THE UNIVERSITY OF NORTH CAROLINA AT ASHEVILLE FACULTY SENATE Senate Document Number 1892S Date of Senate Approval 3/5/92 Signature of Senate Chair __________________________ Date________ Action of Vice Chancellor: Approval _______________________________ Date________________ Denied _______________________________ Date________________ Reasons for denial and suggested modifications: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Statement of Faculty Senate Action: APC DOCUMENT #17: Changes in Mathematics EFFECTIVE DATE: Fall, 1992 1. DELETE: Catalog description for MATH 155, page 146 ADD: "A variety of traditional and nontraditional topics in mathematics. Historical development, generalizations to mathematical theory, and applications to real life are components of each topic. Topics may include set theory and logic, algebraic models, geometry, and number systems. Prerequisite: MATH 104 or satisfactory performance on the mathematics placement examination." IMPACT STATEMENT: No impact. RATIONALE: This change was recommended by a departmental committee made up of recent instructors of MATH 155 who felt these changes (together with a new choice for textbook) would improve the course. 2. DELETE: Catalog description for MATH 291, page 146. (Only change is in last line of description.) ADD: "Functions of several variables, with emphasis on partial differential and multiple integration; introduction to vector analysis; may include an introduction to line and surface integrals. Prerequisite: MATH 192." IMPACT: No impact. RATIONALE: Insertion of "may" makes wording more accurate, reflecting the current policy of optional placement of these topics in the course, to be covered by the better classes, if time permits. 3. DELETE: In the statement concerning the Mathematics Minor for Science Teachers, p 145, the word "SCIENCE" should be deleted both in the title and in the specification. Everything else remains the same. IMPACT: See Department of Education statement. RATIONALE: This change was requested by the Education Department; it is felt this would allow, and encourage, a larger class of teachers to attempt the program. 4. DELETE: Prerequisite statement of MATH 332, p 147. ADD: "Prerequisites: MATH 280 and 291." IMPACT: No impact. RATIONALE: Most students will have already taken MATH 280 at the time they register for MATH 332, and this merely formalizes the unwritten policy, which is deemed quite appropriate for this course. 5. DELETE: In catalog statement pp 144-145 of PART II in EACH of the four programs for the Mathematics Major under "Other required courses", delete: "CSCI 141 or 142, and 243 (6 hours)." or similar wording. ADD: "CSCI 201 and 202 (6 hours)..." IMPACT: Negligible impact. RATIONALE: This recommendation is made after consultation with members of the Computer Science Department. These two courses are the first two suggested by recent ACM recommendations in the area of Computer Science. 6. DELETE: Course description for both MATH 361, 362, p 147. ADD: "MATH 361, Modern Algebra I (3) - An introduction to the algebraic structures: groups, rings, integral domains, and fields. Basic facts about group and ring homomorphisms are included. Prerequisites: MATH 280 and 291, or permission of the instructor. "MATH 362, Modern Algebra II (3) - An in-depth study of one or more of the ideas introduced in MATH 361; e.g., the Sylow theorems for group or elementary Galois theory of fields. Prerequisite: MATH 361." IMPACT: No impact. RATIONALE: MATH 361 is now taught once yearly by various instructors, so we are splitting the course description between MATH 361 and 362 so that instructors of MATH 361 will have definite topics to cover. 7. DELETE: Course description for both MATH 365, 366, p 147. ADD: "MATH 365, Linear Algebra I (3) - Systems of linear equations, vector spaces, matrices, linear transformations, and theory of determinants. An introduction to inner product spaces to include Gram-Schmidt orhogonalization, eigenvectors, and diagonalization of matrices. Prerequisites: MATH 280 and 291, or permission of the instructor. "MATH 366, Linear Algebra II (3) - An in-depth treatment of topics from MATH 365. Other topics include applications of eigenvalues and eigenvectors; Jordan Canonical form, the Hamilton-Cayley theorem, quadratic forms, and linear programming. Prerequisite: MATH 365." IMPACT: No impact. RATIONALE: MATH 365 is now taught once yearly by various instructors, so we are splitting the course description between MATH 365 and 366 so that instructors of MATH 365 will have definite topics to cover. 8. DELETE: Title and course description of MATH 432, Topo- logy II, and delete "I" from title of MATH 431, p 148. IMPACT: No impact. RATIONALE: To our knowledge this course has never been taught, certainly not in the last 9 years. Should student interest arise for this course at some later date, accommodation could be made with a Special Topics course. 9. DELETE: Course description for MATH 492, p 148. ADD: "MATH 492, Analysis II (3) - Sequences and series of functions. Further topics may include, for example, introduction to metric spaces, Lebesgue measure and integration, and functions of more than one variable. Prerequisite: MATH 491." IMPACT: No impact. RATIONALE: The new description reflects the course as currently being taught, which meets the approval of the department. 10. DELETE: Prerequisite statements for both MATH 380 and 381, p 147. ADD: Prerequisite statement for MATH 380: "Prerequisites: MATH 291 and at least Junior standing, or permission of the instructor." Prerequisite statement for MATH 381: "Prerequisites: MATH 380 and 291, and at least Junior standing, or permission of the instructor." IMPACT: No impact. RATIONALE: This change will guarantee a deeper mathematics background for students in these courses.