Students taking mathematics courses at the 2000 level or above are expected to be competent in computer programming using languages such as BASIC, C, FORTRAN or PASCAL. This competency can be obtained through completion of CSCE 1020.

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.

**1100 (MATH 1314 or 1414). 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. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1190 (MATH 1325 or 1425). Business Calculus.** 3 hours. Differential and integral calculus with emphasis on applications to business. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1350 (MATH 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. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1351 (MATH 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. *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. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1580 (MATH 1332). Survey of Mathematics with Applications.** 3 hours. Topics include probability, statistics, algebra, logic and the mathematics of finance. Additional topics are selected from geometry, sets, cryptography, fair division, voting theory and graph theory. Emphasis on applications. Recreational and historical aspects of selected topics are also included. Technology is used extensively. MATH 1580 is not intended to prepare students for calculus, science, engineering or business courses.

**1600 (MATH 1316). Trigonometry.** 3 hours. Trigonometry based on both right triangles and the unit circle: graphs of trigonometric functions; inverse trigonometric functions; trigonometric identities and equations; laws of sines and cosines; polar coordinates; DeMoivre’s theorem; vectors. MATH 1600 and 1610 together cover approximately the same material as MATH 1650. Students who already have credit for MATH 1650 may not receive credit for MATH 1600. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1610. Functions, Graphs and Applications.** 3 hours. Preparatory course for calculus: algebra and graphs of functions; properties and graphs of polynomials and rational functions; graphs and applications of exponential and logarithmic functions; applications of trigonometric functions and graphs; sequences, series and their applications. MATH 1600 and 1610 together cover approximately the same material as MATH 1650. Students who already have credit for MATH 1650 may not receive credit for MATH 1610.

Satisfies the Mathematics requirement of the University Core Curriculum.

**1650 (MATH 2312 or 2412). Pre-Calculus.** 5 hours. Preparatory course for calculus: trigonometric functions, their graphs and applications; sequences and series; exponential and logarithmic functions and their graphs; graphs of polynomial and rational functions; general discussion of functions and their properties. MATH 1650 covers approximately the same material as MATH 1600 and 1610 together. Students who already have credit for both MATH 1600 and MATH 1610 may not receive credit for MATH 1650. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1680 (MATH 1342 or 1442). 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. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1710 (MATH 2313 or 2413 or 2513). Calculus I.** 4 hours. Limits and continuity, derivatives and integrals; differentiation and integration of polynomial, rational, trigonometric, and algebraic functions; applications, including slope, velocity, extrema, area, volume and work. *Satisfies the Mathematics requirement of the University Core Curriculum.*

**1720 (MATH 2314 or 2414). Calculus II.** 3 hours. Differentiation and integration of 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. *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.

**2100. Functions and Modeling for Secondary Mathematics Instruction.** 3 hours. In-depth study of topics in secondary school mathematics. Emphasis is on modeling with linear, exponential and trigonometric functions; curve fitting; discrete and continuous models. Exploratory work with presentations of findings is an integral part of the course. Pedagogical uses of appropriate technology are explored.

**2700 (MATH 2318 or 2418). 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.

**2730 (MATH 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.

**2770 (MATH 2305 or 2405). Discrete Mathematical Structures.** 3 hours. Introductory mathematical logic, mathematical induction, relations and functions, combinatorics, counting techniques, graphs and trees, and finite automata theory.

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

**3000. 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.

**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.

**3310. Differential Equations for Engineering Majors.** 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 majors. Only one of MATH 3310 and MATH 3410 may be used to satisfy requirements for a mathematics major or minor.

**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.

**3400. Number Theory.** 3 hours. Factorizations, congruencies, quadratic reciprocity, finite fields, quadratic forms, diophantine equations.

**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. Only one of MATH 3310 and MATH 3410 may be used to satisfy requirements for a mathematics major or minor.

**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.

**3510. Introduction to Abstract Algebra I.** 3 hours. Groups, rings, integral domains, polynomial rings and fields.

**3520. Abstract Algebra II.** 3 hours. Topics from coding theory, quadratic forms, Galois theory, multilinear algebra, advanced group theory, and advanced ring theory.

**3610. Real Analysis II.** 3 hours. Continuation of 3000. Topics include derivatives, integrals, limits of sequences of functions, Fourier series; and an introduction to multivariable analysis.

**3680. Applied Statistics.** 3 hours. Descriptive statistics, elements of probability, random variables, confidence intervals, hypothesis testing, regression, contingency tables.

**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.

**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 secondary and collegiate curricula. Combinatorics. The Euclidean algorithm, congruence classes, and prime factorization. Modeling with differential equations. Conic sections. Pedagogical techniques.

**4060. Foundations of Geometry.** 3 hours. Selections from synthetic, analytic, projective, Euclidean and non-Euclidean geometry.

**4100. Fourier Analysis.** 3 hours. Application-oriented introduction to Fourier analysis, including Fourier series, Fourier transforms, discrete Fourier transforms, wavelets, orthogonal polynomials and the Fast Fourier Transform (FFT) algorithm. The theoretical portions of the course emphasize interconnections and operator algebraic formalism. Applications are chosen from among differential equations, signal processing, probability and high precision arithmetic.

**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.

**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.

**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.

**4500. Introduction to Topology.** 3 hours. Point set topology; connectedness, compactness, continuous functions and metric spaces.

**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.

**4610. Probability.** 3 hours. Combinatorial analysis, probability, conditional probability, independence, random variables, expectation, generating functions and limit theorems.

**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.

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

**4951. Honors College Capstone Thesis.** 3 hours. Major research project prepared by the student under the supervision of a faculty member and presented in standard thesis format. An oral defense is required of each student for successful completion of the thesis.

Date of initial release: July 1, 2009 — Copyright © 2008 University of North Texas

Page updated:
March 22, 2010
— Comments or corrections: catalog@unt.edu

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