Department of Mathematics

Dr. David C. Carothers, Head

Professors

Carothers, Droms, J. Hanson, Klippert, Lyons, Parker, G. Peterson, Sanders, Spresser

Associate Professors

Babarsky, Chiang, Domangue, Fisher, LePera, Marafino, Marrah, Sochacki, Ziegenfus

Assistant Professors

Kohn, Kuhn, Lee, Liu, Pruett, T. Taylor

Course Descriptions: Mathematics and Interscience Research

As a major in mathematics you can expect to use and build on the skills you have gained in previous courses in mathematics and in other areas: to think critically, to formulate and solve problems, and to communicate your solutions clearly, both orally and in writing. As the breadth of your knowledge of the subject grows, you will increase your 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 you to experience the challenge and rewards of faculty-mentored research, individually or as a member of a team, as you investigate mathematical problems that extend beyond those normally encountered in the classroom. You will increase your abilities to prove theorems, understand complex structures and apply mathematics in many real-world settings. The senior-level courses in abstract algebra and advanced calculus will draw together many of the threads of the major and serve as an appropriate culmination of your study. The program you choose will make it possible for you to acquire strong preparation for graduate work or for professional applications in teaching, statistics, natural and social sciences, or other technical areas.

The Department of Mathematics offers the Bachelor of Arts and Bachelor of Science degrees with a major in mathematics. Minors are offered in mathematics and statistics.

Within the mathematics major, concentrations are available in computational and applied mathematics, pure mathematics and statistics. There is, in addition, a program for a major in mathematics that qualifies a student for initial teaching licensure.

The department also recognizes the importance of providing courses for nonspecialists 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 and individual and small group projects available in the department. Opportunities exist through the Center for Mathematical Modeling, the Office of Statistical Services, and through 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.

B.A./B.S. Degree in Mathematics

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, computing and statistics. The two parts of the program are distinguished by methods of presentation and content. The first two years lead gradually 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 computational and applied mathematics, pure mathematics and statistics.

Initial Secondary, Middle School or Early Childhood Teaching License

Students who want to teach mathematics at the secondary, middle school or early childhood level complete a major in mathematics, together with courses in education and related areas. 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 and Psychology.

Major in Mathematics/Nonteaching (B.A. or B.S. Degree)

Minimum requirements for a B.A. or B.S. degree with a major in mathematics are 43 credit hours in mathematics, as follows:

Credit
Requirements Hours
Liberal studies courses 1 41
MATH 236-237. Analytic Geometry and 8
Calculus II-III
MATH 248. Computer Methods in Engineering 4
and Science
MATH 300. Linear Algebra 3
Choose one of the following: 3
MATH 310. Elementary Theory of Numbers
MATH 315. The Real Number System
MATH 352. Discrete Mathematics
MATH 318. Introduction to Probability and Statistics 3
MATH 336. Elementary Differential Equations 3
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
Concentration (computational and applied 6-12
mathematics, pure mathematics or statistics) or mathematics electives at or above
the 300 level
Electives 34-40
120

1 MATH 235, Analytic Geometry and Calculus I, must be included.

Although students are not required to do so, they are encouraged to select one of the following concentrations which introduce areas where mathematics is applied or in which postgraduate study may be pursued. A minimum of 12 credit hours must be completed in a particular concentration. The mathematics major who selects a concentration in computational and applied mathematics is strongly encouraged to complete PHYS 240-140L; and PHYS 250-150L, University Physics I-II with Laboratories.

Computational and Applied Mathematics

Credit
Hours
Choose four from the following: 12
MATH 337. Applied Calculus
MATH 341. Mathematical Modeling II
MATH 360. Complex Variables with Applications
MATH 387. Fourier Analysis and Partial
Differential Equations
MATH 448. Numerical Mathematics and
Computer Applications
MATH 449. Numerical Mathematics and
Computer Applications
MATH 450. Theory of Ordinary Differential
Equations
MATH 483. Selected Topics in Applied
Mathematics
12

Pure Mathematics

Credit
Hours
MATH 426. Probability and Mathematical 3
Statistics I
MATH 435. Introduction to Topology 3
Choose one of the following: 3
MATH 337. Applied Calculus
MATH 420. Foundations of Euclidean Geometry
MATH 475. Fundamental Concepts of Geometry
Complete the year sequences in both of the following: 3
MATH 410-411. Advanced Calculus
MATH 430-431. Abstract Algebra I-II
12

