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Course Description

Department of Mathematics and Statistics

Dr. David C. Carothers, Head

Phone: (540) 568-6184
E-mail: carothdc@jmu.edu
Web site: www.math.jmu.edu


Professors
C. Chiang, D. Carothers, R. Domangue, C. Droms, J. Hanson, J. Klippert, C. Lyons, G. Marrah, D. Pruett, G. Parker, G. Peterson, J. Sochacki

Associate Professors
S. Garren, P. Kohn, R. Lee, J. Liu, J. Marafino, C. Smith, L. VanWyk, D. Warne, Y. Yesilcay

Assistant Professors
J. Fitzgerald, H. Hamdan, J. Kidd, L. Taalman, P. Warne

Instructors
A. Casiple


Mission Statement
The Department of Mathematics and Statistics provides a program of study in the mathematical sciences, which meets the needs of a wide variety of students and makes a continuing contribution to the advancement of mathematical and statistical knowledge and its dissemination. The program provides opportunities for in-depth study that can lead to careers as mathematicians and statisticians in private and public sectors, teachers of mathematics and further study in graduate school. The program provides support for the mathematical and statistical needs of students in the natural sciences, integrated sciences, social sciences and professional and pre-professional programs. The program meets the general education needs of all students, providing an understanding of mathematical and statistical thinking and approaches to problem solving. We are committed to promoting mathematics and statistics as an art of human endeavor as well as a fundamental method of inquiry into the sciences and a vast array of other disciplines. We are committed to encouraging an attitude of appreciation and support for mathematics and statistics in current university students and, through them, the next generation of citizens. We are also committed to fostering an appreciation for the effective use of applied mathematics and statistics in connection with and support of other disciplines for those students majoring in other subjects.


Goals
As a major in mathematics or statistics a student can expect to use and build on skills such as
  • Thinking critically,
  • Formulating and solving problems, and
  • Communicating solutions clearly, both orally and in writing which have been gained in previous courses in mathematics, statistics and other areas. As the breadth of knowledge of the subject grows, students gain an increased understanding and appreciation of the fact that mathematics is truly a universal language whose creation and applications cut across all boundaries of race, class, culture and time. There also will be opportunities for students to experience the challenge and rewards of faculty-mentored research, individually or as a member of a team, as they investigate mathematical and statistical problems that extend beyond those normally encountered in the classroom. Students increase their abilities to prove theorems, understand complex structures and apply mathematics and statistics in many real-world settings. The program students choose will make it possible for them to acquire strong preparation for graduate work or for professional applications in mathematics and statistics, teaching, natural and social sciences or other technical areas.


The Department of Mathematics and Statistics offers the B.A. and B.S. degrees with a major in mathematics and the B.S. degree with a major in statistics. Within the mathematics major, concentrations are available in actuarial/financial mathematics, computational and applied mathematics, computational sciences, pure mathematics and statistics. In addition, there is a program for a major in mathematics that qualifies a student for initial teaching licensure. Minors are offered in mathematics and statistics.

The department also recognizes the importance of providing courses for non-specialists who need to make effective use of mathematics or statistics in their chosen careers.

The university is an institutional/educational member of the American Mathematical Society, the American Statistical Association, the Mathematical Association of America and the Society for Industrial and Applied Mathematics.

Students are strongly encouraged to participate in the numerous undergraduate research opportunities as well as individual and small group projects available in the department. Opportunities exist through the Center for Mathematical Modeling, the Office of Statistical Services and honors theses and independent studies with individual faculty mentors.

Majors in the department are expected to participate in assessment activities. Assessment information is used to assist faculty members in modifying curricula.


Degree and Major Requirements
Degrees in Mathematics: Non-Teaching
The first two years of introductory mathematics focus on differential and integral calculus. The studies of the last two years are devoted primarily to basic material in the fields of analysis, algebra, geometry, modeling, computing and statistics. The two parts of the program are distinguished by methods of presentation and content. The first two years lead to appreciation of definitions and proofs and to precision in mathematical language. The latter two years anchor basic mathematical concepts, results and methods and increase knowledge of applications. Concentrations are available and encouraged in actuarial/financial mathematics, computational and applied mathematics, computational sciences, pure mathematics, and statistics.


