20102011 General Catalog ARCHIVED CATALOG: To search archives, use search box above. See current catalog at catalog.usu.edu.
Mathematics and Statistics


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Department Head: D. Richard Cutler
Location: Lund Hall 211
Phone: (435) 7970244
FAX: (435) 7971822
Email: mathstat@cc.usu.edu
WWW: http://www.math.usu.edu/
Assistant Department Head:
Kathryn L. Turner, Lund Hall 211B, (435) 7979174, kathryn.turner@usu.edu
Undergraduate Program Director:
Daniel C. Coster, Lund Hall 310, (435) 7972815, dan.coster@usu.edu
Graduate Program Director:
Piotr S. Kokoszka, Lund Hall 321, (435) 7970746, piotr.kokoszka@usu.edu
Mathematics Education Program Director:
James S. Cangelosi, Lund Hall 325C, (435) 7971415, jim.cangelosi@usu.edu
Actuarial Science Program Coordinator:
Daniel C. Coster, Lund Hall 310, (435) 7972815, dan.coster@usu.edu
Undergraduate Advising:
Linda Skabelund, Lund Hall 201, (435) 7970268, linda.skabelund@usu.edu
Degrees offered: Bachelor of Science (BS), Bachelor of Arts (BA), and Master of Science (MS) in Mathematics; BS and BA in Mathematics Education; BS in Composite MathematicsStatistics Education; BS in Composite Mathematics/Statistics; Master of Mathematics (MMath); BS, BA, and MS in Statistics; MS in Industrial Mathematics; Doctor of Philosophy (PhD) in Mathematical Sciences
Graduate specializations: PhD in Mathematical Sciences—College Teaching, Interdisciplinary Studies, Pure and Applied Mathematics, and Statistics
Undergraduate Programs
Objectives
The Department of Mathematics and Statistics offers a variety of programs and courses designed to prepare students for careers in teaching and for positions as mathematicians and statisticians in industry and government. The department also provides service courses for students in many other disciplines and contributes to the University Studies program by providing Quantitative Literacy and Quantitative Intensive classes.
Placement of New Students
Current mathematics ACT/SAT scores, Math Placement Exam scores, and Advanced Placement (AP) calculus and statistics scores are used for placement in 1000level and 2000level mathematics and statistics courses. A current score is defined as a score from an exam taken within the Math Prerequisite Acceptability Time Limit (MPATL).
Prerequisites for MATH 1050 , MATH 1060 , MATH 1100 , MATH 1210 , MATH 2020 and, STAT 2300 must be completed on or after (not before) the following dates, in order to fall within the MPATL for the listed semester: fall semester—August 15 of the previous year; spring semester—January 1 of the previous year; summer semester—June 1 of the previous year.
Students who are registering for a math class at USU for the first time who have a math ACT score of less than 23 or a math SAT score of less than 540 (whether current or not) are required to take the Math Placement Exam administered by the Department of Mathematics and Statistics. A student’s score on the Math Placement Exam will be used to determine his or her placement in appropriate mathematics or statistics course.
Students who are registering for a math class for the first time who have a current math ACT score of at least 23 or a current math SAT score of at least 540 do not need to take the Math Placement Exam. However, for each of the courses listed below, one of the following prerequisites, achieved within the MPATL, is required for enrollment.
For students needing a satisfactory score on the Math Placement Exam (MPE) to meet an enrollment requirement for any course listed below, the deadline for meeting this requirement is the end of the first week of classes. A maximum of three attempts to achieve a satisfactory score on the MPE is allowed each semester.
