Department of Mathematical Sciences
Leonid Kalachev, 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 M 171 or 181, 172 or 182, 221(MATH 152, 153, 221), 273 (MATH 251) (except for students in the Mathematics Education option), M 300 (MATH 300) (except for students in the Mathematics Education option), M 307 (MATH 305) and six additional courses from the following list (at least three of the six must be numbered 400 or above): M 301, 311, 325, 326, 361, 362, 381, 412, 414, 429, 431, 432, 439, 440, 472, 473, 485 and STAT 341, 421 ,422. All mathematical sciences courses counted toward the major must be passed with a grade of C– or better and a 2.00 grade point average is required for these courses. 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 M 381, 431, 432, 472, 473 (MATH 351, 421, 422, 451, 452).
Mathematics Education Option
M 301, 326, 429, 431, 439, (MATH 301, 326, 406, 421, 431) STAT 341 (MATH 341); either M 273 (MATH 251) or one additional course chosen from the above list for the six-course requirement; and the completion of certification requirements for teaching in secondary schools to include C&I 430.
Statistics Option
STAT 341, 421, 422 (MATH 341, 441, 442). (Additional mathematics and statistics courses chosen with advisor.)
Combinatorics and Optimization Option
M 361, 362, 485 (MATH 381, 382, 485); and one course chosen from STAT 341 (MATH 341) M 414, 440 (MATH 414, 471), or CS 332.
Applied Mathematics Option
M 311, 412, 414 (MATH 311, 412, 414) and one of M 472 or 440 (MATH 452 or 471). (M 381 and M 485 (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 two-semester language sequence as specified under "Group III: Modern and Classical Languages" in the General Education section of the Catalog, 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, 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 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: M 429 (Math 406), or any other approved General Education upper–division Writing course, OR a senior thesis M 499 (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: M 171 (or 181)-172 (or 182), 221, 273, 307 or (225) ( MATH 152–153, 221, 251, 305 (or 225)), and twelve credits of mathematical sciences selected from the following list: M 311, 325, 326, 361, 362, 381, 412, 414, 429, 431, 432, 439, 440, 445, 472, 473, 485 and STAT 341, 421, 422, 451, 452 (MATH 311, 325, 326, 341, 351, 381, 382, 406, 412, 414, 421, 422, 431, 441, 442, 444, 445, 451, 452, 471, 475, 485).
The computer science requirements are: CS 121, 131–132 or 133, 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 M 429 (MATH 406) and STAT 451, 452 (MATH 444 and 445)).
Other requirements are: One of the sequences BIOL 108N, 109N, 110N; CHMY 141N, 143N (CHEM 161N, 162N); or PHYS 211N-214N (221N–222N). In addition, WRIT 222 (FOR 220), and either COMM 111A or COMM 242.
Each student plans a program in consultation with a computer science and a mathematical sciences advisor. Students planning to attend graduate school in computer science or the mathematical sciences should consult with their respective advisors.
The upper–division writing requirement is one of the following: CS 415E, M 429 (MATH 406), any other approved General Education upper–division writing course, or a senior thesis (CS 499 or M 499 (MATH 499)).
Suggested Curricula:
Applied Math–Scientific Programming: M 311, 412, 414 (MATH 311, 412, 414), and one course chosen from STAT 341 (MATH 341), M 381, 473, 472, 440 (MATH 351, 451, 452, 471). Three courses chosen from CS 344, 446, 477, 486.
Combinatorics and Optimization–Artificial Intelligence: M 261, 362 (MATH 381, 382), and two courses chosen from M 325, 414, 485 (MATH 325, 414, 485) STAT 341 (MATH 341); and CS 344, 455, and 457.
Statistics–Machine Learning: STAT 341, 421 (MATH 341, 441), and two courses chosen from M 325, 362, 485 (MATH 325, 382, 485) STAT 422 (MATH 442). Three courses chosen from CS 365, 455, 457, 458, and 486
Algebra–Analysis: M 381, 431 (MATH 351, 421), and two courses chosen from M 326, 432, 473, 472 (MATH 326, 422, 451, 452); CS 344, 441, and one other course.
