# 2.2-Option B (Interdisciplinary Mathematics)

**(2.2) Option B (Interdisciplinary Mathematics)**

**(2.2.1) Introduction**

Option B provides a broad background in areas of industrial and applied mathematics. It is aimed at students from undergraduate majors in mathematics, science, and engineering who have an interest in applications of mathematics, have succeeded at a high level in their mathematics and science courses, and have some undergraduate training in application disciplines. The curriculum includes the "classical" areas of applied mathematics (ordinary and partial differential equations), computational methods, modeling, applied probability and statistics, discrete mathematics, optimization, and basic mathematics (advanced calculus of one and several variables, complex variables, linear algebra). While self-contained and suitable as a degree that would prepare a student for employment, with a suitably chosen program of study this degree could also prepare a student to proceed on to doctoral work at WVU or elsewhere in mathematics or the mathematical sciences.

**(2.2.2) Entrance Prerequisites**

Students pursuing Option B should have, at a minimum, the following undergraduate background:

Three semesters calculus.

Linear Algebra (Math 343 or 441).

Elementary Differential Equations (Math 261).

(Students lacking Differential Equations or Linear Algebra may be admitted provisionally under some circumstances.)

**(2.2.3)** **Foundations**

These include areas basic to industrial/applied mathematics, at an upper-division undergraduate level. Each student graduating from the program should have some experience with the subject matter represented in the following areas (with applicable undergraduate courses listed):

Programming experience in a general programming language (e.g., C, Pascal, Basic, Fortran, MATLAB ).

Introductory Partial Differential Equations (Math 465).

Probability theory (Stat 215 or Stat 461).

Numerical Analysis (Math 420).

Mathematical Analysis (advanced calculus Math 451 and complex analysis Math 456).

Algebra/Discrete Math (Math 341, Math 375, or Math 378).

Students will be expected to demonstrate proficiency in all these areas at the level indicated, through examination or course work. More specifically, proficiency may be demonstrated in the following ways:

(1) By examination.

(2) By completion of an appropriate undergraduate course with a grade of A or B, either as an undergraduate, or as a graduate student in the Department.

(3) By completion with a grade of A or B of an appropriate graduate-level course which covers substantially similar material at a more advanced level. The graduate courses (some of which are required) which can be used to satisfy foundation requirements are as follows:

Math 521 will satisfy the Numerical Analysis foundation requirement.

Stat 561 will satisfy the Probability requirement.

Math 567-568, Math 551, or Math 555 will satisfy the mathematical analysis requirement.

Math 571,671,573,545,645,541, or 543 will satisfy the Algebra/Discrete Math requirement.

**(2.2.4) Course Requirements**

Note: Students who intend to pursue doctoral study in mathematics or the mathematical sciences should carefully plan their course work so as to meet the prerequisites of their intended field of study and degree program.

A total of at least 33 credit hours of course work is required, distributed as follows.

__Prerequisite/Foundation Courses__

At most 3 hours of credit toward the 33 hours will be given for one of Math 465, Math 441, Math 456, Math 451, provided these courses (or equivalents) have not been previously taken at WVU or elsewhere.

__Required Core Graduate Courses (12-15 hours)__

Math 567 and either Math 568 or Math 555 (Advanced Calculus/Complex Variables).

The Math 567-568 sequence will include multivariable and vector calculus in Math 567, applied complex variables in Math 568, and other topics important to applied mathematics as time allows. Students may take Math 555 in lieu of Math 568. Students with a grade of B or better in Math 456 may be exempted from the Math 568 or Math 555 requirement.

Math 564 (Differential Equations).

Math 521 (Numerical Analysis).

Math 563 (Modeling).

__Distribution Requirements (at least 15 hours)__

Students must complete at least two courses from Math 452, Math 541, Math 543, Math 551, Math 555 and Math 581, with a grade at least B on these courses.

Including the core courses listed below (Math 521 and Math 563), at least one course from 4 different groups must be included in the program of study. Within two different groups, there must be a sequence of two suitably linked courses, one of which may be a core course listed. Once these conditions are met, the remainder of the 33 hours may be made up of any of the courses below or other mathematics electives, subject to approval by the advisor. Overall, at most 4 courses may be from outside the Mathematics Department.

I. Computation/optimization: Math 521, Math 522 Numerical Solution of PDE's.

II. Probability theory/mathematical statistics: Stat 561-562; (other approved Stat courses provided Stat 562 is also taken).

III. Algebra/Discrete Math: Math 541; Math 543;Math 571,671; Math 573;Math 545,645; other suitable math electives in this area, or CS courses approved by the advisor and the Graduate Director.

IV. Modeling: Math 563; a second semester of modeling.

V. Mathematical Analysis: Math 452, Math 551, Math 651, Math 555.

VI. Graduate courses (one 400-level possible with permission) from outside Math/Stat/CS (students are responsible for meeting prerequisites). These are to be approved by the advisor and the Graduate Director.

**(2.2.5) Examinations**

The Basic Exam in Advanced Calculus and Linear Algebra is given as a placement exam at the beginning of graduate study.

**(2.2.6) Research/Internship/Project** **(1 hour)**

This is required for all students. The work represented should be equivalent to that associated with at least one credit hour of course work. If warranted, more credit can be granted with permission, but course work requirements will not be reduced. A presentation and approval by the advisory committee are required.

Successful completion of the above requirements (2.2.2)-(2.2.6) with a minimum GPA of 3.0 in course work presented will suffice for the granting of the M.S. degree.