MATH 1010
Math ACT score between 18 and 22 (Math SAT score between 480 and 530) and satisfactory Math Placement Exam score or Math ACT score of at least 23 (Math SAT score of at least 540) or Grade of C or better in MATH 0900 or Satisfactory score on Math Placement Exam
MATH 1030 (not currently offered)
Math ACT score of at least 23 (Math SAT score of at least 540) or Grade of C or better in MATH 1010 or Satisfactory score on Math Placement Exam
MATH 1050
Math ACT score of at least 23 (Math SAT score of at least 540) or Grade of C or better in MATH 1050 or AP Calculus AB exam score of 3 or higher or Satisfactory score on Math Placement Exam
MATH 1060
Math ACT score of at least 23 (Math SAT score at least 540) or Grade of C or better in MATH 1010 (or MATH 1050 ) or AP Calculus AB exam score of 3 or higher or Satisfactory score on Math Placement Exam
MATH 1100
Math ACT score of at least 25 (or Math SAT score of at least 580) or Grade of C or better in MATH 1050 or Satisfactory score on Math Placement Exam
MATH 1210
Math ACT score of at least 27 (Math SAT score of at least 620) or Grade of C or better in MATH 1050 and MATH 1060 or AP Calculus AB exam score of 3 or higher or Satisfactory score on Math Placement Exam
MATH 2020
Math ACT score of at least 25 (Math SAT score of at least 580) or Grade of C or better in MATH 1050 or Satisfactory score on Math Placement Exam
STAT 1040
Math ACT score of at least 23 (Math SAT score of at least 540) or Grade of C or better in MATH 1010 or Satisfactory score on Math Placement Exam
Entering students with current passing scores on AP calculus or statistics exams will be awarded credits as shown below:
AP Test 
Score 
Credits 
USU Credit Awarded 
Calculus AB 
3 
6 
3 (QL) credits + 3 elective credits 

45 
6 
1210 (QL) (4) + 2 elective credits 




Calculus BC 
34 
6 
MATH 1210 (QL) (4) + 2 elective credits 

5 
8 
MATH 1210 (QL) (4) + MATH 1220 (QL) (4) 




Statistics 
35 
3 
STAT 2000 (QI) (3) 
Even if not required, students may opt to take the Math Placement Test through the Department of Mathematics and Statistics, strictly for advising purposes.
The calculus courses MATH 1210 , MATH 1220 , and MATH 2210 are designed for students majoring in mathematics, the sciences, and engineering. MATH 1100 (Calculus Techniques) is designed primarily for students majoring in business. All students in calculus classes need strong backgrounds in the material covered in MATH 1010 and MATH 1050 In addition, the MATH 1210 , MATH 1220 , MATH 2210 sequence requires a sound understanding of trigonometry (MATH 1060 ).
Students with outstanding mathematics records in high school and transfer students with some experience in calculus may wish to consult with a departmental advisor prior to registration.
Departmental Admission Requirements
 New freshmen admitted to USU in good standing qualify for admission to the major.
 Transfer students from other institutions need a 2.2 transfer GPA, and students transferring from other USU majors need a 2.0 total GPA for admission to this major in good standing.
 Students may be admitted to the Mathematics Education major by satisfying either of the above conditions. However, in order to be admitted to the Secondary Teacher Education Program (STEP), and to graduate from the Mathematics Education major (and minor), students must have a cumulative GPA of at least 3.0 in the equivalent of MATH 1210 , MATH 1220 , and MATH 2210 , and an overall GPA of at least 2.75.
University Requirements
All students in the Department of Mathematics and Statistics must satisfy the requirements of USU’s University Studies program.
Suggested Fouryear Plans
Suggested semesterbysemester fouryear plans for students working toward a Bachelor of Science or Bachelor of Arts degree within the Department of Mathematics and Statistics can be found at: http://www.usu.edu/degreeplans/
Students should consult with their advisor to develop a plan of study tailored to their individual needs and interests.
Departmental Honors
Students who would like to experience greater academic depth within their major are encouraged to enroll in departmental honors. Through original, independent work, Honors students enjoy the benefits of close supervision and mentoring, as they work oneonone with faculty in select upperdivision departmental courses. Honors students also complete a senior project, which provides another opportunity to collaborate with faculty on a problem that is significant, both personally and in the student’s discipline. Participating in departmental honors enhances students’ chances for obtaining fellowships and admission to graduate school. Minimum GPA requirements for participation in departmental honors vary by department, but usually fall within the range of 3.303.50. Students may enter the Honors Program at almost any stage in their academic career, including at the junior (and sometimes senior) level. The campuswide Honors Program, which is open to all qualified students regardless of major, offers a rich array of cultural and social activities, special classes, and the benefit of Honors early registration. Interested students should contact the Honors Program, Main 15, (435) 7972715, honors@usu.edu. Additional information can be found online at: http://www.usu.edu/honors/
Additional Information
Students who enter the University with AP credit in Mathematics and/ or Statistics, and about 30 additional AP or CLEP credits, may be able to complete both a BS and an MS degree within five years or less. Interested students should consult with a departmental undergraduate advisor.
