# Department of Mathematics

## Course Descriptions

## Mathematics Courses 2010-11

###### The number in parentheses following the course number is the course credit in semester hours.

**MA 099 (0) Beginning Algebra.**. A noncredit course in basic mathematics and introductory algebra required of all students with scores of 15 or below on the ACT Mathematics Subtest. Except as noted below, no other mathematics course may be taken until a grade of S is earned in MA 099. May also serve as a refresher or beginning course in mathematics for other students. Counts as three semester hours in determining hour load. Grading is S (Satisfactory) or U (Unsatisfactory). Students may be exempted only by approval of the Department of Mathematics and Computer Science. A student receiving a grade of U must repeat the course. After the second term in MA 099 the student, no matter what the grade, must proceed to the credit sequence beginning with MA 100. Students will not be allowed to withdraw from non-credit courses unless they are completely withdrawing from school. In the case of a complete withdrawal, a grade of WS, Withdrawal Satisfactory, or WU, Withdrawal Unsatisfactory, will be assigned. Grades of WS or WU have no effect on the student's scholastic standing. (Fall, Spring)

**MA 100. (3) Intermediate Algebra**. Principles and techniques of elementary algebra; products, factors, and quotients of polynomials; operations with rational expressions; ratio and proportion; rectangular coordinate system; systems of equations and inequalities; roots and radicals; second-degree equations; the quadratic formula. Prerequisite: minimum ACT mathematics score of 16 and one unit of high school algebra, or satisfactory completion of MA 099 (Fall, Spring, Summer)

**MA 105. (3) Mathematics for Liberal Arts**. *(Was MA 115 through Summer 1998.)* This course emphasizes the breadth of application of contemporary mathematics to modern society. It is intended primarily for the liberal arts major. Topics covered include charts, graphs, compound interest, problem solving, sets, logic, probability, and statistics. Prerequisite: minimum ACT mathematics score of 16 and one unit of high school algebra, or satisfactory completion of MA 099. *Not open to students with credit in MA 115 prior to Fall 1998. *(Fall, Spring)

**MA 110. (3) Finite Mathematics**. This course is intended to give an overview of topics in finite mathematics together with their applications, and is taken primarily by students who are not majoring in science, engineering, commerce, or mathematics (i.e., students who are not required to take calculus). The course includes sets, counting, permutations, combinations, basic probability (including Bayes' Theorem), an introduction to statistics (including work with Binomial Distributions and Normal Distributions), matrices and their applications to Markov chains and decision theory. Additional topics may include symbolic logic, linear models, linear programming, the simplex method and applications. Prerequisite: Minimum mathematics ACT score of 22 and credit in high school Algebra I, Algebra II, and Geometry; or grade of C or better in Intermediate Algebra or Mathematics for Liberal Arts. (Fall, Spring, Summer)

**MA 112. (3) Pre-calculus Algebra** This course emphasizes the algebra of functions— including polynomial, rational, exponential, and logarithmic functions. The course also covers systems of equations and inequalities, quadratic inequalities, and the binomial theorem. Additional topics may include matrices, Cramer's rule, and mathematical induction. Prerequisite: Minimum mathematics ACT score of 22 and credit in high school Algebra I, Algebra II, and Geometry; or grade of C or better in Intermediate Algebra. * Not open to students with credit in MA 101. * (Fall, Spring, Summer)

**MA 113. (3) Pre-calculus Trigonometry**. This course is a continuation of Pre-Calculus Algebra. It includes the study of trigonometric and inverse trigonometric functions, and includes extensive work with trigonometric identities and trigonometric equations. The course also covers vectors, complex numbers, DeMoivre's Theorem, and polar coordinates. Additional topics may include conic sections, sequences, and using matrices to solve linear systems. Prerequisite: MA 112; or permission of the Chair of the Department of Mathematics and Computer Science.(Fall, Spring, Summer) * Not open to students with credit in MA 103. *(Fall, Spring, Summer)

**MA 115. (4) Pre-calculus Algebra and Trigonometry**. *(NOTE: Old MA 115 now renumbered as MA 105.)*This course is a one semester combination of Pre-calculus Algebra and Pre-calculus Trigonometry intended for superior students. The course covers the following topics: algebra of functions (including polynomial, rational, exponential, and logarithmic functions); systems of equations and inequalities; quadratic inequalities; the binomial theorem; the study of trigonometric and inverse trigonometric functions including extensive work with trigonometric identities and trigonometric equations; vectors; complex numbers; DeMoivre's Theorem; polar coordinates. Prerequisite: Minimum mathematics ACT score of 22 and credit in high school Algebra I, Algebra II, and Geometry; or grade of C or better in Intermediate Algebra. * Not open to students with credit in MA 151. *(Fall, Spring)

**MA 121. (3) Calculus for Business and Life Sciences I**. *(Was MA 221 through Summer 1998.)* Algebraic and some transcendental functions; limits; continuity; derivatives; maxima and minima; applications. Prerequisite: MA 112 or equivalent. *Not open to students with credit in MA 221. * (Fall)

**MA 122. (3) Calculus for Business and Life Sciences II**. *(Was MA 222 through Summer 1998.)* Antiderivatives; the definite integral; applications of the definite integral; functions of two or more variables; partial derivatives; maxima and minima; applications. Prerequisite: MA 121.*Not open to students with credit in MA 222.* (Spring)

**MA 125. (4) Calculus I.** This is the first of three courses in the basic calculus sequence taken primarily by students in science, engineering and mathematics. Topics include the limit of a function; the derivative of algebraic, trigonometric, exponential, and logarithmic functions; and the definite integral and its basic applications to area problems. Applications of the derivatives are covered in detail, including approximations of error using differentials, maximum and minimum problems, and curve sketching using calculus. Prerequisite: Mathematics ACT score of 28 or higher; or MA 115; or both MA 112 and MA 113. *Not open to students with credit in MA 251. *(Fall, Spring) **Satisfies general studies requirements**.

**MA 126. (4) Calculus II.** This is the second of three courses in the basic calculus sequence. Topics include vectors in the plane and in space, lines and planes in space, applications of integration (such as volume, arc length, work and average value), techniques of integration, infinite series, polar coordinates, and parametric equations. *Not open to students with credit in MA 252.* Prerequisite: MA 125. (Fall, Spring)

**MA 147. (3) Elementary Statistics**. Descriptive statistics; probability; confidence intervals; tests of hypothesis; appropriate applications. *Not open to students with credit in MA 190.* Prerequisite: MA 100, MA 110 or MA 112 or equivalent. (Fall, Spring)

**MA 181H. (3) Freshman Honors Seminar.**. A survey of the import of mathematical thought in the evolution of modern society. Prerequisite: Permission of the Chair of the Department of Mathematics and Computer Science. (Offered on sufficient demand.)

**MA 227. (4) Calculus III**. This is the third of three courses in the basic calculus sequence. Topics include vector functions, functions of two or more variables, partial derivatives (including applications), quadratic surfaces, multiple integration, and vector calculus (including Green's Theorem, Curl and Divergence, surface integrals, and Stoke's Theorem). Prerequisite: MA 126. *Not open to students with credit in MA 353.* (Fall; Spring)

**MA 237 (3) Linear Algebra**. This course introduces the basic theory of linear equations and matrices, real vector spaces, bases and dimensions, linear transformations and matrices, determinants, eigenvalues and eigenvectors, inner product spaces, and the diagonalization of symmetric matrices. Additional topics may include quadratic forms and the use of matrix methods to solve systems of linear differential equations. Prerequisite: MA 126. (Offered on sufficient demand.)

**MA 238. (3) Applied Differential Equations I**. An introduction to numerical methods, qualitative behavior of first-order differential equations, techniques for solving separable and linear equations analytically, and applications to various models (e.g., population, motion, chemical mixtures, etc.); techniques for solving higher-order linear differential equations with constant coefficients (general theory, undetermined coefficients, reduction of order, and the method of variation of parameters), with emphasis on interpreting the behavior of the solutions, and applications to physical models whose governing equations are of higher order; the Laplace transform as a tool for the solution of initial-value problems whose inhomogeneous terms are discontinuous. Prerequisite: MA 126. *Not open to students with credit in MA 355.* (Offered on sufficient demand.)

**MA 306. (3) Mathematics for the Elementary School Teacher**. The number system; the number line; sentences and statements; logic; sets; relations and functions; modern trends in mathematics education. Does not satisfy requirements for mathematics major, minor, or general studies component. (Fall, Spring)

**MA 325. (3) Introduction to Discrete Mathematics**. Elementary propositional logic, proof techniques (including induction and contradiction), sets, functions, algorithms, combinatorial counting techniques, Boolean algebra, and graph theory. Prerequisite: MA 115 or both MA 112 and 113. (Fall)

**MA 345. (3) Applied Statistics I**. A course in statistical methods with applications. Descriptive statistics, probability, statistical inference including one- and two-sample problems, Chi-Square applications, one-way analysis of variance, linear correlation and regression analysis, and nonparametric statistics. Prerequisite: MA 112 or equivalent. (Fall, Spring)

**MA 355. (3) Differential Equations**. A survey of techniques for solving differential equations in which the unknown function depends upon one independent variable; emphasis on analytical techniques, with extensive use of integration methods from calculus; solving higher-order linear differential equations both with constant and with variable coefficients; constructing mathematical models using first-order equations; using the Laplace transform for solving initial-value problems with constant coefficients, both with continuous and discontinuous driving functions. Prerequisites: MA 126. *Not open to students with credit in MA 238.* (Spring)

**MA 356. (3) Applied Differential Equations II**. A study of the techniques for solving ordinary differential equations by the use of infinite series; numerical methods of solutions; partial differential equations. Prerequisites: MA 227, 238 or 355. (Offered on sufficient demand)

**MA 421. (3) College Geometry**. Euclidean and non-Euclidean geometry including the topics of congruence, convexity, and plane and space separation. Prerequisite: MA 126. (Fall)

**MA 425. (3) Methods and Materials for Teaching Secondary Mathematics**. Practical aspects of teaching and learning mathematics at the secondary level. Topics covered include secondary mathematics curricula, preparation and presentation of lesson material, classroom management, and professional behaviors. Does not satisfy requirements for mathematics major, minor, or general studies component. Prerequisite: credit or concurrent enrollment in MA 421. (Fall)

**MA 431. (3) Advanced Linear Algebra I**. Systems of linear equations; matrices; determinants; vector spaces; linear transformations. Prerequisites: MA 126 and CS 245 or MA 325. (Fall, Spring odd-numbered years)

**MA 432. (3) Advanced Linear Algebra II**. Eigenvalues and eigenvectors; linear programming; Markov processes; numerical linear algebra; game theory and other applications. Prerequisite: MA 431. (Offered on sufficient demand)

**MA 437. (3) Modern Algebra I**. Sets, relations, and functions; elementary number theory; group theory including subgroups, cyclic groups, cosets, and LaGrange's theorem; introduction to rings. Prerequisite: MA 126 and MA 325. (Fall, odd-numbered years; Summer, even-numbered years)

**MA 438. (3) Modern Algebra II**. Theory of rings; integral domains; fields; group theory II; introduction to Galois theory. Prerequisite: MA 437. (Offered on sufficient demand)

**MA 445W. (3) Applied Statistics II.** A second course in statistical methods with applications. Experimental design, analysis of variance, general regression analysis, orthogonal contrasts, analysis of covariance, and nonparametric statistics. Introduction of statistical computing utilizing the Statistical Analysis System (SAS). Prerequisite: MA 345 or equivalent. (Offered on sufficient demand)

**MA 447. (3) Mathematical Statistics I**. Probability and combinatorial methods; discrete probability functions; probability density functions for continuous variates; mathematical expectation; moment generating functions; appropriate applications. Prerequisite: MA 227. (Fall)

**MA 448. (3) Mathematical Statistics II**. Sampling distributions; confidence intervals; tests of hypothesis; regression analysis; analysis of variance; appropriate applications. Prerequisite: MA 447. (Offered on sufficient demand)

**MA 451. (3) Introduction to Analysis**. Logic and point set theory; real number system; limits; continuity; derivatives. Prerequisite: MA 227 and MA 325. (Spring)

**MA 452. (3) Advanced Calculus**. Functions of several variables; mapping; partial derivatives; power series; uniform convergence; line and surface integrals; vector analysis. Prerequisite: MA 451. (Offered on sufficient demand)

**MA 455. (3) Complex Analysis**. Algebra and geometry of complex numbers; elementary functions and their mappings; analytic functions; integration in the complex plane; Cauchy's integral theorem; Taylor and Laurent expansions; calculus of residues. Prerequisite: MA 451. (Offered on sufficient demand)

**MA 461. (3) Numerical Analysis**. Error analysis for iterative methods; approximation theory; numerical differentiation and quadrature; initial-value problems for ordinary differential equations; iterative techniques in matrix algebra. Also listed as CS 461 but creditable only in the field for which registered. Prerequisites: CS 155; MA 227. (Offered on sufficient demand)

**MA 471W. (3) Applied Mathematics**. Mathematical models and modeling techniques in the fields of engineering, ecology, economics, medicine, chemistry, traffic engineering, and simulation of experiments. Prerequisite: MA 227 and MA 325. (Fall)

**MA 475W. (3) Introduction to Operations Research**. The nature of operations research; modeling problems using operations research techniques; linear programming; the Simplex Method, theory and practice; special problems; network analysis; dynamic programming; theory of games. Prerequisites: MA 126 and CS 110 or 155. Corequisite: MA 431. (Offered on sufficient demand)

**MA 491. (3) Senior Seminar**. Mathematics topics selected according to the interest and needs of the individual student, with study at advanced undergraduate level. Prerequisite: senior classification, approval of the chair of the department. (Offered on sufficient demand)

### Graduate Mathematics Courses

###### The number in parentheses following the course number is the course credit in semester hours.

##### Courses numbered 500-599 are senior-level courses which may be taken for graduate credit.

Courses numbered 600-699 are graduate courses.

**MA 537. (3) Modern Algebra I.** Sets, relations, and functions; elementary number theory; group theory including subgroups, cyclic groups, cosets, and LaGrange’s theorem. Prerequisite: MA 126 and MA 325 (formerly MA 245).

**MA 538. (3). Modern Algebra II.** Theory of rings; integral; domains; fields; group theory II; Galois theory. Prerequisite: MA 437 or 537.

**MA 547. (3) Mathematical Statistics I** . Probability and combinatorial methods, discrete probability functions; probability density functions for continuous variates; mathematical expectation; moment generating functions; appropriate applications. Prerequisite: MA 227.

**MA 548. (3) Mathematical Statistics II**. Sampling distributions; confidence intervals; tests of hypothesis; regression analysis; analysis of variance; appropriate applications. Prerequisite: MA 447 or 547.

**MA 551. (3) Introduction to Analysis**. Logic and point set theory; real number system; limits; continuity; derivatives. Prerequisite: MA 227 and MA 325 (formerly MA 245).

**MA 552. (3) Advanced Calculus.** Functions of several variables; mapping; partial derivatives; power series; uniform convergence; line and surface integrals; vector analysis. Prerequisite: MA 451 or 551.

**MA 555. (3) Complex Analysis.** Algebra and geometry of complex numbers; elementary functions and their mappings; analytic functions; integration in the complex plane; Cauchy’s integral theorem; Taylor and Laurent expansions; calculus of residues. Prerequisite: MA 451 or 551.

**MA 561. (3) Numerical Analysis. **Error analysis for iterative methods, approximation theory ; numerical differentiation and quadrature; initial-value problems for ordinary differential equations; iterative techniques in matrix algebra. Also listed as CS 561 but creditable only in the field for which registered. Prerequisites: CS 155 or 210; MA 227.

**MA 571. (3) Applied Mathematics. **Mathematical model and modeling techniques in the field of engineering, ecology, economics, medicine, chemistry, traffic engineering, and simulation of experiments. Prerequisite: MA 227 and MA 325 (formerly MA 245).

**MA 575. (3) Introduction to Operations Research**. The nature of operations research; modeling problems using operations research techniques; linear programming; the Simplex Method, theory and practice, special problems; network analysis; dynamic programming; theory of games. Prerequisites: MA 126 and one of CS 110, 155, 210. Corequisite: MA 431.

**MA 591. (3) Graduate Seminar. 3 semester hours.** Mathematics topics selected according to the interest and needs of the individual student, with study at the graduate level. Prerequisites: graduate classification and approval of the chair of the department.

**MA 601. (3) Fundamental Concepts in Mathematics for Elementary School Teacher**. Mathematics as a language and a tool for thinking. Emphasis is placed on teaching with meaning and on seeing arithmetic as a unified system of correlated ideas, facts, and principles. Includes fundamental notions of number, measure, logic, proof, and function.

**MA 611. (3) Applied Mathematics for the Secondary School Teacher.** Process approach to problem solving. Emphasis placed on fundamental steps in the solution of problems.

**MA 612. (3) Selected Topics in Mathematics for the Secondary Teacher**. Selected topics suitable for laboratory mathematics; mathematics modeling; secondary school mathematics from an advanced point of view.

**MA 615. (3) History and Philosophy of Mathematics**. Development of mathematics in algebra, geometry, and analysis. Impact of science and philosophy made by Euclid, Descartes, Newton, Euler, Gauss, Weierstrass, Cantor, Hamilton, Boole, and Galois.

**MA 617. (3) Symbolic Logic**. Concept of a logistic system and the propositional calculus. Truthtables and their applications to problems. Syllogistic inference and rules. Class membership and inclusion, the algebra of classes.

**MA 621. (3) Foundations in Algebra for the Secondary Teacher**. Elementary number theory. Groups, fields, systems of linear equations and transformations. Vector algebra.

**MA 623. (3) Foundations in Analysis for the Secondary Teacher**. Development of the real number system, limits and continuity, and basic point set theory.

**MA 625. (3) Foundations in Geometry for the Secondary Teacher**. Development of Euclidean geometry in two and three dimensions using the axiomatic methods. Introduction to non-Euclidean geometries.