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.
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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
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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,
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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
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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.