the qualitative and quantitative
solution of nonlinear and differential integral equations, dynamical
systems, and perturbation methods. Applications of these methods
to other sciences.
G 512 Advanced Mathematical Methods 3 cr. Offered spring
even-numbered years. Prereq., MATH 511. Continuation of 511.
G 514 Topics in Applied Mathematics Variable cr. (R 12)
Offered autumn even-numbered years. Prereq., consent of instr.
or Math 511 512. Topics of current interest in applied mathematics,
mathematical modeling, dynamic modeling, and optimal management
in stochastic or deterministic environments.
G 520 Algebra for Teachers 3 cr. Offered intermittently
in summer. Prereq., MATH 421 or equiv. Topics include algebraic
number fields, linear algebra topics, and applications appropriate
for secondary teachers.
G 521 Advanced Algebra 3 cr. Offered autumn. Prereq.,
MATH 422 or consent of instr. General topics from groups, rings,
modules, commutative algebra, fields and categories.
G 522 Advanced Algebra 3 cr. Offered spring. Prereq.,
MATH 521 or consent of instr. Continuation of 521.
G 524 Topics in Algebra I 3 cr. Offered autumn odd-numbered
years. Prereq., MATH 422 or consent of instr. Topics include
algebraic geometry, category theory, Lie algebras, and advanced
linear algebra.
G 525 Topics in Algebra II 3 cr. Offered spring even-numbered
years. Prereq., MATH 524 or consent of instr. Continuation of
524.
G 526 Discrete Mathematics for Teachers 3 cr. Offered
intermittently in summer. Prereq., MATH 305 or consent of instr.
Elements and operations of finite structures, combinatorics,
recursion, graph theory, matrix representations, and finite
state transition models.
G 530 Geometries for Teachers 3 cr. Offered intermittently
in summer. Prereq., MATH 431 or equiv. Comparison of synthetic,
analytic, vector, and transformational approaches to geometry.
Includes classification of geometries, geometric representations,
axiomatics, and the applications of modern geometries.
G 531 Topology 3 cr. Offered autumn even-numbered years.
Prereq., MATH 451 or consent of instr. Set theory, topological
spaces, metrizability, continuous mappings and selected topics.
G 532 Topology 3 cr. Offered spring odd-numbered years.
Prereq., MATH 531 or consent of instr. Continuation of 531.
G 540 Probability and Statistics for Teachers 3 cr. Offered
intermittently in summer. Prereq., MATH 341 or equiv. A survey
of modern topics in probability and statistics. Emphasis will
be on applications of statistics in real situations.
G 541 Advanced Algebra I 3 cr. Offered autumn even-numbered
years. Prereq., MATH 442. Introduction to the core topics of
abstract algebra. Group theory, field theory and Galois theory.
G 542 Advanced Algebra II 3 cr. Offered spring odd-numbered
years. Prereq., MATH 442 or consent of instr. Continuation of
MATH 521; rings, modules, commutative algebra, and further topics.
G 543 Applied Multivariate Statistical Analysis 4 cr. Offered
spring even-numbered years. Prereq., MATH 445 or MATH 442, or
consent of instr. Introduction to multivariate statistical methods
and applications. Includes appropriate linear algebra, random
vectors, multivariate normal distribution, multivariate ANOVA,
principal components, clustering, discriminant analysis, and
related topics. Use of the computer and real data sets integrated
throughout. Intended for students in mathematics and in other
fields.
G 544 Topics in Probability and Statistics 3 cr. (R-12)
Offered intermittently. Prereq., MATH 442 and consent of instr.
May include theory of nonparametric statistics, generalized
linear models, stochastic processes or other topics chosen by
the instructor.
G 545 Theory of Linear Models 3 cr. Offered autumn odd-numbered
years. Prereq., MATH 442. Multivariate normal distribution,
distribution of quadratic forms, estimation and hypothesis testing
in the full rank and less than full rank general linear models.
