MATHEMATICS (MA)

MA 100 Mathematics in Society 4 cr
A terminal course designed to provide the liberal-arts student with practical mathematics for everyday use in our society, such as installment buying, compound interest, mathematics used in advertising media, and practical statistics. Topics covered include those needed to provide competency in these and similar areas.

MA 110 Introduction to Mathematical Thought 4 cr
A course designed to give the nonscience major - especially humanities and fine arts majors - an appreciation of the method, content, and scope of mathematics.
NOTE: The two courses listed above are not prerequisites for nor are they intended to be preparatory for any course listed below.
NOTE: A graphing calculator is required for MA 120 and MA 121. Contact the Department for specific details.

MA 120 Precalculus I 5 cr
Relations and functions; inequalities. Polynomial, rational, exponential, logarithmic, and algebraic functions and their graphs. In this course extensive use is made of graphing calculators to study the topics of the course. Students are required to have a graphing calculator. Prerequisite: See comments under the heading "Where to Begin in the Mathematics Courses."

MA 121 Precalculus II 4 cr
Analytic trigonometry and geometry; polar coordinates and graphs; matrices and systems of equations; binomial theorem. In this course extensive use is made of graphing calculators to study the topics of the course. Students are required to have a graphing calculator. Prerequisite: MA 120.
NOTE: A graphing calculator is required for MA 131, 132, 233, and 234. Contact the Department for specific details.

MA 131 Calculus and Analytic Geometry I 5 cr
This course emphasizes the numerical and graphical meanings of functions. Only after the concepts of derivatives and definite integral are introduced through the numerical and graphical capacity of graphing calculators are the algebraic techniques of differentiation studied. A wide variety of applications of differentiation are covered. Students are required to have a graphing calculator. See "To Avoid Duplication." Prerequisite: MA 121.

MA 132 Calculus and Analytic Geometry II 5 cr
This course makes extensive use of graphing calculators. The definition of definite integral is motivated using the calculator. The Fundamental Theorem is illustrated by using the graphing calculator to study functions which are expressed as integrals. Emphasis is placed on evaluating integrals using numerical techniques. Techniques of integration such as substitution and integration by parts are covered. A wide variety of applications of the definite integral is covered throughout the course in which setting up problems using an increment is stressed. Approximate solutions to ordinary differential equations are found using slope fields and Euler's methods. Students are required to have a graphing calculator. Prerequisite: MA 131.

MA 171 Basic Algebra I 4 cr
Real numbers; sets, equations and inequalities; linear, quadratic, exponential, and logarithmic functions; graphing; and polynomial manipulations. Prerequisite: DS 070 or placement. (Note: Placement is based on ACT/SAT scores, high school mathematics background, and scores on the Mathematics Placement Test. Times and places for taking this test may be obtained by calling the Mathematics Department.)
NOTE: A graphing calculator is required for MA 171. Contact the Department for specific details.

MA 172 Basic Algebra II 4 cr
Complex numbers, polynomial functions, systems of equations, matrices, determinants, permutations and combinations, and the binomial theorem. See "To Avoid Duplication." Prerequisite: MA 171.

MA 181 Mathematics for Elementary Teachers I 5 cr
An examination of some of the major ideas encountered in the teaching of elementary mathematics with emphasis on number and operation.
NOTE: MA 181 and MA 281 are service courses and do not fulfill graduation requirements for any curriculum other than elementary education.

MA 215 Linear Algebra I 3 cr
An introduction to the theory of linear algebra and the writing of formal mathematical proofs. Topics include vector spaces, linear independence, bases, dimension, and linear transformations. Prerequisite: MA 233.

MA 233 Calculus and Analytic Geometry III 5 cr
Taylor polynomials, Taylor series, sequences and series, indeterminate forms, functions of several variables, and vectors. Students are required to have a graphing calculator. See "To Avoid Duplication." Prerequisite: MA 132.

