In the 2017-2018 Catalog

# Mathematics (MA)

### Courses

MA 106  Basic Algebra and Trigonometry  3 Credits (3,0)

A study of the basic laws of fractions, exponents, radicals, inequalities, quadratic equations, complex numbers, and the elements of trigonometry. (This is a developmental course; credit is not applicable to any degree.)

MA 111  College Mathematics for Aviation I  3 Credits (3,0)

A pre-calculus course designed for the student of aviation. Review of the fundamentals of algebra; linear equations and inequalities; quadratic equations; variation; polynomial, rational, exponential, logarithmic, and trigonometric functions; radian measure; right triangle solutions, vectors, and the laws of sines and cosines.

MA 112  College Mathematics for Aviation II  3 Credits

This course presents basic calculus, designed for the student of aviation. Topics include differentiation and integration of algebraic functions; applications to velocity, acceleration, area curve sketching and computation of extreme values.

MA 120  Quantitative Methods I  3 Credits (3,0)

An algebra methods course with applications to business and economics. Operations, relations, functions, modeling, and problem solving; systems of linear equations and inequalities.

MA 140  College Algebra  3 Credits (3,0)

This course focuses on fundamentals of exponents, radicals, linear and quadratic equations, inequalities, functions, graphing techniques, and complex numbers. It includes an introduction to function; curve sketching; elementary theory of equations; sequences and series; matrix algebra and systems of equations; linear; polynomial; logarithmic; exponential; inverse and composite functions; variation; and systems of equations.

MA 142  Trigonometry  3 Credits (3,0)

Trigonometric functions and their graphs; identities; radian measure with applications; compound, half, and double angle identities; solving elementary trigonometric equations, right and oblique triangles; law of sines and cosines; inverse trigonometric functions; vectors and trigonometric form of a complex number.

MA 143  Precalculus Essentials  3 Credits

An introduction to the calculus sequence with an emphasis on functions and their graphs, including polynomial, rational, exponential, logarithmic and trigonometric; radian measure; trigonometric identities and equations.

MA 145  College Algebra and Trigonometry  5 Credits (5,0)

Fundamentals of exponents, radicals, linear and quadratic equations, inequalities, elementary theory of equations, sequences and series, functions, exponential, logarithmic, and trigonometric functions, radian measure, trigonometric identities and equations, vectors, laws of sines, cosines, solutions of right triangles, and complex numbers.

MA 199  Special Topic in Mathematics  1-6 Credit

Individual independent or directed studies of selected topics in mathematics.

MA 220  Quantitative Methods II  3 Credits (3,0)

This course is an introductory calculus course with applications to business and economics; limits; differentiation and integration of algebraic, exponential, and logarithmic functions; applications of differentiation to maximizing and minimizing; curve sketching; and marginal values.
Prerequisites: MA 111 or MA 120.

MA 222  Business Statistics  3 Credits (3,0)

This course is a study of basic descriptive and inferential statistics. Topics include types of data, sampling techniques, measures of central tendency and dispersion, elementary probability, discrete and continuous probability distributions, sampling distributions, hypothesis testing, confidence intervals, and simple linear regression.
Prerequisites: MA 111 or MA 120 or MA 140 or MA 145.

MA 225  Introduction to Discrete Structures  3 Credits (3,0)

An introduction to the fundamental algebraic, logical, and combinatorial concepts of mathematics that provides a foundation for the study of computer science.

MA 241  Calculus and Analytical Geometry I  4 Credits (4,0)

Limits and continuity; differentiation and integration of algebraic and elementary transcendental functions; applications of first and second derivatives.

MA 242  Calculus and Analytical Geometry II  4 Credits (4,0)

Differentiation and integration of transcendental functions; special integration techniques; applications of the definite integral; numerical methods; infinite series.
Prerequisites: MA 241.

MA 243  Calculus and Analytical Geometry III  4 Credits (4,0)

Solid analytic geometry; vector functions in three dimensions; partial differentiation; directional derivative and gradient; line integrals; multiple integrals
Prerequisites: MA 242.

MA 299  Special Topics in Mathematics  1-6 Credit

Individual independent or directed studies of selected topics in mathematics.

MA 320  Decision Mathematics  3 Credits (3,0)

The mathematical concepts and applications in mathematical model building and problem solving. Included are mathematical areas that are basic to decision theory
Prerequisites: MA 222.