Bachelor of Arts in Mathematics

Degree Requirements

Credit Hours
General Education1,2 41
Foreign Language classes (Intermediate level required) 0-14
Philosophy course(s) (In addition to General Education courses) 3
University electives 26-38
Major requirements (listed below) 41-53

120


1 MATH 235, Calculus I, must be included. 2 The General Education program contains a set of requirements each student must fulfill. The number of credit hours necessary to fulfill these requirements may vary.

Minimum requirements for a B.A. degree with a major in mathematics are 45 credit hours in mathematics.

Major Requirements

Core Corses Credit Hours
MATH 236-237. Calculus II-III 8
MATH 238. Linear Algebra with Differential Equations 4
MATH 248. Computers and Numerical Algorithms 4
Choose one of the following: 3
MATH 310. Elementary Theory of Numbers
MATH 312. Discrete Mathematics
MATH 315. The Real Number System
MATH 318. Introduction to Probability and Statistics 4
MATH 410. Advanced Calculus 3
MATH 430. Abstract Algebra I 3
Choose one of the following: 3
MATH 411. Advanced Calculus
MATH 431. Abstract Algebra II
Mathematics concentration courses or mathematics electives 9-21 numbered at or above MATH 310 9-21

Bachelor of Science in Mathematics

Degree Requirements
Minimum requirements for a B.S. degree with a major in mathematics are 45 credit hours in mathematics.
Credit Hours
General Education 1,2 41
Social science or natural science course(s) 3-4
University electives 29-41
Major requirements (listed below) and electives 41-53

120


1 MATH 235, Calculus I, must be included. 2 The General Education program contains a set of requirements each student must fulfill. The number of credit hours necessary to fulfill these requirements may vary.

Minimum requirements for a B.S. degree with a major in mathematics is 45 credit hours in mathematics.

Major Requirements

Core Corses Credit Hours
MATH 236-237. Calculus II-III 8
MATH 238. Linear Algebra with Differential Equations 4
MATH 248. Computers and Numerical Algorithms 4
Choose one of the following: 3
MATH 310. Elementary Theory of Numbers
MATH 312. Discrete Mathematics
MATH 315. The Real Number System
MATH 318. Introduction to Probability and Statistics 4
MATH 410. Advanced Calculus 3
MATH 430. Abstract Algebra I 3
Choose one of the following: 3
MATH 411. Advanced Calculus
MATH 431. Abstract Algebra II
Mathematics concentration courses or mathematics electives 9-21 numbered at or above MATH 310 9-21

Concentrations

Actuarial/Financial Mathematics

FIN 360. Money and Capital Markets
FIN 380. Elemental and Derivative Securities Analysis
MATH 340. Mathematics Modeling I - Optimization
MATH 426-427. Probability and Mathematical Statistics I-II
MATH/FIN 328. Time Series Analysis
MATH/FIN 395. Mathematical Finance

Computational and Applied Mathematics

Choose four from the following:
MATH 337. Methods of Applied Calculus
MATH 340. Mathematical Modeling I - Optimization
MATH 341. Mathematical Modeling II – Dynamical Systems
MATH 360. Complex Variables with Applications
MATH 387. Fourier Analysis and Partial Differential Equations
MATH 448. Numerical Analysis
MATH 449. Numerical Analysis for Differential Equations
MATH 450. Analysis and Dynamics of Differential Equations
MATH 483. Selected Topics in Applied Mathematics

Computational Sciences Concentration

The Departments of Mathematics and Physics offer a coordinated sequence of courses that prepare students for careers in the rapidly expanding field of computer modeling of complex systems. This program is structured so that students can earn a major in one department and a minor in the other. Students need not decide on a major field until their junior year.

The computational sciences concentration will prepare students to design and use computer models in any of those areas in which applied mathematics is used to understand complex systems (meteorology, astronomy, geology/geophysics, oceanography, physics, etc.). The preparation is appropriate for both those students who plan to enter the work force after graduation and those who plan to enter graduate school in applied mathematics, physics or one of the other fields mentioned above.

