**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.

**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.

**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.

**1650 (2312or 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.

**1680 (2342). 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.

**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.

**1720 (2414). 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.

**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.

**2090. Structure and Applications of the Number System.** 3 hours. Logic and set theory; number theory;
geometry; probability and statistics. Only for students requiring course for teacher certification except for those seeking
secondary certification. Prerequisite(s): MATH 1100 with grade of C or better.

**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 or 2415). 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 1650 and 2090.

**3140. Topics for Basic Mathematics.** 3 hours. For prospective or in-service teachers; fundamental contemporary
mathematical concepts. Prerequisite(s): MATH 2090.

**3150. Topics in Geometry.** 3 hours. For prospective or in-service elementary school teachers; fundamental
contemporary concepts in geometry. Prerequisite(s): MATH 2090.

**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.

**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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