MA 234 Calculus and Analytic Geometry IV 5 cr
The partial derivative, local linearity, directional derivatives, the gradient, differential of a function, the chain rule, higher order partial derivatives, quadratic approximations, optimization of functions of several variables, multiple integrals and their applications, parametric curves and surfaces, vector fields and line integrals. See "To Avoid Duplication." Prerequisite: MA 233.

MA 267 Discrete Mathematical Structures 4 cr
An introduction to combinatorics and graph theory for students majoring in computer-related areas. Topics include sets, relations and functions, asymptotic growth, algorithmic efficiency, mathematical induction, elementary counting principles, recurrence relations, graphs and trees, network algorithms. Prerequisite: CIS 142 and either MA 132 or MA 278.

MA 277 Differential Calculus Survey 4 cr
Calculus of polynomials, limits, maxima and minima problems, exponential and logarithmic functions, applications. See "To Avoid Duplication." Prerequisite: MA 172.

MA 278 Integral Calculus Survey 4 cr
Integration of elementary functions, area and volume, partial differentiation, multiple integration, applications, numerical techniques, probability and calculus. See "To Avoid Duplication." Prerequisite: MA 277.

MA 281 Mathematics for Elementary Teachers II 5 cr
Topics covered are those that a prospective elementary or middle-school teacher should expect to encounter in the teaching of geometry. Prerequisite: MA 181.
NOTE: MA 181 and MA 281 are service courses and do not fulfill graduation requirements for any curriculum other than elementary education.

MA 287 Calculus Survey for Business and Economics 4 cr
Differentiation and integration of polynomial, exponential and logarithmic functions. Applications to problems taken from business and economics. See "To Avoid Duplication." Prerequisite: MA 171 or Placement.

MA 290 Special Topics 1-4 cr
Selected topics in elementary undergraduate mathematics.

MA 311 Introduction to Number Theory 4 cr
An introduction to some of the classical concepts of number theory as well as to the writing of formal mathematical proofs. Topics include the Binomial Theorem, divisibility theory, properties of prime numbers, the theory of congruences, the study of number theoretic functions. Prerequisite: MA 233.

MA 316 Linear Algebra II 3 cr
A continuation of MA 215. Further development of linear transformations. Additional topics include inner product spaces, eigenvectors, diagonalization. Prerequisite: MA 215.

MA 318 Matrix Theory 4 cr
A theoretical as well as computational treatment of the notions of determinant, inverse, rank and diagonalization of a matrix with real or complex entries. Eigenvalues and eigenvectors, similarity, solutions of linear systems of algebraic equations. Prerequisite: MA 233.

MA 320 Foundations of Mathematics (W) 4 cr
The axiomatic method, sets, order relations, structure of the number system. Prerequisite: MA 233.

MA 321 Elementary Geometry 4 cr
Plane and solid Euclidean geometry from the modern viewpoint; axioms, undefined terms, definitions, theorems, and proofs. Prerequisite: MA 320.

MA 331 Differential Equations I 4 cr
First-order differential equations. Higher-order linear differential equations. Systems of linear differential equations. Laplace transforms. Approximate methods of solving first-order equations. Applications. Prerequisite: MA 233.

MA 332 Differential Equations II 4 cr
Series solutions of linear differential equations. Sturm-Liouville problems and Fourier series. Partial differential equations. Separation of variables and applications. Prerequisites: MA 234 and MA 331.

MA 334 Advanced Calculus I 3 cr
A comprehensive coverage of the more theoretical concepts encountered in MA 131 through MA 234. Completeness Axiom, Extremum Theorem, Intermediate Value Theorem. Applications and extensions of the Law of the Mean. Functions of several variables. Differentiable functions. Prerequisites: MA 215 and MA 234.

MA 335 Advanced Calculus II 3 cr
A continuation of the study and functions of several variables from MA 334 through the Implicit Function Theorem and the Inverse Function Theorem. In addition, line and surface integrals will be studied through the derivations of the Divergence Theorem and Stokes' Theorem. Prerequisite: MA 334.

MA 336 Advanced Calculus III 3 cr
Topics will include a careful treatment of a theory of integration, sequences and series, uniform convergence, power series, improper integrals. Prerequisite: MA 335.