Students should complete the following courses during the first two years of the program:

MATH 235-237. Calculus I-III
MATH 248. Computers and Numerical Algorithms
MATH 336. Elementary Differential Equations, or
MATH 238. Linear Algebra with Differential Equations
PHYS 140L-150L. General Physics Laboratory I-II
PHYS 240-260. University Physics I-III
MATH/PHYS 265. Introduction to Fluid Mechanics
During the junior and senior years students will normally complete the necessary course work for their major and minor. Mathematics majors will take PHYS 340, Mechanics, and MATH/PHYS 365, Introduction to Computational Fluid Mechanics, counted as a physics course to complete their physics minor. Physics majors will take MATH/PHYS 365 counted as a mathematics course and either MATH 337, Methods of Applied Calculus, or MATH 387, Fourier Analysis and Partial Differential Equations, to complete their mathematics minor. Seniors in either major must complete at least one “topics” or independent-study/research course that involves computer modeling.

Pure Mathematics Concentration

Complete the year sequences in both of the following: \
MATH 410-411. Advanced Calculus
MATH 430-431. Abstract Algebra I-II
In addition to core requirements, choose three of the following or complete an honors thesis in pure mathematics and take one course from the following:
MATH 310. Elementary Theory of Numbers
MATH 312. Discrete Mathematics
MATH 315. The Real Number System
MATH 353. Graph Theory
MATH 360. Complex Variables with Applications
MATH 426. Probability and Mathematical Statistics I
MATH 427. Probability and Mathematical Statistics II
MATH 435. Introduction to Topology
MATH 448. Numerical Analysis
MATH 449. Numerical Analysis for Differential Equations
MATH 450. Analysis and Dynamics of Differential Equations
MATH 475. Fundamental Concepts of Geometry

Statistics Concentration


MATH 426-427. Probability and Mathematical Statistics I-II
Choose one of the following:
MATH 321. Analysis of Variance and Experimental Design
MATH 322. Applied Linear Regression
Choose one from the following:
MATH 321. Analysis of Variance and Experimental Design
MATH 322. Applied Linear Regression
MATH 324. Applied Nonparametric Statistics
MATH 325. Survey Sampling Methods
MATH 326. Statistical Quality Control
MATH 327. Categorical Data Analysis
MATH 328. Time Series Analysis
MATH 421. Applied Multivariate Statistical Analysis
MATH 423. Stochastic Processes
MATH 424. Statistical Decision Theory
MATH 485. Selected Topics in Statistics

Students seeking a concentration should carefully plan a program of study in conference with their adviser to make maximum use of electives permitted by the major.


Recommended Schedule for Majors

First Year Credit Hours
Skills of the 21st Century (Cluster One) 9-12
MATH 235-236. Calculus I-II 4
MATH 248. Computers and Numerical Algorithms 4
General Education courses 6-9

30

Second Year Credit Hours
MATH 237. Calculus III 4
MATH 238. Linear Algebra with Differential Equations 4
Choose one of the following: 3
MATH 310. Elementary Theory of Numbers
MATH 312. Discrete Mathematics
MATH 315. The Real Number System
MATH 318. Introduction to Probability and Statistics 4
General Education courses/electives 15

30


Third Year Credit Hours
Choose one of the following: 6
MATH 410-411. Advanced Calculus
MATH 430-431. Abstract Algebra I-II
General Education courses/electives 18-21
Mathematics concentration courses or mathematics electives numbered at or above MATH 310 3-6

30


Fourth Year Credit Hours
Choose one of the following: 3
MATH 410. Advanced Calculus
MATH 430. Abstract Algebra I
Mathematics concentration courses or mathematics electives numbered at or above MATH 310 6-9
Electives 18-21

30

Initial Secondary, Middle School or Early Childhood Teaching License
Students who want to teach mathematics at the secondary level complete a major in mathematics with courses in education and related areas. Students who want to teach at the middle or early/elementary levels must major in Interdisciplinary Liberal Studies (IDLS). It is necessary to be admitted to the teacher education program prior to enrolling in professional education courses. Students seeking licensure are encouraged to consult regularly with the appropriate program in the College of Education. The Master of Arts in Teaching degree is required for licensure in middle and secondary education.

Initial Secondary Teaching License
Students desiring secondary teaching licensure must complete the pre-professional education requirements and then the Master of Arts in Teaching degree.

