Students taking mathematics courses at the 2000 level or above are expected to be competent in computer programming using such languages as BASIC, C, FORTRAN or PASCAL. This competency can be obtained through completion of CSCI 1110.

For all mathematics courses, a grade of C or better is strongly recommended before progressing to the next course.

**1010. Fundamentals of Algebra.** 3 hours. Basic algebraic operations, linear equations and inequalities,
polynomials, rational expressions, factoring, exponents and radicals, and quadratic equations. Prerequisite(s): consent of
department. Students may not enroll in this course if they have credit for any other UNT mathematics course. Credit in
this course does not fulfill any degree requirement. Pass/no pass only.

**1100 (1314). College Algebra.** 3 hours. Quadratic equations; systems involving quadratics; variation, ratio
and proportion; progressions; the binomial theorem; inequalities; complex numbers; theory of equations;
determinants; partial fractions; exponentials and logarithms. Prerequisite(s): two years of high school algebra and one year
of geometry, and consent of department. A grade C or better in MATH 1100 is required when MATH 1100 is
a prerequisite for other mathematics courses. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1190 (1325). Business Calculus.** 3 hours. Differential and integral calculus with emphasis on applications to
business. Prerequisite(s): MATH 1100 with grade of C or better.
*Satisfies the Mathematics requirement of the University
Core Curriculum.*

**1350. Mathematics for Elementary Education Majors I.
** 3 hours. Concepts of sets, functions, numeration
systems, different number bases, number theory, and properties of the natural numbers, integers, rational, and real
number systems with an emphasis on problem solving and critical thinking. Only for students requiring course for
teacher certification. Prerequisite(s): MATH 1100 with a grade of C or better.
*Satisfies the Mathematics requirement of the University Core Curriculum.*

**1351. Mathematics for Elementary Education Majors II.
** 3 hours. Concepts of geometry, probability and
statistics, as well as applications of the algebraic properties of real numbers to concepts of measurement with an emphasis
on problem solving and critical thinking. Only for students requiring course for teacher certification.
Prerequisite(s): MATH 1350. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1400. College Math with Calculus.** 3 hours. An applied mathematics course designed for non-science majors.
All topics are motivated by real world applications. Equations, graphs, functions; exponentials and logarithms;
mathematics of finance; systems of linear equations and inequalities, linear programming; probability; basic
differential calculus with applications. Prerequisite(s): two years of high school algebra and consent of department; or
MATH 1100 with grade of C or better. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1650 ( 2412). Pre-Calculus.** 5 hours. A preparatory course for calculus. Trigonometric functions, their graphs
and applications; the conic sections, exponential and logarithmic functions and their graphs; graphs for polynomial and
rational functions; general discussion of functions and their
properties. Prerequisite(s): MATH 1100 with grade of C or
better. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1680 (1342). Elementary Probability and
Statistics.** 3 hours. An introductory course to serve students of any
field who want to apply statistical inference. Descriptive statistics, elementary probability, estimation, hypothesis
testing and small samples. Prerequisite(s): MATH 1100 with grade of C or better.
*Satisfies the Mathematics requirement of the University Core Curriculum.*

**1710 (2413). Calculus I.** 4 hours. Limits and continuity, derivatives and integrals; differentiation and integration
of polynomial, rational and algebraic functions; applications, including slope, velocity, extrema, area, volume
and work. Prerequisite(s): MATH 1650. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1720 (2314). Calculus II.** 3 hours. Differentiation and integration of trigonometric, exponential, logarithmic
and transcendental functions; integration techniques; indeterminate forms; improper integrals; area and arc length in
polar coordinates; infinite series; power series; Taylor's theorem. Prerequisite(s): MATH 1710.
*Satisfies the Mathematics requirement of the University Core Curriculum.*

**1780. Probability Models. **3 hours. Probability theory, discrete and continuous random variables, Markov
chains, limit theorems, stochastic processes, models for phenomena with statistical regularity. Prerequisite(s): MATH 1710.

**2510. Real Analysis I.** 3 hours. Introduction to mathematical proofs through real analysis. Topics include
sets, relations, types of proofs, continuity and topology of the real line. Prerequisite(s): MATH 1720.

**2520. Real Analysis II.** 3 hours. Continuation of 2510. Topics include derivatives, integrals, limits of sequences
of functions, Fourier series; and an introduction to multivariable analysis. Prerequisite(s): MATH 2510 and 2700
(may be taken concurrently).

**2700 (2318). 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 transformations, matrices, determinants
and eigenvalues. Prerequisite(s): MATH 1720.

**2730 (2315). Multivariable Calculus.** 3 hours. Vectors and analytic geometry in 3-space; partial and
directional derivatives; extrema; double and triple integrals and applications; cylindrical and spherical
coordinates. Prerequisite(s): MATH 1720.

**2770 (2305). Discrete Mathematical
Structures.** 3 hours. Introductory mathematical logic, mathematical
induction, relations and functions, combinatorics, counting techniques, graphs and trees, and finite automata
theory. Prerequisite(s): MATH 1710 and CSCI 1110 (may be taken concurrently).

**2900-2910. Special Problems.** 1-3 hours each. May be repeated for credit.

**3010. Seminar in Problem-Solving
Techniques.** 1 hour. Problem-solving techniques involving binomial
coefficients, elementary number theory, Euclidean geometry, properties of polynomials and calculus. May be repeated
for credit.

**3130. Mathematical Proofs.** 3 hours. Axioms of the real numbers; proofs of the basic facts of arithmetic.
Careful logical reasoning is emphasized. Prerequisite(s): MATH 1350 and 1650.

**3140. Topics for Basic Mathematics.** 3 hours. For prospective
or in-service teachers; fundamental contemporary mathematical
concepts. Prerequisite(s): MATH 1350.