G 547 Applied Nonparametric Statistics 3 cr. Offered
autumn odd-numbered years. Prereq., MATH 441 or 445 or consent
of instr. Statistical estimation and inference based on ranks
and elementary counting methods. Applications to a variety of
situations including one- and two-sample, correlation, regression,
analysis of variance, and goodness-of-fit problems. Use of the
computer and real data sets integrated throughout. Intended
for students in mathematics and in other fields.
G 549 Applied Sampling 3 cr. Offered autumn even-numbered
years. Theory and application of methods for selecting samples
from populations in order to efficiently estimate parameters
of interest. Includes simple random, systematic, cluster, stratified,
multistage, line transect, distance and adaptive sampling. Use
of the computer and real data sets integrated throughout. Intended
for students in mathematics and in other fields.
G 550 Analysis for Teachers 3 cr. Offered intermittently
in summer. Prereq., MATH 251 or equiv. Notions of limits, continuity,
differentiation, and integration in Rn.
G 551 Real Analysis 3 cr. Offered spring even-numbered
years. Prereq., MATH 451 or 452 or consent of instr. Measure
theory, abstract integration theory, theory of Lp-spaces.
G 555 Functional Analysis 3 cr. Offered autumn even-numbered
years. Prereq., MATH 451 or 452 or consent of instr. Normed
linear spaces, linear functionals, separation theorems, topological
linear spaces, weak topologies, dualities.
G 564 Topics in Analysis 3 cr. (R 12) Offered spring odd-numbered
years. Prereq., consent of instr. Research projects or topics
in analysis. May include but not restricted to Banach algebras,
Fourier analysis, Harmonic analysis, Hilbert space theory, integral
equations, or operator theory.
G 581 Combinatorics 3 cr. Offered autumn odd-numbered
years. Prereq., consent of instr. Theory and applications of
discrete mathematics. Topics chosen from enumeration, combinatorial
analysis, and graph theory.
G 582 Optimization 3 cr. Offered autumn even-numbered
years. Prereq., consent of instr. Theory and applications of
optimization. Topics chosen from linear, non-linear, and discrete
optimization, including duality theory, convexity and networks.
G 584 Topics in Combinatorics and Optimization 3 cr.
(R 12) Offered spring odd-numbered years. Prereq., consent of
instr. Topics chosen from the areas of combinatorics and optimization.
May include classical problems, current trends, research interests
or other topics chosen by the instructor.
G 593 Professional Project Variable cr. (R 6) Offered
autumn and spring. Prereq., consent of advisor.
G 595 Special Topics Variable cr. (R 12) Offered autumn
and spring. Prereq., consent of instr. Experimental offerings
of visiting professors, experimental offerings of new courses,
or one time offerings of current topics.
G 596 Independent Study Variable cr. (R 12) Offered
autumn and spring. Prereq., consent of instr.
G 597 Research Variable cr. (R 12) Offered autumn and
spring. Prereq., consent of instr.
G 598 Cooperative Education Experience Variable cr. (R
12) Offered autumn and spring. Prereq., consent of department.
Extended classroom experience which provides practical application
of classroom learning during placements off campus. Prior approval
must be obtained from the faculty supervisor and the Center
for Work-Based Learning.
G 599 Thesis Variable cr. (R 6) Offered autumn and spring.
Prereq., consent of instr.
G 600 Mathematics Colloquium 1 cr. (R 3) Offered autumn and
spring. Prereq., consent of advisor.
G 602 Teaching College Mathematics 3 cr. Prereq., second
year standing in graduate school. Topics include publishing,
grant writing, writing in mathematics classes, media use in
mathematics, evaluation and assessment of curricular materials
and programs, instructional methods in university mathematics
courses, and other selected topics.
G 605 Learning Theories in Mathematics 3 cr. Prereq.,
graduate status. How children learn mathematical content and
processes. Models of mental development, concept formation,
problem solving, reasoning, and creative thinking.
G 606 Current Topics in the History of Mathematics 3 cr.
Examination of mathematical history topics from the latter part
of the 20th century. Discussions may focus on the impact of
Hilbert's Problems. Research on current mathematics.