Students seeking middle or early childhood licensure should consult the appropriate program in the College of Education. It is necessary to be admitted to the teacher education program prior to enrolling in professional education courses. For a full description of the program in secondary education, refer to the College of Education.


Degree in Mathematics: Teaching


Bachelor of Science in Mathematics
Requirements for a B.S. degree with a major in mathematics, qualifying for secondary teaching licensure, include a minimum of 45 credit hours in mathematics:
Degree Requirements

Credit Hours
General Education 1,2 41
Social science or natural science course(s) 3-4
University electives 39
Major requirements (listed below) and electives 44-57
Pre-professional education requirements 31

120


1 MATH 235, Calculus I, must be included. 2 The General Education program contains a set of requirements each student must fulfill. The number of credit hours necessary to fulfill these requirements may vary.

Major Requirements

Core Corses Credit Hours
MATH 236-237. Calculus II-III 8
MATH 238. Linear Algebra with Differential Equations 4
MATH 248. Computers and Numerical Algorithms 4
Choose one of the following: 3
MATH 310. Elementary Theory of Numbers
MATH 312. Discrete Mathematics
MATH 315. The Real Number System
MATH 318. Introduction to Probability and Statistics 4
MATH 410. Advanced Calculus 3
MATH 430. Abstract Algebra I 3
MATH 475. Fundamental Concepts of Geometry 3
Mathematics electives numbered ator above MATH 3101 9

Recommended Schedule for Majors

First Year Credit Hours
Skills for the 21st Century (Cluster One) 9-12
MATH 235-236. Calculus I-II 8
MATH 248. Computers and Numerical Algorithms 4
General Education courses 6-9

30

Second Year Credit Hours
MATH 237. Calculus III 4
MATH 238. Linear Algebra with Differential Equations 4
MATH 318 . Introduction to Probability and Statistics 4
Choose one of the following: 3
MATH 310. Elementary Theory of Numbers
MATH 312.Discrete Mathematics
MATH 315. The Real Number System
Professional education requirements 9
General Education courses 6

30


Third Year Credit Hours
MATH 430. Abstract Algebra I 3
Choose two of the following: 6
MATH 475. Fundamental Concepts of Geometry
MATH 410. Advanced Calculus
Mathematics elective(s) numbered at or above MATH 310
Professional education requirements 11
General Education courses/electives 10

30


Fourth Year Credit Hours
Choose three from the following: 9
MATH 475. Fundamental Concepts of Geometry
MATH 410. Advanced Calculus
Mathematics elective(s) numbered at or above MATH 310
Professional education requirements 11
General Education courses/electives 10

30

Bachelor of Science in Statistics

The Department of Mathematics and Statistics offers a major in statistics to meet the needs of both the public and the private sectors for graduates with degrees in statistics. The program has two tracks, Applied Statistics and Mathematical Statistics, one of which must be chosen by each student completing the major.

Students interested in the applications of statistics and planning to seek immediate employment as practicing statisticians upon graduation are advised to choose the Applied Statistics track. Emphasis in this track is on the applications of statistics to various fields of study. Students in this track will take courses on the design and analysis of experiments, regression analysis and sample surveys, as well as other courses in applied and theoretical statistics, probability and mathematics. Students who choose the applied statistics track are encouraged to take as many elective courses as possible in applied fields of their choice.

The Mathematical Statistics track is designed for students who have an interest in the mathematics of statistics or plan to go to graduate school in statistics. Students in this track will see more emphasis on probability and the theory of statistics. These students will also have a chance to take additional courses in applied and theoretical statistics as well as courses in mathematics. Students in this track are recommended to take elective courses from the statistics and mathematics courses offered by the department that will prepare them for graduate studies.

Students of statistics are advised to choose between the two tracks by the end of their sophomore year. However, there are a large number of courses common to both tracks, so students may be able to change tracks later in their academic career with little loss of time.

Degree Requirements

Credit Hours
Credit Hours
General Education 1,2 41
Social science or natural science course(s) 3-4
University electives 33-36
Major requirements (listed below) and electives 50-53



1 The General Education program contains a set of requirements each student must fulfill. The number of credit hours necessary to fulfill these requirements may vary.

