Mathematics

Mathematics, MATH = 0150

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.

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 (2312 or 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 or 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. 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 (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. 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.

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. Satisfies the Mathematics requirement of the University Core Curriculum (for elementary education students).

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 and 2730.

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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