For detailed information about requirements for majors and minors within the Mathematics and Statistics Department, see the major requirement sheet, which is available from the department, or online at: http://www.usu.edu/majorsheets/
Financial Support
The department offers several one, two, and fouryear scholarships to qualified students who enroll as fulltime Mathematics, Mathematics Education, or Statistics majors. The winner of the Hunsaker Scholarship receives a cash award each semester for two years. This award is given in addition to any fouryear scholarship or tuition waiver for which the student is eligible. During the final two years, the recipient is expected to work as a grader for the department. The department also offers other scholarships (Elich, Ellis, van Vliet, and departmental). The amount of these scholarships varies from year to year. The Ellis Scholarship is awarded to a junior or senior Mathematics Education major, and the recipient is selected by the department. To apply for any of these scholarships (except for the Ellis Scholarship, for which there is no application) fill out the scholarship application form located at http://www.math.usu.edu/PDF/scholarship%20appl%20Oct08.pdf, and send a statement of qualifications, including high school transcripts and SAT or ACT scores, and three letters of recommendation to:
Scholarship Committee
Department of Mathematics and Statistics
Utah State University
3900 Old Main Hill
Logan UT 843223900
Applications must be received by March 15.
Learning Objectives
All students having majors within the Department of Mathematics and Statistics are expected to achieve competency in: (1) precalculus algebra; (2) calculus of one and several variables; (3) ordinary differential equations; (4) linear algebra/matricies, eigenvalues/ eigenvectors, determinant, rank; and (5) analysis (introduction to formal proofs/analysis theory).
Students enrolled in specific departmental majors should also havecompetence in additional areas pertaining to their major. These areas are listed in the following paragraphs.
Mathematics Major
(1) algebraic structures; (2) analysis/advanced calculus; (3) complex variables; (4) topology; (5) algebraic theory; and (6) partial differential equations.
Statistics Major
(1) theory of probability and statistics; (2) linear regression/time series; (3) experiment design; and (4) one or more of sampling, categorical analysis, multivariate analysis, quality control.
Mathematics Education Major (including Composite MathematicsStatistics Education)
(1) algebraic structures; (2) probability; (3) history of mathematics; (4) methods for secondary school teaching of mathematics and/or statistics; and (5) inservice teaching experiences.
Other Majors and Emphases (e.g., Computational Mathematics Emphasis, Actuarial Science Emphasis, etc.)
Replace general competencies in traditional areas (i.e., algebra, topology, analysis) with specific topics related to the specialized emphasis. For example, students in the Computational Mathematics Emphasis need the ability to write computer code to solve linear, nonlinear, stochastic, and (partial and ordinary) differential equations; and students in the Actuarial Science Emphasis need two semesters of actuarial mathematics.
Assessment
Assessment of General Education Courses (MATH 1050 and STAT 1040 )
Beginning with Spring Semester 2004, the department has conducted an annual assessment of student performance in primary General Education courses (including MATH 1050 and STAT 1040 ). The performance of approximately 100 randomly selected students from each of MATH 1050 and STAT 1040 was evaluated by topic area on the common finals of these courses. Summary results will be available soon. The process was repeated for Spring Semester 2005. Together, these two years of data provide a baseline against which future groups of students will be compared. Weaknesses in topic learning will then be identified, and the Undergraduate Committee and course supervisors will provide feedback to instructors in an effort to bring overall student performance to target levels.
Core content of these courses changes infrequently and is primarily addressed through the selection of textbooks at threeyear to fiveyear intervals. Primary assessment of these courses is through semester evaluations and final examination scores and course grade profiles. Competency in these areas is essential for any student majoring in mathematics or statistics.
Assessment of Upperdivision Major Courses
These courses are reevaluated by subcommittees of the Undergraduate Committee in terms of: level and appropriateness of content relative to learning objectives, textbook selection, final examinations, course grades, and student evaluations. At twoyear to fiveyear intervals, courses are redesigned if the subject matter develops beyond traditional norms, or if market demand indicates that an underutilized course should be replaced by a course having greater demand (e.g., development of a new cryptography course).
Undergraduate Research Opportunities
Students interested in undergraduate research opportunities in the Department of Mathematics and Statistics at Utah State University should begin by contacting the department head and undergraduate research liaison, D. Richard Cutler, (435) 7970244, richard.cutler@usu.edu.