Statistics

Credit
Hours
Choose one of the following: 3
MATH 321. Analysis of Variance and
Experimental Design
MATH 322. Applied Linear Regression
MATH 426-427. Probability and Mathematical 6
Statistics I-II
Choose one from the following: 3
MATH 321. Analysis of Variance and
Experimental Design
MATH 322. Applied Linear Regression
MATH 323. Exploratory Data Analysis
MATH 324. Applied Nonparametric Statistics
MATH 325. Survey Sampling Methods
MATH 326. Statistical Quality Control
MATH 421. Applied Multivariate Statistical
Analysis
MATH 423. Stochastic Processes
MATH 424. Statistical Decision Theory
MATH 485. Selected Topics in Statistics
12

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.

Major in Mathematics/Teaching (B.S. Degree)

Requirements for a B.S. degree with a major in mathematics, qualifying for secondary, middle school or early childhood teaching licensure, include a minimum of 43 credit hours in mathematics, as follows:

Credit
Requirements Hours
Liberal studies courses 41
MATH 236-237. Analytic Geometry and 8
Calculus II-III
MATH 248. Computer Methods in Engineering 4
and Science
MATH 300. Linear Algebra 3
MATH 318. Introduction to Probability and 3
Statistics
MATH 336. Elementary Differential Equations 3
MATH 430. Abstract Algebra I 3
Choose one of the following: 3
MATH 310. Elementary Theory of Numbers
MATH 315. The Real Number System
MATH 352. Discrete Mathematics
Choose one of the following: 3
MATH 420. Foundations of Euclidean
Geometry
MATH 475. Fundamental Concepts of
Geometry
Professional education requirements 33-46
(choose one below):
Secondary licensure (33 credits)
Middle school licensure (40 credits)
Early childhood licensure (46 credits)
Mathematics electives 9
at or above the 300 level
Electives 0-7
120

1 MATH 235, Analytic Geometry and Calculus I, must be included.

Students who plan to teach are strongly urged to complete one or more of the following electives:

MATH 410. Advanced Calculus
MATH 415. History of Mathematics

Initial Secondary Teaching License

Students desiring secondary teaching licensure must complete the following professional courses:

Credit
Hours
EDUC 360. Foundations of American Education 3
(junior year)
EDUC 370. Instructional Technology (junior year) 3
EDUC 410. Multicultural Education (senior year) 1
EDUC 416. School Discipline and Classroom 1
Management (senior year)
HTH 370. The School Health Program 2
(any appropriate time)
PSYC 270. Psychology for Teachers of the 3
Pre-adolescent and Adolescent Child 1
(sophomore year)
READ 414. Reading and Writing in the 1
Content Areas (senior year)
SEED 371K. Secondary Mathematics Methods 3
(normally in first semester of senior year)
SEED 381. Field Experience (Practicum) in 3
Secondary Education (normally in first semester
of senior year)
SEED 480. Student Teaching (senior year) 12
SPED 402. Teaching Mildly Disabled Students 1
in Regular Classes (senior year)

1 PSYC 160 is a prerequisite for PSYC 270.

Students desiring middle or early childhood licensure should consult the appropriate program in the School of Education.

It is necessary to be admitted to the teacher education program prior to enrolling in professional education courses. See pages 147-149 of this catalog for admission and retention procedures in the teacher education programs. All students seeking teaching licensure should consult regularly with the appropriate program in the School of Education.

Credit By Examination

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

Minor in Mathematics

A minor in mathematics will require a minimum of 24 credit hours, distributed as follows:

Credit
Hours
MATH 235-236. Analytic Geometry and 8
Calculus I-II
Mathematics courses numbered 237 or above 16
24

Students may use MATH 205, Introductory Calculus I, toward the requirements for the minor in lieu of mathematics courses numbered 237 or above. (Note: MATH 205 is not open to students who have already received credit In MATH 235 or equivalent.) 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 head of the department.

Minor in Statistics

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 adviser, Dr. Rickie J. Domangue, or from the head of the department.

A minor in statistics requires a minimum of 18 credit hours, distributed as follows:

Mathematics Majors

The minor program for a mathematics major shall include MATH 318 together with at least 15 credit hours not credited toward the student's mathematics major.