**3150. Topics in Geometry.** 3 hours. For prospective or in-service elementary school teachers;
fundamental contemporary concepts in geometry. Prerequisite(s): MATH 1350.

**3310. Differential Equations with Applications.
**3 hours. First order linear equations, separable equations,
second order linear equations, method of undetermined coefficients, variation of parameters, regular singular points,
Laplace transforms, 2x2 and 3x3 first order linear systems, phase plane analysis, introduction to numerical methods
and various applications. Topics include motion problems, electric circuits, growth and decay problems,
harmonic oscillators, simple pendulums, mechanical vibrations, Newton's law of gravity and predator-prey
problems. Recommended for engineering technology majors. May not use both 3310 and 3410 to satisfy a requirement
of differential equations. Prerequisite(s): MATH 1720.

**3350. 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, systems of linear
equations, polynomial interpolation and approximation, least-squares approximation, numerical solution of ordinary
differential equations. Prerequisite(s): MATH 2700 and computer programming ability.

**3400. Number Theory.** 3 hours. Factorizations, congruencies, quadratic reciprocity, finite fields, quadratic
forms, diophantine equations. Prerequisite(s): MATH 3510.

**3410. Differential Equations I.** 3 hours. First-order equations,
existence-uniqueness theorem, linear equations, separation of variables, higher-order linear equations, systems of linear equations, series solutions and
numerical solutions. Prerequisite(s): MATH 1720 and MATH 2700.

**3420. Differential Equations II.** 3 hours. Ordinary differential equations arising from partial differential
equations by means of separation of variables; method of characteristics for first-order PDEs; boundary value problems
for ODEs; comparative study of heat equation, wave equation and Laplace's equation by separation of variables
and numerical methods; further topics in numerical solution of ODEs. Prerequisite(s): MATH 2700 and 3410.

**3510. Introduction to Abstract Algebra
I.** 3 hours. Groups, rings, integral domains, polynomial rings and
fields. Prerequisite(s): MATH 2520.

**3520. Abstract Algebra II.** 3 hours. Topics from coding theory, quadratic forms, Galois theory, multilinear
algebra, advanced group theory, and advanced ring theory. Prerequisite(s): MATH 3510.

**3740. Vector Calculus.** 3 hours. Theory of vector-valued functions on Euclidean space. Derivative as best
linear-transformation approximation to a function. Divergence, gradient, curl. Vector fields, path integrals,
surface integrals. Constrained extrema and Lagrange multipliers. Implicit function theorem. Jacobian matrices.
Green's, Stokes', and Gauss' (divergence) theorems in Euclidean space. Differential forms and an introduction to
differential geometry. Prerequisite(s): MATH 2700 and 2730.

**4050. Advanced Study of the Secondary Mathematics Curriculum.
**3 hours. Study of mathematical topics in the secondary curriculum from an advanced viewpoint. Discussion of the relationship between the secondary
and collegiate curricula. As each of the mathematical topics is studied, related issues involving cognitive
development, pedagogical methods and the philosophy of teaching and learning are considered. Prerequisite(s): MATH 3510
and 4060, EDSE 3830, and acceptance into the secondary teacher education program.

**4060. Foundations of Geometry.** 3 hours. Selections from synthetic, analytic, projective, Euclidean and
non-Euclidean geometry. Prerequisite(s): MATH 2520.

**4100. Fourier Analysis.** 3 hours. Comprehensive theory of Fourier transforms, Fourier series and discrete
Fourier transforms, with emphasis on interconnections. The calculus of Fourier transforms. Operator algebraic
formalism. Hartley transforms. FFT and other fast algorithms. High precision arithmetic. Introduction to generalized
functions (tempered distributions). Applications to signal processing, probability and differential equations.
Prerequisite(s): MATH 3410.

**4200. Dynamical Systems.** 3 hours. One-dimensional dynamics. Sarkovskii's theory, routes to chaos,
symbolic dynamics, higher-dimensional dynamics, attractors, bifurcations, quadratic maps, Julia and Mandelbrot
sets. Prerequisite(s): MATH 2520.

**4430. Introduction to Graph Theory. **3 hours. Introduction to combinatorics through graph theory.
Topics introduced include connectedness, factorization, Hamiltonian graphs, network flows, Ramsey numbers,
graph coloring, automorphisms of graphs and Polya's Enumeration Theorem. Connections with computer science
are emphasized. Prerequisite(s): MATH 2510 or 2770.

**4450. Introduction to the Theory of
Matrices.** 3 hours. Congruence (Hermitian); similarity; orthogonality,
matrices with polynomial elements and minimal polynomials; Cayley-Hamilton theorem; bilinear and quadratic
forms; eigenvalues. Prerequisite(s): MATH 2700.

**4500. Introduction to Topology.** 3 hours. Point set topology; connectedness, compactness, continuous functions
and metric spaces. Prerequisite(s): MATH 2520.

**4520. Introduction to Functions of a Complex
Variable.** 3 hours. Algebra of complex numbers and
geometric representation; analytic functions; elementary functions and mapping; real-line integrals; complex integration;
power series; residues, poles, conformal mapping and applications. Prerequisite(s): MATH 2730.

**4610. Probability.** 3 hours. Combinatorial analysis, probability,
conditional probability, independence, random variables, expectation, generating functions and limit theorems. Prerequisite(s): MATH 2730.

**4650. Statistics.** 3 hours. Sampling distributions, point estimation, interval estimation, hypothesis testing,
goodness of fit tests, regression and correlation, analysis of variance, and non-parametric methods. Prerequisite(s):
MATH 4610.

**4900-4910. Special Problems.** 1-3 hours each.

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