Senate Document #21 (APC Document #19) Mathematics Curriculum Revisions MATHEMATICS PROPOSAL 1. Replace the material in present Catalog, page 148, first two paragraphs after personnel listing by this statement: The mathematics major is designed to provide the student with a substantial foundation in mathematics, yet allow him enough flexibility in specifying his course of studies to reflect his own special interests and competencies. Upon declaration of a major in mathematics, each student must, in consultation with his advisor, present a proposed program of study to the department's Curriculum Committee for their perusal and ultimate approval. Any subsequent change in a program proposal must be approved by both the student's advisor and the Curriculum Committee. The department encourages each student to take an active role in the design of his program. The Mathematics Department offers an extensive assortment of courses, enabling the student to specify programs of study emphasizing the following areas: Pure (Theoretical) Mathematics Applied Mathematics Discrete Mathematics and Mathematical Modeling Mathematics Education Statistics Computer Science Actuarial Science Each of these areas may be pursued within the degree tracks described below. Students interested in the particulars should contact the Chairperson of the Mathematics Department for additional information. RATIONALE: This statement makes it clear to students that various popular fields of mathematics often commonly associated with certain careers are covered in the mathematics (and statistics) curriculum. For example, a student may actually desire a major in mathematics but feel obliged to major in computer science as a career choice. The above statement assures the student that a mathematics major which emphasizes computer science is a viable option. Page 2 MATHEMATICS PROPOSAL 2. (See catalog, page 149) Following paragraph under MATHEMATICS MINOR add: MATHEMATICS MINOR FOR SCIENCE TEACHERS 21 hours in Mathematics and Computer Science: Mathematics 191, 192, 291, 280, 332 and Computer Science 141. At least Mathematics 280, 332 must be taken at UNCA. This minor may be used towards endorsement in a second area of concentration (mathematics) by science teachers in grades 6-9 and will be granted only if a student completes the other requirements for endorsement. RATIONALE: To implement requirements demanded of teachers for concentration in a second area, recently passed by the State Board of Education. MATHEMATICS PROPOSAL 3. Change prerequisites of Math 162 INTERMEDIATE ALGEBRA to: Prerequisite: Developmental Studies 106 and a satisfactory performance on the departmental placement exam, or special department approval. RATIONALE: To aid in the proper placement of students. MATHEMATICS PROPOSAL 4. (See catalog, page 150) Change prerequisite statement of Math 191 CALCULUS I to: Prerequisite: Math 163, 164 and a satisfactory performance on the departmental placement exam, or special departmental approval. A student with a sufficiently strong background in high school mathematics that includes geometry and trigonometry can be expected to succeed in calculus if a sufficiently high score is made on the placement exam, without Math 163, 164. RATIONALE: Trigonometry (Math 164) is needed in the calulus sequence. MATHEMATICS PROPOSAL 5. (See catalog, page 150) Add the course NUMERICAL ANALYSIS, described below. 341 NUMERICAL ANALYSIS (3). An introduction to efficient methods for numerically solving many mathematical problems. Course content includes polynomial approximation, approxima- tion theory, numerical differentiation and integration, numerical methods in matrix algebra, numerical solution of Page 3 nonlinear equations, and numerical methods to solve dif- ferential equations. Prerequisites: Math 291 and C Sci 141, 142, or 143, or permission of the department. RATIONALE: This course is recommended to complement the present course in Computer Science, C Sci 344 (Numerical Computing) and to utilize the expertise of one of our faculty members (Ed Allen) whose Ph.D. is in this area. Possible text: NUMERICAL ANALYSIS, by Burden, Paires and Reynolds, Prindle, Weber, and Schmidt, 2nd Ed., 1982. MATHEMATICS PROPOSAL 6. (See catalog, p. 150) Add the course MATHEMATICS SEMINAR, described below: 380 MATHEMATICS SEMINAR (1). A seminar program in which students are required to be active participants; read background papers, participate in discussions, and, on occasion, lead the seminar. Mathematics majors are required to enroll in the seminar three semesters, and, under the supervision of a faculty director, each student must write an expository or a research