OEO Office of Equal Opportunity - Department of Mathematics and ...

248 ARTS AND SCIENCES
181. Elements of Calculus II. (3) 1
Includes the definite integral, multivariate calculus, simple
differential equations, basic review of trigonometry and its
relation to calculus.
Prerequisites: 180. {Summer, Fall, Spring}
264. Calculus III. (4)
Vector operations, vector representation of planes and
curves, functions of several variables, partial derivatives,
gradient, tangent planes, optimization, multiple integrals in
Cartesian cylindrical and spherical coordinates, vector fields,
line integrals and Green’s theorem.
Prerequisite: C (not C-) or better in 163. {Summer, Fall,
Spring}
Footnote:
1 See Restrictions earlier in Mathematics and Statistics.
II. Courses for Teachers and
Education Students
The following courses are intended primarily for undergraduate
and graduate students in the College of Education and for
others seeking teaching certification. Other persons may be
admitted to these courses by permission of the department
chairperson.
111. Mathematics for Elementary and Middle School
Teachers I. (3)
The intuitive and logical background of arithmetic; properties
of sets; algorithms of arithmetic in base ten and other bases;
properties of the integers, mathematical terminology; elements
of number theory; problem solving.
Prerequisites: ACT=>19 or SAT=>450 or IS-M 100 or
Compass Pre-Algebra >56 or Algebra >33. {Summer, Fall,
Spring}
112. Mathematics for Elementary and Middle School
Teachers II. (3)
The properties of the rational number system; extension to
the irrationals; decimal and fractional representation of real
numbers; geometry.
Prerequisite: C (not C-) or better in MATH 111. {Summer,
Fall, Spring}
215. Mathematics for Elementary and Middle School
Teachers III. (3)
Topics from probability and statistics, coordinate geometry and
measurement, and algebra; some applications of mathematics;
elements of logic; enrichment topics for the classroom.
Prerequisites: 112. {Summer, Fall, Spring}
300. Computing in the Mathematics Curriculum. (3) 2
Use of computers and graphing utilities in the mathematics
classroom. Introduction to hardware and commercial software.
Applications of selected programming languages to the
teaching of mathematics.
Prerequisite: 162 or 181.
305. Mathematics from a Historical Perspective. (3) 2
A survey of mathematical developments prior to 1800;
emphasis on problem solving techniques; comparison of
older and more modern methods.
Prerequisite: 163. {Fall}
306. College Geometry. (3) 2
An axiomatic approach to fundamentals of geometry, both
Euclidean and non-Euclidean. Emphasis on historical development
of geometry. {Spring}
308. Theory and Practice of Problem Solving. (3) 2
An experience in mathematical invention and discovery at
the level of high school geometry and algebra that includes
a deeper look at sequences, series, and recursions. {Offered
upon demand}
Prerequisite: 180 or 162. Corequisite: 306.
309. Applications of Mathematics. (3) 2
An experience in mathematical invention and discovery at
the level of high school geometry and algebra that includes a
deeper look at sequences, series, and recursions.
Prerequisite: 181 or 163.
338. Mathematics for Secondary Teachers. (3) 2
Topics from secondary mathematics presented from an
advanced standpoint and designed to meet the needs of
pre- and in-service teachers. Open only to prospective and
in-service teachers of mathematics.
Prerequisite: 163 or 181. {Fall}
339. Topics in Mathematics for Elementary and Middle
School Teachers. (1-3, no limit) ∆ 2
Presents mathematical topics of concern to elementary and
mid-school teachers. Open only to in-service and prospective
teachers. May be repeated for credit by permission of instructor.
{Offered upon demand}
Restriction: permission of instructor.
350. Topics in Mathematics for Secondary Teachers.
(1-3, no limit) ∆ 2
Presents mathematical topics of concern to secondary teachers.
Open only to in-service and prospective teachers. May
be repeated for credit by permission of instructor. {Offered
upon demand}
Restriction: permission of instructor.
Footnote:
2 These courses are available for graduate credit for
Masters Programs in the College of Education.
III. Upper-Level Undergraduate
Courses
311. Vector Analysis. (3)
Vector algebra, lines, planes; vector valued functions, curves,
tangent lines, arc length, line integrals; directional derivative
and gradient; divergence, curl, Gauss’ and Stokes’ theorems,
geometric interpretations.
Prerequisite: 264. {Summer, Fall, Spring}
**312. Partial Differential Equations for Engineering. (3)
Solution methods for partial differential equations; science
and engineering applications; heat and wave equations,
Laplace’s equation; separation of variables; Fourier series
and transforms; special functions.
Prerequisites: 264, 316. {Summer, Fall, Spring}
**313. Complex Variables for Engineering. (3)
Theory of functions of a complex variable with applications to
physical and engineering problems.
Prerequisite: 264. Recommended: 311. {Spring}
**314. Linear Algebra with Applications. (3) 1
Systems of linear equations, matrices, linear transformations,
determinants, eigenvalues and eigenvectors. Efficient computational
methods emphasized.
Prerequisite: 163 or 181. {Summer, Fall, Spring}
**316. Applied Ordinary Differential Equations. (3)
An introduction to the algorithmic theory of ordinary differential
equations. Topics to be covered: elementary theory of
ordinary differential equations, numerical methods, phaseplane
analysis, introduction to Laplace transformations.
Prerequisite: 163. 264 is recommended. {Summer, Fall,
Spring}
**317. Elementary Combinatorics. (3)
Basic enumeration including combinations, permutations,
set and integer partitions, distributions, and rearrangements,
binomial and multinomial theorems together with pigeon-hole
and inclusion-exclusion principles and mathematical induction
principles. Discrete probability, elementary ordinary generating
functions, recurrence relations, and sorting algorithms.
Prerequisite: 163 or 181. {Fall}
UNM CATALOG 2006–2007 Symbols, page 611.