Suggested Course of Study
| First Year |
A |
S |
| M 171-172 (MATH 152-153) Calculus I, II |
4 |
4 |
| WRIT 101 (ENEX 101) Composition and other General Education Courses (including two sciences courses) |
12 |
12 |
|
16 |
16 |
| Second Year |
A |
S |
| M 221 (MATH 221) Intro to Linear Algebra |
4 |
– |
| M 273 (MATH 251) Multivariable Calculus |
4 |
– |
| M 307 (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 M, MATH, or STAT courses listed in a UM-Missoula Catalog (or in transfer courses equivalent to such courses), M courses must be numbered 115 or higher, and MATH courses must be numbered 111 or higher. Courses must include: (a) one of M 162 or 172 or 182 (MATH 150 or 153), and (b) at least three 3– or 4– credit courses at the 300 level or above. M 172 or 182 (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 for these courses. 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 M 171-172, 221, 301, 307, 326, 439 (MATH 152-153, 221, 301, 305, 326, 431), and STAT 341, (MATH 341 ). 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 (M)
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 STAT 216 (MATH 241) may take M 115 (MATH 117) for credit.
See the College of Technology section for Introductory Algebra, M 090 (MAT 005), and Intermediate Algebra, M 095 (MAT 100).
Statistics (STAT)
- U 216 (MATH 241) Introduction to Statistics 4 cr. Offered autumn and spring. Prereq., M 115 (MATH 117)or consent of instr. Introduction to major ideas of statistical inference. Emphasis is on statistical reasoning and uses of statistics.
- UG 341 (MATH 341) Introduction to Probability and Statistics 3 cr. Offered autumn and spring. Prereq., M 162 or 172 (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 421 (MATH 441) Probability Theory 3 cr. Offered autumn. Prereq., M 273 (MATH 251) and STAT 341 (MATH 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 422 (MATH 442) Mathematical Statistics 3 cr. Offered spring. Prereq., STAT 421 (MATH 441). Continuation of 421.
- UG 451 (MATH 444) Statistical Methods I 3 cr. Offered autumn. Prereq., one year of college mathematics including M 115 (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 452 (MATH 445) Statistical Methods II 3 cr. Offered spring. Prereq., STAT 451 (MATH 444). Continuation of STAT 451 (MATH 444). May not be counted toward a major in mathematics. Multiple regression, experimental design, analysis of variance, other statistical models.
- UG 457 (MATH 447) Computer Data Analysis I 1 cr. Offered autumn. Coreq., STAT 451 (MATH 444) or consent of instr. An introduction to software for doing statistical analyses. Intended primarily for students in STAT 451 (MATH 444).
- UG 458 (MATH 448) Computer Data Analysis II 1 cr. Offered spring. Coreq., STAT 452 (MATH 445) or consent of instr. Continuation of STAT 457 (Math 447). Intended primarily for students in STAT 452 (MATH 445).
- G 540 (MATH 540) Probability and Statistics for Teachers 3 cr. Offered intermittently in summer. Prereq., STAT 341 (MATH 341) or equiv. A survey of modern topics in probability and statistics. Emphasis will be on applications of statistics in real situations.
- G 541 (MATH 541) Advanced Mathematical Statistics 3 cr. Offered intermittently. Prereq., STAT 422 (MATH 442). Advanced theory of estimation and hypothesis testing including large sample theory.
- G 542 (MATH 542) Applied Linear Models 3 cr. Offered autumn even-numbered years. Prereq., STAT 422 (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 (MATH 543) Applied Multivariate Statistical Analysis 4 cr. Offered spring even-numbered years. Prereq., STAT 452 or 422 (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 (MATH 544) Topics in Probability and Statistics 3 cr. (R-12) Offered intermittently. Prereq., STAT 422 (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 (MATH 545) Theory of Linear Models 3 cr. Offered autumn odd-numbered years. Prereq., STAT 422 (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 (MATH 547) Applied Nonparametric Statistics 3 cr. Offered autumn odd-numbered years. Prereq., STAT 421 or 452 (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 (MATH 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 640 (MATH 640) Graduate Seminar in Probability and Statistics Variable cr. (R-12) Offered autumn and spring. Prereq., consent of instr.
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 (Chair)
- P. Mark Kayll, Ph.D., Rutgers 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
- Bharath Sriraman, Ph.D., Northern Illinois University, 2002
- Emily Stone, Ph.D., Cornell University, 1989
- 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
- John Bardsley, Ph.D., Montana State University, 2002
- Solomon Harrar, Ph.D., Bowling Green State University, 2004
- Greg St. George, Ph.D., The University of Montana, 1989
- Brian Steele, Ph.D., The University of Montana, 1995
Assistant Professors
- Eric Chesebro, Ph.D., University of Texas at Austin, 2006
- Jennifer Halfpap, Ph.D., University of Wisconsin, 2005
- Ke Wu Norman, Ph.D., University of Minnesota, 2008
- Kelly McKinnie, Ph.D., University of Texas at Austin, 2006
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
- 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