Several departmental faculty members have engaged in successful undergraduate research projects. These faculty members, along with their research areas, include: James Powell (mathematical modeling of pine beetle infestations), Ian Anderson (differential geometry applications to theoretical and applied physics), and Richard Cutler (analysis of epidemiological and environmental data). In general, undergraduate research offers students an excellent opportunity to explore mathematical and statistical theory and practice under the guidance of an experienced researcher, to focus their own course selection on particular career paths and research areas (including graduate school), to coauthor professional publications, and to actively make presentations at conferences or local seminars.
Graduate Programs
Admission Requirements
See the general admission requirements for graduate programs at Utah State University in this catalog. In general, students wishing to pursue graduate studies in mathematics or statistics should have a bachelor’s degree in mathematics, statistics, or a closely related field, with extensive coursework in one of the departmental disciplines. The department requires a score of 700 on the quantitative section of the GRE. International applicants must have a TOEFL score of 250 on the computerbased test or a score of 100 on the internetbased test.
Students entering the Master of Mathematics (MMath) program must either possess a valid secondary school teaching license or be concurrently enrolled in a secondary school teacher licensure program.
Course Requirements
Departmental requirements change from time to time. Check with the Department of Mathematics and Statistics for the list of requirements currently in effect.
Research
Mathematics research opportunities within the department are many and varied, and students are urged to contact faculty about mutual interests at as early a stage as feasible. The interdisciplinary option permits and encourages study with a broad spectrum of outstanding nationally recognized University research programs.
Financial Assistance
Graduate students in the PhD program, the MMath program, and the Plan A and B options of the MS programs are eligible for teaching assistantships in the department. Duties of graduate teaching assistants may include full responsibility as instructors for introductory mathematics or statistics courses, leading recitations, and (in rare situations) tutoring and paper grading. Stipends are competitive and may include health insurance benefits. All graduate student stipends described here carry with them a waiver of all nonresident tuition. PhD students with stipends also receive a waiver of resident tuition. The department is also allocated a small number of resident tuition waivers for MS students each year. The department is able to support most PhD students and some MS students with summer teaching assignments. Mathematics and Statistics faculty members who have research grants may choose to partially or fully support students they are advising.
Mathematics and Statistics Faculty
Professors
Ian M. Anderson, differential geometry, global analysis
LeRoy B. Beasley, matrix theory, linear algebra, combinatorics
James S. Cangelosi, mathematics education, psychometrics
Lawrence O. Cannon, topology, mathematics education
Daniel C. Coster, experimental design, linear models
Adele Cutler, statistical computing
D. Richard Cutler, environmental statistics, epidemiology
Mark E. Fels, differential geometry
E. Robert Heal, analysis, statistics, mathematics education
Piotr S. Kokoszka, statistical modeling, time series analysis
James A. Powell, applied mathematics, mathematical biology
Russell C. Thompson, differential equations
ZhiQiang Wang, nonlinear differential equations, nonlinear analysis
Stanley C. Williams, measure theory, modern analysis
Professors Emeritus
Ronald V. Canfield, multivariate and industrial statistics
Chris S. Coray, numerical analysis
Duane Loveland, geometric topology, continuum theory
Jerry Ridenhour, differential equations
Donald V. Sisson, statistical methods, experimental design
Associate Professors
Christopher D. Corcoran, computational biostatistics
Joseph V. Koebbe, numerical analysis, applied mathematics
Juergen Symanzik, computational and graphical statistics
Kathryn L. Turner, numerical analysis, optimization, linear algebra
Dariusz M. Wilczynski, geometric and algebraic topology
Associate Professors Emeritus
Wayne R. Rich, mathematics education
E. Eugene Underwood, matrix theory, linear algebra
Assistant Professors
David E. Brown, discrete mathematics, graph theory
Nathan C. Geer, lowdimensional topology, quantum and super algebras
Mevin B. Hooten, Bayesian methods; hierarchical models; ecological and environmental statistics; spatial, temporal, and spatiotemporal statistics
Peg Howland, numerical linear algebra
Brynja R. Kohler, mathematics education, mathematical biology
Nghiem V. Nguyen, partial differential equations, nonlinear evolution problems, fluid mechanics, nonlinear waves
Kady Schneiter, mathematics education, statistics
John R. Stevens, bioinformatics, applied statistics, metaanalysis
Principal Lecturer
David D. Bregenzer, mathematics, statistics Senior Lecturers
Bryan Bornholdt, mathematics, mathematics education
Claudia Mora Bornholdt, mathematics, mathematics education
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