## MATHEMATICS (MATH-510)

070 Developmental Algebra I (3) Linear equations and inequalities. Exponents, roots, and radicals. Polynomials. Rational expressions. May not be counted toward any degree requirements, but may be substituted for one unit of high school Algebra I.

080 Developmental Algebra II (3) Quadratic equations and inequalities. Graphing and straight lines. Systems of linear equations. Inverse, exponential, and logarithmic functions. May not be counted toward any degree requirements, but may be substituted for one unit of high school Algebra II.

090 Developmental Geometry (3) Selected topics from unified geometry. May not be counted toward any degree requirements, but may be substituted for one unit of high school Unified Geometry.

130 The Nature of Mathematics (3) Selected topics from algebra, geometry, number theory, logic, probability, statistics, management science, finance, computing and numerical techniques. Modeling and problem solving techniques will be illustrated to give students insight into what mathematics is, what mathematics attempts to accomplish, and how mathematics is used to solve real life problems. May not be used to satisfy degree requirements for the B.S. degree in Arts & Sciences. May not be taken for credit by any student who has successfully completed a higher-numbered mathematics course. Prereq: One unit of high school geometry and either two units of high school algebra and a satisfactory score on the placement test or Math 080.

140 College Algebra and Elementary Functions (3) Functions (e.g., polynomial, exponential, and logarithmic). Zeroes of polynomials. Solutions of systems of equations and inequalities. Triangle trigonometry. Selected topics from algebra such as matrices and determinants, and arithmetic and geometric sequences. Prereq: Two units of high school algebra.

160 Calculus for Business and Life Sciences (3) Average and instantaneous rates. The derivative and its application to curve tracing and max-min theory. Antiderivative, area under a curve, fundamental theorem. Natural logarithm and its application to interest, growth, and decay. Prereq: Math 140 or equivalent.

185 Precalculus (5) Algebraic properties of real numbers. Solutions of equations and inequalities. Logarithmic and exponential equations. Survey of conics. Trigonometric functions, identities, graphs, and equations. Trigonometric applications. Prereq: Two units of high school algebra and one unit of high school geometry.

191-192 Principles of Mathematics (3, 3) Algorithms for four basic operations, systems of whole numbers and integers. Relations and functions. Greatest common factor and least common multiple. Fractions, decimals, percent, ratio, and proportion. Statistic and probability. Metric system, measurement, area, volume, informal plane and solid geometry. These are manipulative and activity based courses. Courses must be taken in sequence. Prereq: Math 140.

210 Elementary Statistics and Probability (3) Descriptive measures, elementary probability, sampling, random variables. Discrete probability distributions, normal probability distributions, and introduction to inference theory. Prereq: Math 140 or equivalent.

230 FORTRAN Programming (3) Concepts of the FORTRAN language including file handling techniques. Prereq: Math 160 or Math 251. (Same as Comp Sc 230)

241 Foundations of Mathematics (3) Proof techniques, sets, propositional calculus, functions, relations and properties of integers. Pre-req: Math 140 or equivalent. Credit may not be received for both Math 241 and Comp Sc 301.

251-252 Calculus I, II (4, 4) Limits and continuity. Derivatives and integrals of polynomial, exponential, logarithmic, trigonometric, and hyperbolic functions. Techniques of integration, conics, parametric and polar equations, indeterminate forms, and improper integrals. Infinite series, including Taylor’s series. Must be taken in sequence. Prereq: One unit high school Unified Geometry and either Math 185 or (two units of high school Algebra I and II and 1/2 unit high school trigonometry).

291 Special Topics in Mathematics (1-3) Lectures and/or laboratory work relating to specialized topics in mathematics. Course may be repeated with total credits not to exceed six (6) hours. May be offered on a Pass/Fail basis. Prereq: Instructor’s approval.

310 Linear Algebra (3) Vectors, matrices, systems of linear equations, determinants, inverses of matrices, vector spaces, linear transformations, eigenvalues and eigenvectors. Prereq: Math 160 or Math 241 or Math 251.

320 Multivariate Calculus (4) Vector-valued functions, functions of several variables. Differentials, gradients, and extrema. Multiple integrals, line and surface integrals. Prereq: Math 252.