MA 345 Advanced Engineering Mathematics 5 cr
Arithmetic of matrices; systems of linear equations; determinants; Eigenvalues and eigenvectors of a matrix; applications to systems of differential equations. Scalar fields; vector fields, gradient, divergence, curl; Green's theorem, divergence theorem, Stokes' theorem. Complex numbers, analytic functions; integration in the complex plane; Taylor and Laurent expansions; residue theorem. Prerequisites: MA 234 and MA 331.

MA 354 Computer Assisted Mathematical Modeling 4 cr
Formulation, development, testing and reporting of mathematical models of various real world problems. Deterministic and stochastic models, optimization, simulation. Emphasis on the careful mathematical formulations and the appropriate use of computer software, both as an aid in the solution of mathematical problems and as a tool in the process of model evaluation, simulation, reporting. A term project will be an important component of this course. The course is taught in a laboratory setting with computers as lab equipment. Prerequisites: MA 234 and MA 331.

MA 367 Combinatorial Enumeration 4 cr
Permutations and combinations, generating functions, recurrence relations, principle of inclusion/exclusion, Polya's theory of counting. Prerequisite: MA 233.

MA 410 History of Mathematics (W) 4 cr
Historical survey of the general development of mathematics with a proper balance of historical perspective and mathematical structure. Prerequisites: Senior standing and permission of department chair.

MA 413 Algebra I (W) 4 cr
An introduction to group theory and ring theory. Topics include permutations and symmetries, subgroups, quotient groups, homomorphisms, and examples of rings, integral domains, and fields. Prerequisites: MA 215 and one of the following: MA 311, 316, 320, 334.

MA 414 Algebra II 4 cr
A continuation of group theory, leading to the Sylow theorems and an introduction to ring theory and field extensions. Topics in ring theory include polynomial rings, euclidean rings, euclidean domains, ideals, homomorphism theorems, and quotient rings. Topics in field extensions include finite extensions, algebraic extensions, and splitting fields. Prerequisite: MA 413.

MA 434 Topology 4 cr
An introduction to general topology. Topics include: topological spaces, homomorphisms, connectedness, compactness, metric spaces, separation axioms, quotient spaces. Prerequisite: MA 335.

MA 436 Numerical Analysis I 4 cr
Selected numerical algorithms are analyzed. Topics of study include: error analysis, machine arithmetic, round-off errors, root finding using fixed-point methods, systems of equations, interpolation polynomials, numerical integration, and ordinary differential equations. The algorithms are implemented with the aid of a computer. Also offered as CIS 436. Prerequisites: MA 234 and CIS 141. Credit for or concurrent registration in MA 331.

MA 437 Complex Variables 5 cr
Arithmetic of complex numbers; regions in the complex plane; limits, continuity, and derivatives of complex functions; elementary complex functions; mappings by elementary functions; contour integration; power series; Taylor series; Laurent series; calculus of residues; conformal representation; applications. Prerequisite: MA 331.

MA 438 Numerical Analysis II 4 cr
This course is a continuation of MA 436. Topics include: In-depth error analysis, order of error, interpolation and derivatives using difference techniques, least square analysis and splines, matrix algebra and eigenvalues, and boundary value problems from partial differential equations. Also offered as CIS 438. Prerequisites: MA 436 or CIS 436. Credit for or concurrent registration in MA 316 or 318.

MA 451 Probability 4 cr
Axioms of probability, conditional probability, discrete and continuous random variables, joint distributions, expectation and moment-generating functions, sums of random variables, limit theorems, applications. Prerequisite: MA 234.

MA 458 Optimization Theory 4 cr
n-Dimensional geometry and convex sets. Classical optimization. Search techniques. Linear programming: simplex and duality theory. Branch and bound theory. Non-linear, integer, and dynamic programming. Prerequisite: MA 234.

MA 490 Special Topics 1-4 cr
Selected topics in advanced undergraduate mathematics. This course may be repeated for a maximum of nine credits.