Credit
Hours
MATH 318. Introduction to Probability and Statistics 3
Choose one of the following: 3
MATH 321. Analysis of Variance and
Experimental Design
MATH 322. Applied Linear Regression
Choose one of the following: 3
MATH 423. Stochastic Processes
MATH 424. Statistical Decision Theory
MATH 426-427. Probability and Mathematical 6
Statistics I-II
One additional course from the following list 3
of elective courses in statistics
18

All Other Majors

Credit
Hours
Choose one of the following 3
MATH 220. Elementary Statistics
MATH 318. Introduction to Probability and
Statistics or equivalent
MATH 322. Applied Linear Regression 3
Four additional courses chosen from the 12
following list of elective courses in statistics
18

Elective Courses in Statistics

Credit
Hours
MATH 321. Analysis of Variance and 3
Experimental Design
MATH 322. Applied Linear Regression 3
MATH 323. Exploratory Data Analysis 3
MATH 324. Applied Nonparametric Statistics 3
MATH 325. Survey Sampling Methods 3
MATH 326. Statistical Quality Control 3
MATH 421. Applied Multivariate Statistical Analysis 3
MATH 423. Stochastic Processes 3
MATH 424. Statistical Decision Theory 3
MATH 426. Probability and Mathematical 3
Statistics I
MATH 427. Probability and Mathematical 3
Statistics II
MATH 485. Selected Topics in Statistics 3

Typical Programs

Mathematics Major -- Nonteaching (B.A. or B.S. Degree)

Credit
Freshman Year Hours
ENG 101-102. Reading and Composition 3-6
MATH 235-236. Analytic Geometry and 8
Calculus I-II
MATH 248. Computer Methods in Engineering 4
and Science
Liberal studies courses 12-15
30
Credit
Sophomore Year Hours
MATH 237. Analytic Geometry and Calculus III 4
MATH 300. Linear Algebra 3
Choose one of the following 3
MATH 310. Elementary Theory of Numbers
MATH 315. The Real Number System
MATH 352. Discrete Mathematics
MATH 336. Elementary Differential Equations 3
Liberal studies courses and/or electives 17
30
Credit
Junior Year Hours
MATH 318. Introduction to Probability and Statistics 3
Choose one of the following: 6
MATH 410-411. Advanced Calculus
MATH 430-431. Abstract Algebra I-II
Liberal studies courses and/or electives 15-18
Mathematics concentration courses or 3-6
mathematics electives at or above the
300 level
30
Credit
Senior Year Hours
Choose one of the following: 3
MATH 410. Advanced Calculus
MATH 430. Abstract Algebra I
Mathematics concentration courses or 6-9
mathematics electives
at or above the 300 level
Electives 18-21
30

Mathematics Major -- Teaching (B.S. Degree)

Credit
Freshman Year Hours
ENG 101-102. Reading and Composition 3-6
MATH 235-236. Analytic Geometry and 8
Calculus I-II
MATH 248. Computer Methods in Engineering 4
and Science
Liberal studies courses 12-15
30
Credit
Sophomore Year Hours
MATH 237. Analytic Geometry and Calculus III 4
MATH 300. Linear Algebra 3
MATH 336. Elementary Differential Equations 3
Professional education requirements 6-12
Liberal studies courses 8-14
30
Credit
Junior Year Hours
Choose one of the following: 3
MATH 310. Elementary Theory of Numbers
MATH 315. The Real Number System
MATH 352. Discrete Mathematics
Choose two from the following: 6
MATH 420. Foundations of Euclidean
Geometry
MATH 475. Fundamental Concepts of
Geometry
Mathematics elective(s) at or above the
300 level
MATH 430. Abstract Algebra I 3
Professional education requirements 6-21
Liberal studies courses and/or electives 0-12
30-33
Credit
Senior Year Hours
MATH 318. Introduction to Probability and 3
Statistics
Choose two from the following: 6
MATH 420. Foundations of Euclidean
Geometry
MATH 475. Fundamental Concepts of
Geometry
Mathematics elective(s) at or above the
300 level
Professional education requirements and/or 21-24
liberal studies courses and/or electives
30-33

College of Science and Mathematics Directory

Undergraduate Catalog Contents


1996-97 Undergraduate Catalog
Last reviewed: 30 November 1996
Information Publisher: Division of Academic Affairs
James Madison University