Mathematical Sciences

Department of Mathematical Sciences

Special Degree Requirements
Suggested Course of Study
Courses
Faculty

David Patterson, 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), MATH 300 (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). The following courses do not count toward the six additional 3– or 4–credit courses: MATH 444 and 445, and courses numbered 390–399 and 490–499. 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

Four courses chosen from MATH 351, 421, 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

MATH 381, 382, 485; and one course chosen from 341, 414, 471, or CS 332.

Applied Mathematics Option

MATH 311, 412, 414 and one of 452 or 471. (MATH 351 and 485 are recommended.)

Major Requirements in Courses Outside Mathematics

Except for students in the Mathematics Education option and for students presenting a second major within the University, students must either complete the foreign language requirement as specified in 1. within the Foreign Language/Symbolic Systems section under the General Education requirements or take two courses chosen from CS 101, 131, 132, 201, 207.
All mathematics majors, except those selecting the mathematics education option, must complete 18 credits in at most three sciences selected from astronomy, biology, chem¬istry, com¬puter 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 within the University, or for the student with a mathematics education option to complete an additional teaching minor or major.
The upper–division writing requirement for Mathematical Sciences majors consists of:
1. Math 406, or any other approved General Education upper–division Writing course,
  OR
2. a senior thesis (MATH 499).

Requirements for a B.S. Degree with a Combined Major in Mathematical Sciences–Computer 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–” and a 2.0 grade point average is required in all courses which follow.
The mathematical sciences requirements are: 152–153, 221, 251, 305 (or 225), and twelve credits of 3– or 4–credit MATH electives selected from courses numbered above 305 (not including courses numbered 390–399 and 490–499).
The computer science requirements are: 121, 131–132, 241–242, 281, 332 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 4–credit courses numbered 400 or above, with at least one chosen from each department (not including MATH 406, 444, and 445).
Other requirements are: One of the sequences BIOL 108N, 109N, 110N; CHEM 161N, 162N; or PHYS 221N–222N. In addition, FOR 220, and either COMM 111A or COMM 242. The upper–division writing requirement is one of the following: CS 415E, MATH 406, any other approved General Education upper–division writing course, or a senior thesis (CS 499 or MATH 499).
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, 446, 471, 477, 486.
Combinatorics and Optimization–Artificial Intelligence: MATH 381, 382, and two courses chosen from MATH 325, 341, 414, 485; and 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, 457, 458, 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

First Year	A	S
MATH 152 153 Calculus I, II	4	4
ENEX 101 Composition and other General Education Courses (including two sciences courses)	12	12
	16	16
Second Year	A	S
MATH 221 Linear Algebra	4	–
MATH 251 Calculus III	4	–
MATH 305 Introduction to Abstract Mathematics	–	3
General Education courses, additional science courses and electives	9	13
	17	16

Requirements for a Minor

To earn a minor in mathematics the student must earn 23 credits in mathematics courses numbered 111 or higher, including: (a) MATH 150 or 153, and (b) at least three 3– or 4– credit courses at the 300 level or above. MATH 153 (Calculus II) is recommended since it is a prerequisite for many upper–division mathematics courses. All courses counted toward the minor must be passed with a grade of C– or better and a 2.00 grade point average is required. A handout with detailed advice for math minors, including suggested curricula, is available on the math department’s home page.

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 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. Credits beyond this maximum do not count toward a degree.

Mathematical Sciences (MATH)

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, and Intermediate Algebra, MAT 100.

