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, 412, 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 back to top
The purpose for the 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, 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 graduate advisors.
Suggested Curricula:
Applied Math-Scientific Programming: MATH 311, 412, 414, and one course
chosen from MATH 341, 351, 451, 452, 471. Three courses chosen from
CS 344, 445, 471, 486.
Combinatorics and Optimization-Artificial Intelligence: MATH 381,
382, and two courses chosen from MATH 325, 341, 414, 485; CS 344,
455, and 457.
Statistics-Machine Learning: MATH 341, 441, and two courses chosen
from MATH 325, 382, 442, 485. Three courses chosen from CS 365, 455,
456, and 486
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
back to top
First
Year |
A
|
S
|
MATH 152
153 Calculus I, II |
4
|
4
|
ENEX 101
Composition |
3
|
-
|
Computer
programming language |
-
|
3-4
|
Electives
and General Education |
9
|
9
|
Total |
16
|
16-17
|
Second
Year |
|
|
MATH 221
Linear Algebra |
4
|
-
|
MATH 251
Calculus III |
4
|
-
|
MATH
305 Introduction to Abstract Math |
-
|
3
|
Electives
and General Education |
9
|
13
|
Total |
17
|
16
|
Requirements for a Minor
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 back
to top
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. MATH 317 computer lab recommended.
UG 317 Ordinary Differential Equations Computer Lab 1 cr. Offered
autumn. Coreq., MATH 311 or consent of instr. Intended primarily for
student in MATH 311.
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 412 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. MATH 418 computer
lab recommended.
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 418 Partial Differential Equations Computer Lab 1 cr. Offered
spring. Coreq., MATH 412 or consent of instr. Intended primarily for
students in MATH 412.
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, 412 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 I 3 cr. Offered alternate years. Prereq.,
MATH 422 or consent of instr. Topics covered include group theory,
field theory and Galois theory.
G 522 Advanced Algebra II 3 cr. Offered alternate years. Prereq.,
MATH 521 or consent of instr. Continuation of 521; rings, modules,
commutative algebra, and further topics.
G 524 Topics in Algebra I 3 cr. Offered alternate years. Prereq.,
MATH 422 or consent of instr. May include algebraic geometry, category
theory, Lie algebras, or advanced linear algebra.
G 525 Topics in Algebra II 3 cr. Offered alternate 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 541Advanced Mathematical Statistics 3 cr. Offered intermittently.
Prereq., MATH 442. Advanced theory of estimation and hypothesis testing
including large sample theory.
G 542 Applied Linear Models 3 cr. Offered autumn even-numbered
years. Prereq., MATH 442 or consent of instr. Numerical and graphical
data summaries, simple linear and multiple regression and analysis
of variance, including estimation, hypothesis testing, residual analysis,
diagnostics, and model-building strategies. Use of the computer and
real data sets integrated throughout.
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 spring odd-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 autumn 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 back
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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)
Leonid Kalachev, Ph.D., Moscow State University, 1987 (on leave 2002-2003)
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
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
Jonathan Graham, Ph.D., North Carolina State University, 1995
P. Mark Kayll, Ph.D., Rutgers University, 1994
Libby Krussel, Ph.D., Oregon State University, 1994
Jennifer McNulty, Ph.D., University of North Carolina at Chapel Hill,
1993
Greg St. George, Ph.D., The University of Montana, 1989
Nikolaus Vonessen, Ph.D., Massachusetts Institute of Technology, 1988
(on leave 2002-2003)
Assistant Professors
Regina Souza, Ph.D., Massachusetts Institute of Technology, 1990 (Visiting)
Brian Steele, Ph.D., The University of Montana, 19951984 (Visiting)
Bharath Sriraman, Ph.D., Northern Illinois University, 2002
Carol Ulsafer, Ph.D., The University of Montana, 1984 (Visiting)