G 610 Graduate Seminar in Applied Mathematics Variable cr. (R
12) Offered autumn and spring. Prereq., consent of instr.
G 620 Graduate Seminar in Algebra Variable cr. (R 12)
Offered autumn and spring. Prereq., consent of instr.
G 630 Graduate Seminar in Geometry/Topology Variable cr.
(R 12) Offered autumn and spring. Prereq., consent of instr.
G 640 Graduate Seminar in Probability and Statistics Variable
cr. (R 12) Offered autumn and spring. Prereq., consent of
instr.
G 650 Graduate Seminar in Analysis Variable cr. (R 12) Offered
autumn and spring. Prereq., consent of instr.
G 670 Graduate Seminar in Numerical Analysis Variable cr.
(R 12) Offered autumn and spring. Prereq., consent of instr.
G 680 Graduate Seminar in Combinatorics and Optimization Variable
cr. (R 12) Offered autumn and spring. Prereq., consent of
instr.
G 691 Research Methods in Mathematics Education 3 cr. Prereq.,
consent of instr. Resources for learning of reported research,
critical reviews of research, quantitative and qualitative processes.
G 694 Seminar Variable cr. (R 12) Offered autumn and spring.
Prereq., consent of instr.
G 699 Dissertation Variable cr. (R 9) Offered autumn
and spring.
Faculty
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Professors
William R. Ballard, Ph.D., University of Chicago, 1957 (Emeritus)
Richard W. Billstein, Ed.D., The University of Montana, 1972
Charles A. Bryan, Ph.D., University of Arizona, 1963 (Emeritus)
William R. Derrick, Ph.D., Indiana University, 1966
Rudy A. Gideon, Ph.D., University of Wisconsin, 1970
Stanley I. Grossman, Ph.D., Brown University, 1969 (Emeritus)
Gloria C. Hewitt, Ph.D., University of Washington, 1962 (Emeritus)
James J. Hirstein, Ed.D., University of Georgia, 1976 (Chair)
Don O. Loftsgaarden, Ph.D., Montana State University, 1964 (Emeritus)
Johnny W. Lott, Ph.D., Georgia State University, 1973
Merle E. Manis, Ph.D., University of Oregon, 1964 (Emeritus)
Robert W. McKelvey, Ph.D., University of Wisconsin 1954 (Emeritus)
D. George McRae, Ph.D., University of Washington, 1967
William M. Myers, Jr., Ph.D., Ohio State University, 1952 (Emeritus)
David A. Patterson, Ph.D., University of Iowa, 1984 (on leave
2001-2002)
Howard E. Reinhardt, Ph.D., University of Michigan, 1959 (Emeritus)
Karel M. Stroethoff, Ph.D., Michigan State University, 1987
Thomas Tonev, Ph.D., Moscow State University, 1973
George F. Votruba, Ph.D., University of Michigan, 1964 (Emeritus)
I. Keith Yale, Ph.D., University of California, Berkeley, 1966
(Emeritus)
Associate Professors
Mary Jean Brod, M.A., Stanford University, 1969
Lynn D. Churchill, Ph.D., University of Washington, 1985 (Research)
Jonathan Graham, Ph.D., North Carolina State University, 1995
Leonid Kalachev, Ph.D., Moscow State University, 1987
P. Mark Kayll, Ph.D., Rutgers University, 1994 (on leave 2001-2002)
Libby Krussel, Ph.D., Oregon State University, 1994
Jennifer McNulty, Ph.D., University of North Carolina at Chapel
Hill, 1993 (on leave 2000-2001)
Greg St. George, Ph.D., The University of Montana, 1989
Nikolaus Vonessen, Ph.D., Massachusetts Institute of Technology,
1988
Assistant Professors
Regina Souza, Ph.D., Massachusetts Institute of Technology,
1990 (Visiting)
Brian Steele, Ph.D., The University of Montana, 1995
Scott Stevens, Ph.D., University of Vermont, 1999
Carol Ulsafer, Ph.D., The University of Montana, 1984 (Visiting)
Mark Wilson, Ph.D., University of Wisconsin, Madison, 1995
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