Catalog of North Texas State University: 1982-1983, Undergraduate Page: 82
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vlathematics
180. Finite Mathematics. 3 hours. Elemen-
tary symbolic logic, set operations
and counting problems, probability theory,
vectors and matrices, and selected
topics from game theory, linear program-
ming, computer programming and
statistics. Prerequisite: admission to honors
program or consent of department.
209. Structure of the Number System.
3 hours. Laws of the real number system;
fundamental concepts and structure of
modern elementary mathematics.
For elementary education majors.
270. Linear Algebra and Vector
Geometry. 3 hours. Vector spaces over the
real number field; applications to
systems of linear equations and analytic
geometry in En Linear transforma-
tions, matrices, determinants, eigenvalues.
Prerequisite: Mathematics 172.
273. Multi-Variable Calculus. 3 hours.
Infinite series, power series, Taylor's
theorem; vectors and analytic geometry in
3-space; partial and directional
derivatives; extrema; double and triple
integrals; applications; cylindrical
and spherical coordinates. Prerequisite:
Mathematics 172.
306. Undergraduate Seminar in Selected
Axiomatic Theories. 3 hours. Selec-
tions from sets, relations, functions and
other basic field of mathematics,
stressing rigor, discrimination, technique in
mathematical reasoning. Prerequi-
site or corequisite: Mathematics 270.
311. Structure of the Real Number
System. 3 hours. Continuation of 209; real
numbers; rationals; irrationals; func-
tions. Prerequisite: Mathematics 209.
312. Fundamental Concepts in
Geometry. 3 hours. Geometric concepts;
logic and proof; postulation method;
congruence; parallels; space figures;
similarity and trigonometry; area and
its generalizations; spherical geometry;
plane coordinate geometry. Prere-
quisite: Mathematics 209 or consent of
department.
314. Topics for Basic Mathematics.
3 hours. For prospective or in-service
teachers. Fundamental contemporary
mathematical concepts; associated
teaching techniques used in grades 6, 7, 8
and in general mathematics courses.
Prerequisite: 12 semester hours of
mathematics including 311, or consent of
department.
315. Topics in Geometry. 3 hours. For
prospective or in-service teachers;
fundamental contemporary concepts in
introductory geometry.
319. Topics in Secondary School
Mathematics Teaching. 3 hours. For
prospective or in-service teachers; meth-320. Topics in Algebra. 3 hours. For
prospective or in-service teachers; funda-
mental contemporary concepts in
introductory algebra.
325. Introduction to Discrete Applied
Mathematics. 3 hours. Introduction to the
techniques of discrete applied
mathematics. Topics include basic combi-
natorial analysis, error-correcting
codes, graphs and graphic algorithms and
discrete combinatorial optimization.
Prerequisite: Mathematics 172.
341 Differential Equations. 3 hours.
First-order differential equations; linear
differential equations with constant
coefficients; other linear equations; sys-
tems of differential equations; power
series solutions. Prerequisite: Mathematics
172.
342. Intermediate Differential Equations.
3 hours. Laplace transforms; boundary
value and eigenvalue problems; oscillation
and comparison theorems; stability
theory. Prerequisite: Mathematics 270, 273
and 341.
406. Foundations of Geometry. 3 hours.
Selections from synthetic, analytic,
projective, Euclidean, and non-Euclidean
geometry. Prerequisite: consent of
department.
411. Mathematical Methods in the
Physical Sciences. 3 hours. Vector
analysis, ordinary differential equa-
tions, functions of a complex variable and
group theoretic methods. Prerequi-
site: Mathematics 273 or consent of
instructor. (Mathematics majors may
not use 411 to satisfy any part of
mathematics requirement for graduation.)
415. Introduction to Partial Differen-
tial Equations. 3 hours. Existence and
uniqueness theorems; hyperbolic,
parabolic and elliptic differential equations
of the second order; method of
characteristics; certain boundary value
problems. Prerequisite: Mathematics
341 or equivalent.
435. Introduction to Numerical Analysis.
3 hours. Description and mathematical
analysis of methods used for solving
problems of a mathematical nature on the
computer. Roots of equations, sys-
tems of linear equations, polynomial
interpolation and approximation,
least squares approximation, numerical
solution of ordinary differential equa-
tions. Prerequisite: Mathematics 270 and
a programming language.
440. Introduction to Abstract Algebra.
3 hours. Groups, rings, integral
domains, polynomial rings and fields.
Prerequisite: Mathematics 306.ods and materials. Prerequisite:
Mathematics 440 or consent of department.441. Advanced Calculus. 3 hours. Theories
of limits, continuity and differentiability
for functions of one and more variables;
vectors; transformations and implicit
functions; extreme values. Prerequisite:
Mathematics 270 and 273.
445. Introduction to the Theory of Matrices.
3 hours. Congruence (Hermitian);
similarity; orthogonality, matrices with
polynomial elements; minimal polyno-
mials; Cayley-Hamilton Theorem; bilinear
and quadratic forms; eigenvalues.
Prerequisite: Mathematics 270.
450. Introduction to Topology. 3 hours.
Point set topology; connectedness,
compactness, continuous functions,
metric spaces. Prerequisite: Mathematics
306.
451. Fourier Series. 3 hours. Expansion of
functions in Fourier series; represen-
tation theory; convergence theory; orthogo-
nal sets of functions; introduction to
Bessel functions, Legendre polynomials
and Fourier integrals; applications to
boundary value problems. Prerequisite:
Mathematics 341.
452. Introduction to Functions of a
Complex Variable. 3 hours. Algebra of
complex numbers, geometric representation;
analytic functions; elementary func-
tions, map ping; real line integrals;
complex integration; power series;
residues, poles; conformal mapping, appli-
cations. Prerequisite: Mathematics
273.
461. Probability. 3 hours. Combina-
torial analysis, probability, conditional
probability, independence, random
variables, expectation, generating func-
tions, limit theorems. Prerequisite:
Mathematics 172.
465. Statistics. 3 hours. Sampling
distributions, point estimation, interval
estimation, hypothesis testing, good-
ness of fit tests, regression and correlation,
analysis of variance, nonparametric
methods. Prerequisite: Mathematics 461.
490-491. Special Problems. 1-3
hours each.
496-497. Mathematics Institute. 1-6
hours each. For students accepted by
NTSU as participants in special
institute courses. May be repeated for
credit but not to exceed a total of 6
hours in each course.
Graduate Courses
501. Foundations of Mathematics. 3 hours.
511-512. Introduction to Analysis.
3 hours each.
521-522. Numerical Analysis.
3 hours each.525. Theory of Algorithms. 3 hours.
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North Texas State University. Catalog of North Texas State University: 1982-1983, Undergraduate, book, May 1982; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc799596/m1/84/?q=%22Department+of+English%22: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .