Mathematics

Mathematics is the unique language of all physical and social sciences. Students who pursue the study of mathematics are trained to solve problems and to communicate such solutions effectively. This gives the foundation for further professional study in many fields as well as for employment in business and industry.

Major

(B.A. degree) A minimum of thirty hours in mathematics including MAT 125, 225, 325, 301, 310, 415, and 431. The remaining nine hours in mathematics must be chosen from courses numbered above 225. Allied course: CSC 115. Total hours required: 33. (Secondary education mathematics majors are required to include MAT 331 and 335 in the major course selections. Total hours in mathematics and computer science required: 33.)

(B.S. degree) A minimum of thirty-six hours in mathematics including MAT 125, 225, 301, 310, 325, 415, 431 and 432. The remaining twelve hours are to be chosen from courses numbered above 225, and nine hours must be chosen from MAT 331, 332, 343, 345, 405 or MAT/CSC 327. Allied course: CSC 115. Total hours required: 39 (Secondary education mathematics majors are required to take MAT 331 and 335 in the major course selections. Total hours in mathematics and computer science required: 39.)

Minor

A minimum of eighteen hours including MAT 125, 225 and 301. The remaining hours must be chosen from courses numbered above 301. Total hours required: 18.

Students with strong backgrounds in mathematics will be placed at course levels commensurate with demonstrated ability.

A prerequisite must be taken before the course; a co-requisite may be taken before or concurrently with a course.

Course Offerings

103. Mathematics for Elementary School Teachers I. (3 hours) A detailed development of the mathematics taught in elementary school using a problem-solving approach. Topics include sets, numeration, and the real numbering system. For elementary education majors and middle grades mathematics certification students only. Fall

104. Mathematics for Elementary School Teachers II. (3 hours) A continuation of MAT 103. Topics include further development of the real numbering system, informal geometry, probability and statistics. Elementary Education majors only. Prerequisite: MAT 103. Spring

107. College Algebra. (3 hours) A survey of algebraic techniques and of functions. Topics include theory of equations and inequalities, graphs, transformations of functions, inverse functions, and exponential and logarithmic functions. Can be used as preparation for calculus. Not applicable to a major or minor in mathematics. Fall and Spring

109. Calculus for Business and the Social Sciences. (3 hours) An introductory survey of calculus, less theoretical in nature than MAT 125. Topics include derivatives of algebraic, exponential, and logarithmic functions, the definite integral, and applications to business and the social sciences. Prerequisite: None, but MAT 107 is recommended for students with weak backgrounds. Not applicable to a major or minor in mathematics. Fall and Spring

111. Elementary Probability and Statistics. (3 hours) An introductory study of statistics and basic probability theory including such topics as frequency distributions, measures of central tendency, variation, normal distribution and tests of hypotheses. Not applicable to a major or minor in mathematics. Fall and Spring

125. Calculus I. (3 hours) A study of the derivative, its applications, and an introduction to the integral. Topics include limits, continuity, techniques of differentiation, optimization, the Fundamental Theorem of Calculus, and indefinite integrals. Prerequisite: MAT 107 or high school precalculus and knowledge of trigonometric functions. Fall and Spring

170. Special Topics in Mathematics (.5-3 hours)

225. Calculus II. (3 hours) A continuation of the study of the integral and a study of infinite series. Topics include techniques of integration, applications of the definite integral, introduction to differential equations, tests for convergence of series, and power series. Prerequisite: MAT 125 or high school calculus. Fall and Spring

280. Science Careers Seminar. (2 hours) An interdisciplinary seminar in STEM (science, technology, engineering and mathematics) disciplines that will introduce students interested in scientific research to an array of professions and professionals in these fields. This introduction will emphasize comprehension and analysis of published scientific research and provide students with the opportunity to meet the science professional who produced the work. Prerequisites: One science or mathematics course for majors, sophomore or junior standing, and approval of the instructor. Fall

301. Discrete Mathematics. (3 hours) An introduction to fundamental theoretical concepts of mathematics and of mathematics in computer science. Topics include logic, techniques of proof, elementary set theory, mathematical induction, numeration systems, relations and functions, counting techniques, and Boolean algebra. Prerequisite: MAT 107 or its equivalent. Fall and Spring

310. Linear Algebra. (3 hours) A theoretical study of systems of linear equations and vector spaces. Topics include matrix algebra, linear transformations, eigen values and eigenvectors, determinants, and linear programming. Prerequisite: MAT 225 and 301. Spring

325. Calculus III. (3 hours) A continuation of the study of single-variable calculus, and a study of multivariable calculus. Topics include parametric equations, polar coordinates, vectors and vector-valued functions, partial differentiation, Lagrange multipliers, double and triple integrals, and line integrals. Prerequisite: MAT 225. Fall and Spring

327. Introduction to Numerical Methods. (3 hours) An introduction to the analysis and implementation of numerical methods. Topics include number representation and errors, locating roots of equations, interpolation, numerical differentiation, numerical integration, numerical solution of linear systems of equations, approximation by spline functions, numerical solution of differential equations, and the method of least squares. Prerequisites: CSC115 and MAT301. Odd Springs

331. Probability Theory. (3 hours) A study of chance phenomena and probability distributions. Topics include probability laws and elementary combinatorics, random variables, mean and variance, discrete and continuous probability distributions, the Central Limit Theorem, and laws of large numbers. Prerequisite: MAT 225. Even Falls

332. Mathematical Statistics. (3 hours) A study of statistical methods and tests of hypotheses. Topics include estimation of parameters, test of hypotheses, linear regression, and analysis of variance. Prerequisite: MAT 331. Odd Springs

335. Advanced Geometry. (3 hours) A rigorous but non-axiomatic treatment of advanced geometry on the Euclidean plane, from two or more points of view. Possible viewpoints include synthetic geometry, vector geometry, and geometry using complex numbers. Usually additional topic(s) will be covered, with such topics typically being drawn from axiomatic development of elementary geometry, geometry in higher dimensions, non-Euclidean geometries, and historical studies, especially geometry in non-Western cultures. Prerequisites: MATH 125 and 301. Odd Falls

343. Mathematical Modeling. (3 hours) An introduction to the study of modeling real-world phenomena, with an emphasis on applications to science. Topics include modeling using difference equations and differential equations, simulation, matrix modeling and Markov chains, and dimensional analysis. Prerequisite: MAT 125. Odd Falls

345. Ordinary Differential Equations. (3 hours) A study of solution methods and applications of differential equations. Topics include first order equations, higher order linear equations, the Laplace transform, and power series techniques. Corequisite: MAT 325. Spring

405. Complex Analysis. (3 hours) An introduction to the study of functions of one complex variable. Topics include the algebra of complex numbers, analytic functions, contour integrals, power series, the Residue Theorem, and conformal mappings. Corequisite: MAT 325. Odd Springs

413. Number Theory and Cryptology. (3 hours) A survey of topics in elementary number theory, with an emphasis on applications to cryptology. Topics include modular arithmetic, the Chinese Remainder Theorem, the Euler phi function, pseudoprimes, and various cyptosystems, including affine substitutions, the Vigenere square, and RSA. Prerequisite: MAT301. Even Springs

415. Abstract Algebra. (3 hours) A theoretical development of basic algebraic structures, with an emphasis on group theory. Topics include cyclic groups, Lagrange’s Theorem, quotient groups, and homomorphisms. Rings, integral domains, and fields are introduced. Prerequisites: MAT 225 and 301. Even Falls

431. Real Analysis I. (3 hours) A theoretical development of the elements of calculus. Topics include sequences, continuity, derivatives and integrals of single-variable functions. Prerequisite: MAT 225 and 301. Odd Falls

432. Real Analysis II. (3 hours) A continuation of MAT 431. Topics include integration theory, infinite series, and series and sequences of functions. Prerequisite: MAT 431. Even Springs

440. Independent Study. (1 to 3 hours)

470. Advanced Topics. (.5 to 3 hours)



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