Major Requirements

Minimum requirements for a B.S. degree with a major in statistics, applied statistics track, are 47 credit hours in statistics and cognate mathematics courses which must include one of the electives in statistics listed below:
Core Corses Credit Hours
Statistics Courses 29-31
MATH 220. Elementary Statistics 3
MATH 280. SAS Programming and Data Management 3
MATH 318. Introduction to Probability and Statistics 4
MATH 321. Analysis of Variance and Experimental Design 3
MATH 322. Applied Linear Regression 3
MATH 324. Applied Nonparametric Statistics 3
MATH 325. Survey Sampling Methods 3
MATH 421. Applied Multivariate Statistical Analysis 3
MATH 426. Probability and Mathematical Statistics I 3
MATH 429. Research Project in Statistics 1-3
Choose one of the following electives in statistics: 3
MATH 327. Categorical Data Analysis
MATH 328. Time Series Analysis
MATH 423. Stochastic Processes
MATH 424. Statistical Decision Theory
MATH 427. Probability and Mathematical Statistics II
Mathematics Cognates: 15-16
MATH 235-236-237. Calculus I - II - III 12
MATH 300. Linear Algebra2 3-4

25

1 Waived for those who have C or better in MATH 318. No additional course will be required to substitute for MATH 220 in this program. 2 MATH 238 (Linear Algebra with Differential Equations) may be substituted.

In addition to elective statistics courses offered by the department, students in this track are strongly recommended to take as many elective courses as possible from fields of application such as management, business administration, economics, biology, or health sciences in which they are interested and in which they might like to be employed.

Recommended Schedule for Majors

First Year Credit Hours
Skills for the 21st Century (Cluster One) 9
MATH 220. Elementary Statistics 3
MATH 280. SAS Programming and Data Management 3
MATH 235. Calculus I 4
General education courses 11

30

Second Year Credit Hours
MATH 236-237. Calculus II-III 8
MATH 318. Introduction to Probability and Statistics 4
MATH 325. Survey Sampling Methods 3
General education courses/electives 15

30


Third Year Credit Hours
MATH 321. Analysis of Variance and Experimental Design 3
MATH 322. Applied Linear Regression 3
MATH 324. Applied Nonparametric Statistics 3
MATH 300. Linear Algebra 3
MATH 426. Probability and Mathematical Statistics I 3
General education courses/electives 15

30


Fourth Year Credit Hours
MATH 421. Applied Multivariate Statistical Analysis 3
MATH 429. Research Projects in Statistics 1-3
Elective in Statistics 3
Electives 21-23

30

Bachelor of Science in Statistics: Mathematical Statistics Track

Degree Requirements

Credit Hours
Credit Hours
General Education 1,2 37
Social science or natural science course(s) 3-4
University electives 33-36
Major requirements (listed below) and electives 55-56

120


1 The General Education program contains a set of requirements each student must fulfill. The number of credit hours necessary to fulfill these requirements may vary.

Major Requirements

Minimum requirements for a B.S. degree with a major in statistics, mathematical statistics track, are 52 credit hours in statistics and cognate mathematics courses:
Core Corses Credit Hours
Statistics Courses 29-31
MATH 220. Elementary Statistics 3
MATH 280. SAS Programming and Data Management 3
MATH 318. Introduction to Probability and Statistics 4
MATH 321. Analysis of Variance and Experimental Design 3
MATH 322. Applied Linear Regression 3
MATH 324. Applied Nonparametric Statistics 3
MATH 421. Applied Multivariate Statistical Analysis 3
MATH 426-427. Probability and Mathematical Statistics I-II 6
Choose one of the following electives in statistics: 3
MATH 328. Time Series Analysis
MATH 423. Stochastic Processes
MATH 424. Statistical Decision Theory
Mathematics Cognates: 15-16
MATH 235-236-237. Calculus I - II - III 12
MATH 300. Linear Algebra2 3-4
MATH 312. Discrete Mathematics 3
MATH 410. Advanced Calculus 3

120

1 Waived for those who have C or better in MATH 318. No additional course will be required to substitute for MATH 220 in this program. 2 MATH 238 (Linear Algebra with Differential Equations) may be substituted.

