James Hirstein, Chair
Mathematics is studied both as a tool and for its own sake. Its usefulness in the sciencesphysical, biological, social, behavioral, and environmental and in decisionmaking 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 SciencesComputer 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 4credit 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 and a 2.00 grade point average is required.. 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 34 credit 400level 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 1. within the Foreign Language/Symbolic Systems section 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 upperdivision writing requirement for Mathematical Sciences majors consists of:
a. An approved General Education upperdivision 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 SciencesComputer Science
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: 152153, 221, 251, 305 (or 225), and twelve credits of 3 or 4credit MATH electives selected from courses numbered above 305.
The computer science requirements are: 131132, 231232, 331, 332, 335, and nine credits of CS electives selected from courses numbered 300 and above. A total of at most three of the nine credits of CS electives may be in CS 398 or 498.
The combined nine additional credits of computer science electives and twelve additional credits of mathematical sciences electives must include at least three 3 or 4credit courses numbered 400 or above, with at least one chosen from each department (not including MATH 406, 444, and 445).
Other requirements are: PHYS 221N222N, 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 the mathematical sciences or computer science should consult with their respective graduate advisors.
Suggested Curricula:
Applied MathScientific 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 OptimizationArtificial Intelligence: MATH 381, 382, and two courses chosen from MATH 325, 341, 414, 485; CS 344, 455, and 457.
StatisticsMachine Learning: MATH 341, 441, and two courses chosen from MATH 325, 382, 442, 485. Three courses chosen from CS 365, 455, 456, and 486
AlgebraAnalysis: MATH 351, 421, and two courses chosen from MATH 326, 422, 451, 452; CS 344, 441, and one other course.
Suggested Course of Study
Courses 
Autumn 
Spring 
First Year 


MATH 152153 Calculus I, II 
4 
4 
ENEX 101 Composition 
3 
 
Computer programming language 
3 
34 
Electives and General Education 
9 
9 
Total 
16 
1617 
Second Year 