U 107 Contemporary Mathematics 3 cr. Offered every term. Prereq., MAT 005 with a grade of B–or better, or MAT 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., MAT 005 with a grade of B– or better, or MAT 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 111 College Algebra 3 cr. Offered autumn and spring. Prereq., MAT 100 or appropriate placement score. Intended to strengthen algebra skills. The study of functions and their inverses; polynomial, rational, exponential, and logarithmic functions. Credit not allowed for both MATH 111 and any of MAT 118, MAT 120, and MATH 121.
U 112 Functions and Trigonometry 3 cr. Offered autumn and spring. Prereq., MATH 111 or appropriate placement score. Preparation for calculus based on college algebra. Review of functions and their inverses, exponential and logarithmic functions. Trigonometric functions and identities, polar coordinates and an optional topic such as conic sections or parametric functions. Credit not allowed for both MATH 112 and any of MAT 119, MAT 120, and MATH 121.
U 117 Probability and Linear Mathematics 3 cr. Offered every term. Prereq., MAT 005 with a grade of B– or better, or MAT 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., appropriate placement score. A one semester preparation for calculus (as an alternative to MATH 111–112). Functions of one real variable are introduced in general and then applied to the usual elementary functions, namely polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, and miscellaneous others. Inverse functions, polar coordinates and trigonometric identities are included. Credit not allowed for both MATH 121 and any of MAT 110, MAT 118, MAT 120, MATH 111 or MATH 112.
U 130 Mathematics for Elementary Teachers 5 cr. Offered autumn and spring. Prereq., MAT 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., appropriate placement score or one of MATH 111, 112, or 121. 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 112 or 121 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. (R–6) 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 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 150 or 152 or consent of instr. 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 intermittently. 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 291 Practicum 1–3 cr. (R–3) Offered intermittently. Prereq., consent of instr.
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.
U 300 Undergraduate Math Seminar 1 cr. (R–6) Offered every semester. Prereq., MATH 152. Discussion seminar focused on topics and issues of interest to students in the mathematical sciences.
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. Students planning to take both MATH 221 and 305 are encouraged to take MATH 221 first.
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 150 or 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 150 or 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 150 or 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 390 Supervised Internship 1–9 cr. (R–9) Prereq., consent of dept.
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 Internship Variable cr. 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. A maximum of 6 credits of Internship (198, 298, 398, 498) may count toward graduation.
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 221 and 305 or consent of instr. 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.
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 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. (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 Internship Variable cr. 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. A maximum of 6 credits of Internship (198, 298, 398, 498) may count toward graduation.
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 Internship 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 Internship Services office.
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 690 Supervised Internship Variable cr. (R–6) Offered autumn and spring. Prereq., consent of department. Supervised Teaching Internship.
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

Professors

Richard W. Billstein, Ed.D., The University of Montana, 1972
Jonathan Graham, Ph.D., North Carolina State University, 1995
James J. Hirstein, Ed.D., University of Georgia, 1976
Leonid Kalachev, Ph.D., Moscow State University, 1987
P. Mark Kayll, Ph.D., Rutgers University, 1994 (Associate Chair)
Libby Knott, Ph.D., Oregon State University, 1994
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 (Chair)
Karel M. Stroethoff, Ph.D., Michigan State University, 1987
Thomas Tonev, Ph.D., Moscow State University, 1973
Nikolaus Vonessen, Ph.D., Massachusetts Institute of Technology, 1988

Associate Professors

Greg St. George, Ph.D., The University of Montana, 1989
Adam Nyman, Ph.D., University of Washington, 2001
Bharath Sriraman, Ph.D., Northern Illinois University, 2002
Brian Steele, Ph.D., The University of Montana, 1995
Emily Stone, Ph.D., Cornell University, 1989

Assistant Professors

John Bardsley, Ph.D., Montana State University, 2002
Jennifer Halfpap, Ph.D., University of Wisconsin, 2005
Solomon Harrar, Ph.D., Bowling Green State University, 2004
Ke Wu Norman, Ph.D., University of Minnesota, 2008

Lecturers

Lauren Fern, M.S., Northern Illinois University, 1994
Regina Souza, Ph.D., Massachusetts Institute of Technology, 1990

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
Rudy A. Gideon, Ph.D., University of Wisconsin, 1970
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
Johnny W. Lott, Ph.D., Georgia State University, 1973
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

The University of Montana

2008 - 2009 Course Catalog