MA 335  Introduction to Linear and Abstract Algebra  3 Credits (3,0)

Theoretical aspects of modern algebra are presented. Methods of proof writing are introduced. Introductory topics in linear and abstract algebra will be discussed, as well as some of their applications.
Prerequisites: MA 242 Corequisites: MA 243.

MA 341  Introduction to Mathematical Analysis  3 Credits (3,0)

Careful treatment of the theoretical aspects of the calculus of functions of a real variable. Topics include the real number system, limits, continuity, derivatives, the Riemann integral, elementary notions of topology, and metric spaces.
Prerequisites: MA 243.

MA 345  Differential Equations and Matrix Methods  4 Credits (4,0)

Treatment of ordinary differential equations to include principal types of first and second order equations; methods of substitution on simple higher order equations; linear equations and systems of linear equations with constant coefficients; methods of undetermined coefficients and variation of parameters; Laplace transforms; series solutions; linear algebra and matrix methods of solutions; and applications to physics and engineering.
Prerequisites: MA 243.

MA 348  Numerical Analysis I  3 Credits (3,0)

Floating point arithmetic, error analysis, algorithms in interpolation, integration, differentiation, matrix algebra, approximation and solution of equations, use of numerical software packages.
Prerequisites: CS 210 and MA 345.

MA 399  Special Topics in Mathematics  1-6 Credit

Individual independent or directed studies of selected topics in mathematics.

MA 404  Statistics and Research Methods  3 Credits (3,0)

Elements of probability theory including finite probability spaces, conditional probabilities, independence, correlation, Bayes Theorem, and Gaussian random variables. Statistical methods including contingency tables, regression, hypothesis testing. Experimental design. Ethical considerations in experimentation. Nonquantitative research methodologies. Numerical methods including the introduction of at least one computer-based statistics package.
Prerequisites: MA 112 or MA 241.

MA 412  Probability and Statistics  3 Credits (3,0)

Finite sample spaces; conditional probability and Bayes Theorem, discrete and continuous random variables and their functions; expected value, variance, and standard deviation; systematic study of the major discrete and continuous distributions; moment generating functions; hypothesis testing and estimation.
Prerequisites: MA 243.

MA 432  Linear Algebra  3 Credits (3,0)

Review of vector and matrix operations including matrix inverses, eigenvectors, and eigenvalues. Equations of lines and planes, vector spaces including basis and dimensions, linear transformations, change of basis, diagonalization of matrices, inner products and orthonormal bases, applications.
Corequisites: MA 345.

MA 433  Introduction to Optimization  3 Credits (3,0)

This course will cover mathematical optimization methods, problem formulation, and optimality criteria, linear programming methods for optimality problems, numerical methods for unconstrained and constrained problems, sequential linear programming, genetic algorithms, and hybrid optimal control.
Prerequisites: EGR 115 and MA 345 and Junior Standing.

MA 435  Linear and Abstract Algebra II  3 Credits (3,0)

This course is designed to provide students with some advanced skills and knowledge of linear and abstract algebra. Brief introductions of several advanced topics are expected to be discussed. Assuming a basic knowledge of linear and abstract algebra, topics that are covered in this course include but are not limited to: Hilbert spaces, finite-dimensional spectral theorem for normal operators, a brief introduction to tensor products, and non-associative algebra.

MA 441  Mathematical Methods for Engineering and Physics I  3 Credits (3,0)

Line and surface integrals; vector fields with the study of Green, Gauss, and Stokes Theorems; applications of vector field theory; Fourier series.
Prerequisites: MA 243.

MA 442  Mathematical Methods for Engineering and Physics II  3 Credits (3,0)

The solution of linear differential equations with variable coefficients; study of the derivation, characteristics, and solutions of partial differential equations; Fourier series, Fourier transform, Laplace transform, and Green's function; applications in science and engineering.
Prerequisites: MA 345 and MA 441.

MA 443  Complex Variables  3 Credits (3,0)

Algebra of complex numbers; complex functions, analytic functions; mapping by elementary functions; conformal mappings and their applications; additional topics may include complex integration, power series expansion.
Prerequisites: MA 441.

MA 499  Special Topics in Mathematics  1-6 Credit

Individual independent or directed studies of selected topics in mathematics.