330 Differential Equations (3) Setting up and solving first order equations, applications of first order equations. Wronskians, use of operators and the exponential shift theorem, solutions of higher order equations with constant coefficients, systems of first order equations, solutions in series, Laplace transform methods. Prereq: Math 252.

340 (540) Numerical Analysis (3) Formulation of numerical problems for solution on a digital computer. Error analysis and control, nonlinear equations, differentiation, integration, systems of equations, differential equations, curve fitting and eigenvalue problems. Prereq: Math 252, Math 310 or Comp Sc 301, and FORTRAN or Pascal or "C". (Same as Comp Sc 340/540)

350 Number Theory (3) The integers: well-ordering, different bases, divisibility, primes, and factoring. The fundamental theorem of arithmetic and the division algorithm. Diophantine equations and applications of congruences. Pseudorandom numbers, pseudoprimes, and cryptography. Prereq: Math 241.

360 Applied Statistical Methods: Regression Analysis and Analysis of Variance (3) Simple and multiple regression models. One factor and two factor analysis of variance. Use of least squares to estimate parameters. Estimation, hypothesis testing, and model fitting. Applications using appropriate software packages. Prereq: Math 210 and Math 251.

370 Topics in Applied Statistics: Time Series Analysis (3) Stochastic Time Series methods, analysis and applications, model building techniques, estimation of model parameters, relevant hypothesis tests and forecasting. Appropriate software packages will be used. Prereq: Math 210 and Math 252, or equivalent.

410 (610) Geometry (3) Euclidean geometry (Birkhoff’s and Hilbert’s Postulates), non-Euclidean geometries (hyperbolic and elliptic), finite geometries, transformational geometry, and theory of area. Prereq: Math 241.

420 (620) History of Mathematics (3) Study of the development of mathematics from ancient to modern times through problem solving. The investigation of the lives and works of specific mathematicians with particular attention to the development of ideas, notation, and the influence of mathematics on society. Prereq: Math 160 or Math 251.

430 (630) Complex Variables (3) Algebraic operations and geometry of complex numbers, definitions of limit continuity, and analytic functions, differentiation, mapping of simple functions, line integrals, Cauchy integral formula, Laurent series, evaluation of real integrals using residue theorem. Prereq: Math 320.

451 (651) Applications and Modeling (3) Practical applications of mathematics including optimization, interpolation and best fit, simulation, dimensional analysis and graph theory. Mathematical model building including problem identification, model construction or selection, fine tuning and validation. Prereq: Math 310 and Math 320.

461-462 (661-662) Probability and Statistics I, II (3, 3) Discrete and continuous probability spaces, statistical independence, distributions, discrete and continuous random variables, expectations, moment-generating functions, limiting distributions, estimation of parameters, confidence intervals, hypothesis testing with applications, linear regression and correlation, multiple linear regression. Must be taken in sequence. Prereq: Math 252 is a prerequisite for Math 461. Math 320 and Math 461 are prerequisites fro Math 462.

471-472 (671-672) Abstract Algebra I, II (3, 3) Equivalence relations and partitions. Properties of the integers. Elementary theory of groups and rings. Polynomial rings, integral domains, divisibility, unique factorization domains, fields, Vector spaces, and linear transformations. Students are required to submit written work and make an oral presentation. Must be taken in sequence. Prereq: Math 241 and Math 310.

481-482 (681-682) Real Analysis I, II (3, 3) Sets and countability. The real number systems. Sequences, limits, infinite series, metric spaces, continuous functions, uniform continuity, and convergence. Riemann and Lebesgue integration. Students are required to submit written work and make an oral presentation. Must be taken in sequence. Prereq: Math 241 and Math 320.

491-492 (691-692) Special Topics (1-3, 1-3) Selected topics in mathematics, student research, or seminar. Course may be repeated with total credits not to exceed six hours. Prereq: Math 320 and departmental approval.

710 Selected Topics in Arithmetic for Teachers (3) Selected topics in arithmetic through student research, seminars, or workshops. Prereq: Departmental approval.

720 Selected Topics in Algebra for Teachers (3) Selected topics in algebra through student research, seminars, or workshops. Prereq: Departmental approval.

730 Selected Topics in Geometry for Teachers (3) Selected topics in geometry through student research, seminars, or workshops. Prereq: Departmental approval.