In addition to elective statistics courses, students in this track are recommended to take elective courses from the mathematics courses offered by the department that will prepare them to continue in their studies toward an M.S. and/or a Ph.D. degree in statistics.

Recommended Schedule for Majors

First Year Credit Hours
Skills for the 21st Century (Cluster One) 9
MATH 220. Elementary Statistics 3
MATH 280. SAS Programming and Data Management 3
MATH 235. Calculus I 4
General education courses 11

30

Second Year Credit Hours
MATH 236-237. Calculus II-III 8
MATH 318. Introduction to Probability and Statistics 4
MATH 321. Analysis of Variance and Experimental Design 3
General education courses/electives 15

30


Third Year Credit Hours
MATH 322. Applied Linear Regression 3
MATH 300. Linear Algebra 3
MATH 312. Discrete Mathematics 3
MATH 426-427. Probability and Mathematical Statistics I-II 6
General education courses/electives 15

30


Fourth Year Credit Hours
MATH 324. Applied Nonparametric Statistics 3
MATH 421. Applied Multivariate Statistical Analysis 1-3
MATH 410. Advanced Calculus 3
Elective in Statistics 3
Electives 18

30

Minor Requirements

Mathematics Minor

Each student must obtain prior approval of all courses to be counted in the minor from the mathematics minor adviser, Dr. Peter D. Kohn, or from the department head.

A minor in mathematics requires a minimum of 18 credit hours.

MATH 235-236. Calculus I-II
Mathematics courses numbered 237 or above, excluding mathematics courses numbered 301 - 309

Statistics Minor

The minor in statistics is open to any student. Mathematics majors who seek a minor in statistics will be expected to fulfill different requirements than those for students with other majors. Each student must obtain prior approval of the courses to be counted in the minor from the statistics minor advisers: Drs. Chiang, Domangue, or Hamdan for mathematics majors; and Drs. Garren, Marrah, or Yesilcay for other majors.

Minor in Statistics: Mathematics Majors

A minor in statistics requires a minimum of 19 credit hours.

The minor program for a mathematics major shall include MATH 318 and at least 12 credit hours not counted toward the student’s mathematics major.

MATH 318. Introduction to Probability and Statistics
MATH 426-427. Probability and Mathematical Statistics I-II
Choose one of the following:
MATH 321. Analysis of Variance and Experimental Design
MATH 322. Applied Linear Regression
Choose one of the following:
MATH 423. Stochastic Processes
MATH 424. Statistical Decision Theory
Choose one of the following:
MATH 280. SAS Programming and Data Management
MATH 321. Analysis of Variance and Experimental Design
MATH 322. Applied Linear Regression
MATH 324. Applied Nonparametric Statistics
MATH 325. Survey Sampling Methods
MATH 326. Statistical Quality Control
MATH 327. Categorical Data Analysis
MATH 328. Time Series Analysis
MATH 421. Applied Multivariate Statistical Analysis
MATH 423. Stochastic Processes
MATH 424. Statistical Decision Theory
MATH 485. Selected Topics in Statistics

Minor in Statistics: All Other Majors

A minor in statistics requires a minimum of 18 credit hours.

MATH 322. Applied Linear Regression
Choose one of the following
MATH 220. Elementary Statistics
MATH 318. Introduction to Probability and Statistics or equivalent
Choose four of the following:
MATH 280. SAS Programming and Data Management
MATH 321. Analysis of Variance and Experimental Design
MATH 324. Applied Nonparametric Statistics
MATH 325. Survey Sampling Methods
MATH 326. Statistical Quality Control
MATH 327. Categorical Data Analysis
MATH 328. Time Series Analysis
MATH 421. Applied Multivariate Statistical Analysis
MATH 423. Stochastic Processes
MATH 424. Statistical Decision Theory
MATH 426. Probability and Mathematical Statistics I
MATH 427. Probability and Mathematical Statistics II
MATH 485. Selected Topics in Statistics

Credit By Examination
The Department of Mathematics offers credit by examination for some of the courses taught in the department. Students who want to take an examination must apply to the department head. Upon application students will receive details regarding approval to take the examination.

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Last Modified: 6/11/2003