MA 494 Directed Studies 1-4 cr
Directed individual study. Prerequisite: Permission of the department chair. May be repeated for a maximum of eight credits.

MA 502 Introduction to Abstract Algebra 4 cr
Elementary theory of groups including permutation groups, subgroups, and Lagrange's theorem. Elementary theory of rings with emphasis on the ring of integers. Polynomials with rational coefficients. Complex numbers and geometric constructions.

MA 503 Introduction to Analysis 4 cr
A careful look at the elements, procedures, and applications of differential and integral calculus. Prerequisite: One year of calculus.

MA 504 Introduction to Geometry 4 cr
An introduction to the foundations of geometry using both the synthetic and metric approaches. Hilbert's work on the foundations of geometry and coordinate geometry are surveyed.

MA 505 Number Systems 4 cr
A case study of Axiom Systems and the deductive method for graduate students in Mathematics Education. It is expected that students in this course will practice and improve their logical skills, better understand proof as a mathematical activity, and study the similarities and differences between several commonly utilized number systems. Prerequisites: MA 321 or MA 413 or permission of the instructor.

MA 507 Applicable Mathematics I 4 cr
A graduate-level introduction to topics in mathematics of proven application including application of ordinary differential equations, Fourier series, Laplace transforms, introduction to partial differential equations, Bessel functions, and Legendre polynomials.

MA 508 Applicable Mathematics II 4 cr
A continuation of MA 507. Topics will include introductions to linear algebra and to the theory and application of complex variables. Prerequisite: MA 507.

MA 511 Abstract Algebra I 4 cr
Group theory including the Sylow Theorems. Theory of rings.

MA 512 Abstract Algebra II 4 cr
Elements of field theory. Introductory Galois theory. Finite field theory. Representation theory. Prerequisite: MA 511.

MA 515 Number Theory I 4 cr
Modular arithmetic. Euler's Theorem. Arithmetic functions. Quadratic forms. Gauss' Reciprocity Theorem.

MA 516 Number Theory II 4 cr
Diophantine equations. Algebraic numbers. Rational approximations. Continued fractions. Fibonacci sequences and allied sequences. Pell's Equation. Prerequisite: MA 515.

MA 518 Linear Algebra I 4 cr
Vector spaces. Linear transformations. Eigenvalues and eigenvectors. Determinants.

MA 519 Linear Algebra II 4 cr
Rational and Jordan forms. Inner product spaces. Bilinear forms. Sylvester's Theorem. Prerequisite: MA 518.

MA 521 Discrete Mathematics 4 cr
Overview of combinatorics, pigeonhole principle, basic techniques of enumeration, binomial coefficients, binomial theorem and its generalizations, recurrence relations, generating functions, matching theory, introduction to combinatorial optimization.

MA 525 Graph Theory 4 cr
Fundamental concepts, connectedness, graph coloring, planarity and Kuratowski's theorem, the four-color theorem, chromatic polynomials, Eulerian and Hamiltonian graphs, matching theory, network flows, NP-complete graph problems.

MA 535 Real Analysis I 4 cr
The metric topology of R. Convergence. Limits and continuity of functions. Differentiation. The Riemann integral. Functions of bounded variation. The Riemann-Stieltjes integral. Elements of the theory of Fourier series. Prerequisite: Undergraduate sequence in advanced calculus or real analysis.

MA 536 Real Analysis II 4 cr
The metric topology of Rn. Functions of several variables; mappings from Rn into Rn. Multivariable differential calculus. The inverse function theorem. The implicit function theorem. Sequences of functions. Uniform convergence. The Stone-Weierstrass Theorem. Prerequisite: MA 535.

MA 537 Complex Analysis I 4 cr
Arithmetic of complex numbers; regions in the complex plane; limits, continuity, and derivatives of complex functions; elementary complex functions; mappings by elementary functions; contour integration; power series; Taylor series; Laurent series; calculus of residues; conformal representations; applications. Credit for both MA 537 and MA 437 is not allowed.

MA 538 Complex Analysis II 4 cr
Conformal mapping. Complex integral representations of special functions. The two-dimensional potential theory with applications to electrostatics and fluid flows. Fourier transforms. Complex inversion integral. Global analytic functions. Prerequisite: MA 537.

MA 539 Measure Theory 4 cr
Sets and classes. Measures and outer measures. Extension of measures. Measurable sets. Measurable functions. Integration. General set functions. Measures and probability theory. Prerequisite: MA 536.

MA 542 Topology I 4 cr
An introduction to topology with emphasis on the geometric aspects of the subject. Topics covered include surfaces, topological spaces, open and closed sets, continuity, compactness, connectedness, product spaces, and identification spaces. Credit for both MA 542 and 434 is not allowed.

MA 543 Topology II 4 cr
A continuation of MA 452. Topics covered include the fundamental group, triangulations, classification of surfaces, simplicial homology, the Euler-Poincare formula, the Borsuk-Ulam theorem, the Lefschetz fixed-point theorem, knot theory, and covering spaces. Prerequisite: MA 542 or MA 434 and permission of the instructor.

MA 550 Probability 4 cr
Axioms of probability. Random variables. Expectation. Sums of random variables. Limit theorems. Credit for both MA 550 and MA 451 is not allowed.

MA 551 Mathematical Statistics 4 cr
A comprehensive introduction to statistical distributions and their characterizations, generating functions, conditional expectations, order statistics, sampling distributions, convergence concepts, maximum likelihood and moment estimation, properties of estimators, confidence and intervals. Prerequisite: MA 550. Credit for both MA 551 and ST 471 is not allowed.

MA 555 Statistical Analysis I 4 cr
A first course in an integrated two-course sequence in applied statistical theory and methods for research workers. Coverage includes estimation, hypothesis testing, power analysis, analysis of count data, regression model building, correlation, design and analysis of experiments. Computer-assisted data analysis is used.

MA 556 Statistical Analysis II 4 cr
A continuation of MA 555. Coverage includes further designs and analysis, analysis of covariance, factorial experimentation, fractional replication, quality control, reliability life testing, and evolutionary operation (EVOP). Computer-assisted data analysis is used. Prerequisite: MA 555.

MA 565 Numerical Analysis 4 cr
A study of the mathematics of numerical computation with emphasis on the mathematical formulation of the solution to problems. Topics will include a careful treatment of error analysis, the solution of linear and nonlinear equations, the solution of systems of equations, solutions to ordinary differential equations. Prerequisite: a programming course.

MA 567 Operations Research I 4 cr
n-Dimensional geometry and convex sets. Classical optimization. Search techniques. Linear programming. Simplex duality theory. Non-linear, integer and dynamic programming. Credit for both MA 567 and MA 458 is not allowed.

MA 568 Operations Research II 4 cr
A continuation of MA 567. An expanded presentation of the practices and techniques of operation research. Coverage includes non-linear programming, project scheduling by PERT-CPM, inventory models, queueing theory, simulation, decision and game theory. Prerequisite: MA 567.

MA 571 Differential Equations 4 cr
Power series solution of second-order linear differential equations and special functions of the mathematical physics. Sturm-Liouville problems and Fourier series. Non-linear differential equations. Elements of the calculus of variations. Existence and uniqueness of the solution of a first-order differential equation.

MA 572 Partial Differential Equations 4 cr
An introduction to the theory, solution, and application of partial differential equations. Boundary-value problems for second-order equations. Green's functions and eigen-function expansions. First-order equations. Variational method. Laplace transforms. Numerical methods. Prerequisite: MA 571.

MA 590 Special Topics 2-4 cr
Selected topics in Graduate Mathematics. This course may be repeated for a maximum of eight credit hours.

MA 592 Seminar 1 cr
Student seminar. Topics covered vary. This course may be repeated indefinitely, but only four credits count towards the degree. Grading system: satisfactory/unsatisfactory.

MA 594 Directed Studies 1-4 cr
Directed individual studies. Prerequisite: approval of the department chair.

MA 599 Thesis 1-8 cr
Prerequisite: Approval of research prospectus by Department Graduate Committee.

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