MATH 221Linear Algebra 
4 
 
MATH 251 Calculus III 
4 
 
MATH 305 Introduction toAbstract 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 4credit courses at the 300level or above. All courses counted toward the minor must be passed with a grade of C or better and a 2.00 grade average is required.
Mathematics Education Minor: For a teaching minor endorsement in the field of mathematics, a student must complete MATH 152153, 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 and a 2.00 grade average is required.
Courses
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.
Mathematical Sciences (MATH)
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. Credit no allowed for both MAT 100 and MATH 100.
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. Credit not allowed for both MAT 117 and MATH 117.
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 problemsolving, 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 195 Special Topics Variable cr. (R6) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or onetime offerings of current topics.
U 221 Linear Algebra 4 cr. Offered autumn and spring. Prereq., MATH 153. Vectors in the plane and space, systems of linear equations and GaussJordan 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 612 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 291 Practicum 13 cr. (R3) Offered intermittently. Prereq., consent of instr.
U 294 Seminar Variable cr. (R9) Offered autumn and spring. Prereq., consent of instr. Guidance in special work for advanced students.
U 295 Special Topics Variable cr. (R9) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or onetime offerings of current topics.
U 296 Independent Study Variable cr. (R9) 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 upperdivision proofbased 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 225 or 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 evennumbered 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 nonmathematics 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 nonmathematics 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. (R9) Offered autumn and spring. Prereq., consent of instr. Guidance in special work for advanced students.
U 395 Special Topics Variable cr. (R9) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or onetime offerings of current topics.
U 396 Independent Study Variable cr. (R9) 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. (R9) 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 Internship Services office.
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, SturmLiouville 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, phaseplane 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 NonEuclidean Geometry 3 cr. Offered autumn. Prereq., MATH 305; MATH 231 recommended. Euclidean geometry from a rigorous, axiomatic viewpoint and NonEuclidean 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 nonmathematics 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 oddnumbered years. Prereq., MATH 251, 305. Theory of metric spaces and point set topology, RiemannStieltjes integral, sequences and series of functions. StoneWeierstrass theorem, theorem of ArzelaAscoli, 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. (R6) 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 nonlinear equations, numerical integration of ordinary and partial differential equations.
UG 485 Graph Theory 3 cr. Offered autumn. 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. (R9) Offered autumn and spring. Prereq., consent of instr. Guidance in special work for advanced students.
UG 495 Special Topics Variable cr. (R9) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or onetime offerings of current topics.
U 496 Independent Study Variable cr. (R9) 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. (R9) 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 Internship Services office.
U 499 Senior Thesis Variable cr. (R12) 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. (R12) 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 oddnumbered 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 evennumbered years. Prereq., MATH 511. Continuation of 511.
G 514 Topics in Applied Mathematics Variable cr. (R12) Offered autumn evennumbered years. Prereq., consent of instr. or Math 511512. 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 evennumbered 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 oddnumbered 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 evennumbered 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 modelbuilding strategies. Use of the computer and real data sets integrated throughout.
G 543 Applied Multivariate Statistical Analysis 3 cr. Offered spring evennumbered 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. (R12) 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 oddnumbered 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 oddnumbered 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 twosample, correlation, regression, analysis of variance, and goodnessoffit 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 evennumbered 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 R^{n} .
G 551 Real Analysis 3 cr. Offered spring evennumbered years. Prereq., MATH 451 or 452 or consent of instr. Measure theory, abstract integration theory, theory of Lpspaces.
G 555 Functional Analysis 3 cr. Offered spring oddnumbered 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. (R12) Offered autumn oddnumbered 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 oddnumbered 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 evennumbered years. Prereq., consent of instr. Theory and applications of optimization. Topics chosen from linear, nonlinear, and discrete optimization, including duality theory, convexity and networks.
G 584 Topics in Combinatorics and Optimization 3 cr. (R12) Offered spring oddnumbered 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. (R6) Offered autumn and spring. Prereq., consent of advisor.
G 595 Special Topics Variable cr. (R12) Offered autumn and spring. Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or onetime offerings of current topics.
G 596 Independent Study Variable cr. (R12) Offered autumn and spring. Prereq., consent of instr.
G 597 Research Variable cr. (R12) Offered autumn and spring. Prereq., consent of instr.
G 598 Cooperative Education Experience Variable cr. (R12) 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 Internship Services office.
G 599 Thesis Variable cr. (R6) Offered autumn and spring. Prereq., consent of instr.
G 600 Mathematics Colloquium 1 cr. (R3) 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. (R12) Offered autumn and spring. Prereq., consent of instr.
G 620 Graduate Seminar in Algebra Variable cr. (R12) Offered autumn and spring. Prereq., consent of instr.
G 630 Graduate Seminar in Geometry/Topology Variable cr. (R12) Offered autumn and spring. Prereq., consent of instr.
G 640 Graduate Seminar in Probability and Statistics Variable cr. (R12) Offered autumn and spring. Prereq., consent of instr.
G 650 Graduate Seminar in Analysis Variable cr. (R12) Offered autumn and spring. Prereq., consent of instr.
G 670 Graduate Seminar in Numerical Analysis Variable cr. (R12) Offered autumn and spring. Prereq., consent of instr.
G 680 Graduate Seminar in Combinatorics and Optimization Variable cr. (R12) 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. (R12) Offered autumn and spring. Prereq., consent of instr.
G 699 Dissertation Variable cr. (R9) Offered autumn and spring.
Faculty
Professors
Richard W. Billstein, Ed.D., The University of Montana, 1972
Rudy A. Gideon, Ph.D., University of Wisconsin, 1970
James J. Hirstein, Ed.D., University of Georgia, 1976 (Chair)
Leonid Kalachev, Ph.D., Moscow State University, 1987
P. Mark Kayll, Ph.D., Rutgers University, 1994 (Associate Chair)
Johnny W. Lott, Ph.D., Georgia State University, 1973
Jennifer McNulty, Ph.D., University of North Carolina at Chapel Hill, 1993
D. George McRae, Ph.D., University of Washington, 1967
David A. Patterson, Ph.D., University of Iowa, 1984
Karel M. Stroethoff, Ph.D., Michigan State University, 1987
Thomas Tonev, Ph.D., Moscow State University, 1973
Associate Professors
Jonathan Graham, Ph.D., North Carolina State University, 1995
Libby Krussel, Ph.D., Oregon State University, 1994 (on leave 20042005)
Greg St. George, Ph.D., The University of Montana, 1989
Brian Steele, Ph.D., The University of Montana, 1995
Nikolaus Vonessen, Ph.D., Massachusetts Institute of Technology, 1988
Assistant Professors
John Bardsley, Ph.D., Montana State University, 2002
Adam Nyman, Ph.D., University of Washington, 2001
Bharath Sriraman, Ph.D., Northern Illinois University, 2002
Lecturers
Lauren Fern, M.S., Northern Illinois University, 1994
Matt Roscoe, M.Ed., The University of Montana, 2000
Regina Souza, Ph.D., Massachusetts Institute of Technology, 1990
Carol Ulsafer, Ph.D., The University of Montana, 1984
Emeritus Professors
William R. Ballard, Ph.D., University of Chicago, 1957
Charles A. Bryan, Ph.D., University of Arizona, 1963
William R. Derrick, Ph.D., Indiana University, 1966
Stanley I. Grossman, Ph.D., Brown University, 1969
Gloria C. Hewitt, Ph.D., University of Washington, 1962
Don O. Loftsgaarden, Ph.D., Montana State University, 1964
Merle E. Manis, Ph.D., University of Oregon, 1964
Robert W. McKelvey, Ph.D., University of Wisconsin 1954
William M. Myers, Jr., Ph.D., Ohio State University, 1952
Howard E. Reinhardt, Ph.D., University of Michigan, 1959
George F. Votruba, Ph.D., University of Michigan, 1964
I. Keith Yale, Ph.D., University of California, Berkeley, 1966