paper or lead one of the seminars each semester (leading at least one seminar is required). Prerequisite: Permission of the department. RATIONALE: This formalizes what has been offered as a topics course the past 4-5 semesters, and has become a trademark of the Mathematics Department. This seminar is the focus of the department's efforts to keep a weekly colloquium series going. Not only department members give talks, but outside speakers as well. All talks are aimed at the undergraduate level, however, a feature which often attracts members from other departments who wish to become more acquainted with mathematics. Such a wide variety of topics is presented each semester that a mathematics major can greatly broaden his/her education by attending the lectures. MATHEMATICS PROPOSAL 7. (See catalog, p. 150) Add the course PARTIAL DIFFERENTIAL EQUATIONS, described below: 395 PARTIAL DIFFERENTIAL EQUATIONS (3). A course emphasizing the three basic types of second order partial differential equations which occur frequently in applications throughout the physical sciences - elliptic, hyperbolic, and parabolic, such as Laplace's equation, wave equation, and heat equation. Topics covered include first order partial differential equations, properties of and derivation of second order partial differential equations, Page 4 and methods of solution, including series, transform, and numerical methods. Prerequisites: Math 291 and 394. RATIONALE: This is a core course for any scientist, engineer or applied mathematician. The classical derivation of the wave equation which mathematically models the phenomenon of a vibrating string is still important today and forms a basis for a whole class of fundamental partial differential equations. Students majoring in physics or engineering will find this course of tremendous importance. Possible text: ELEMENTARY PARTIAL DIFFERENTIAL EQUATIONS, by Berg and MacGregor,Holden-Day (1966). MATHEMATICS PROPOSAL 8. (See catalog, p. 151) Change the course description for Math 391 ADVANCED CALCULUS to: Selected topics in calculus, including differentiation and integration of vectors, Stoke's theorem, Gauss' theorem, divergence theorem; other topics such as gamma and beta functions, implicit function theorems and infinite series may be included. Prerequisite: Math 291. RATIONALE: This more accurately describes the course as currently taught. MATHEMATICS PROPOSAL 9. (See catalog, p. 195) Drop the prerequisite Math 266 in the course description for Stat 325. NOTE: The course description for Stat 327 has been erroneously repeated and one of them should be deleted. MATHEMATICS PROPOSAL 10. To implement in a more efficient and equitable manner the prerequisites for Math 162 INTERMEDIATE ALBEGRA (assuming Proposal 3 passes), Math 163 COLLEGE ALGEBRA, AND Math 191 CALCULUS I, it is recommended that the following procedure be adopted to determine whether the prerequisite concerning Placement Exam is satisfied: At registration circulate a copy of (1) Review sheet (contains sample problems covered on test, with answers) and (2) Sample test (a test of same type to be given in class, with answers). On the first day of class the placement exam is given and graded. The passing grade is to be determined statistically by past placement exams and retention rates. (The department has been keeping records for the past several years.) If a student fails the placement exam that student has not satisfied the prerequisites for the course and Page 5 will not be permitted to take the course without the permission of the department (the normal procedure under University regulations regarding course prerequisites). RATIONALE: This recommendation is an attempt to combat the extremely high attrition rates presently being experienced in the lower division mathematics courses (Intermediate Algebra, College Algebra, and Calculus I). The procedure recommended would do two things: It would actually inform students at registration about the level of the course and the type of mathematics they can expect (solving the problem of placement for transfer students and others who simply do not know whether they are ready for a particular course), and it would cut down on the failure rate due to misplacement. In no other discipline is a sequence of courses so prerequisite-sensitive as in mathematics, so it needs to be realized that success in a pre- requisite course is mandatory for success in the course itself for a vast majority of students. Success in a prerequisite course is not always measured by a passing grade -- sometimes such students still fail the placement exam and exhibit evidence of not being ready for the course.