Mathematics (3450)
Mathematics (3450)
| 100 | INTERMEDIATE ALGEBRA | 3 credits |
| Prerequisite: Completion of 2010:052 or 057 with a grade of C or better or placement test. Review of high school algebra: real numbers, exponents, radicals, factoring, linear and quadratic equations, graphing, and problem solving. Does not meet General Studies mathematics requirement. | ||
| 135 | EXCURSIONS IN MATHEMATICS | 3 credits |
| Prerequisites: Completion of 2010:052 with a grade of C- or better or placement test. Contemporary applications of mathematics for the non-science major to develop skills in logical thinking and reading technical material. Topics include voting, apportionment, scheduling, patterns, networks. | ||
| 140 | FUND OF MATH FOR PRIMARY EDUC | 3 credits |
| Prerequisites: Either completion of 3450:100 with a C- or better, or completion of 3470:250 with a grade of C- or better, or placement test. Corequisite: 5100:200. A problem-solving and inquiry-based approach to number systems; bases; operations, properties, relationships, algorithms of Real Numbers; patterns and algebra. | ||
| 145 | COLLEGE ALGEBRA | 4 credits |
| Prerequisite: Mathematics Placement Test or completion of 100 with a grade of C- or better. Real numbers, equations and inequalities, linear and quadratic functions. Exponential and logarithmic functions. Systems of equations, matrices, determinants. Permutations and combinations. | ||
| 149 | PRECALCULUS MATHEMATICS | 4 credits |
| Prerequisite: Completion of 145 with a grade of C- or better or placement. Functions, polynomial functions, complex numbers, exponential and logarithmic functions, systems of equations, trigonometric functions, mathematical inductions, sequences, and binomial theorem. | ||
| 208 | INTRO TO DISCRETE MATH | 4 credits |
| Prerequisites: Completion of 145 or 149 with a grade of C- or better or placement. A foundation course in discrete mathematics with applications. Topics include sets, number systems, Boolean Algebra, logic, relations, functions, recursion, matrices, induction, graphs, and trees. | ||
| 209 | DISCRETE MATH FOR EDUCATORS | 4 credits |
| Prerequisite: Completion of 140 with a grade of C- or better. Corequisite: 231. Introduction to discrete mathematics topics for middle school instruction: sets, counting, probability, recurrence relations, graph theory, logic and elementary proof techniques. | ||
| 210 | CALCULUS WITH BUSINESS APPLIC | 3 credits |
| Prerequisites: Mathematics Placement Test or completion of 145 with a grade of C- or better. Review of functions, derivatives of functions, extrema and concavity, optimization, logarithmic and exponential functions, extrema for multivariate functions. Graphing calculator required. For business majors only. | ||
| 215 | CONCEPTS OF CALCULUS | 4 credits |
| Prerequisite: Completion of 145 or 149 with a grade of C- or better or placement. Functions; limits and continuity; differentiation and applications of differentiation; logarithmic and exponential functions; integration and applications of integration; partial differentiation. | ||
| 221 | ANALYTIC GEOMETRY-CALCULUS I | 4 credits |
| Prerequisite: Completion of 149 with a grade of C- or better. Analytic geometry, limits, continuity, derivatives, tangent and normal lines, extrema of functions, Rolle's theorem, mean value theorem, related rates, antiderivative, definite integrals, areas, volumes, arc length. | ||
| 222 | ANALYTIC GEOMETRY-CALCULUS II | 4 credits |
| Prerequisite: Completion of 221 with a grade of C- or better. Derivatives of exponential, logarithmic trigonometric, inverse trigonometric, hyperbolic and inverse hyperbolic functions; methods of integration, sequences, series; moments, centroids, indeterminate forms, polar coordinates. | ||
| 223 | ANALYTIC GEOMETRY-CALC III | 4 credits |
| Prerequisite: Completion of 222 with a grade of C- or better. Vector algebra, cylindrical, spherical coordinates, vector-valued functions, curvature; functions of several variables, limit, continuity, partial derivatives, differentials, directional derivatives, maxima and minima, multiple integrals, Divergence Theorem. | ||
| 231 | MODEL WTH ALGEB & TRANSCEND FN | 4 credits |
| Prerequisites: Completion of 140 with a grade of C- or better; and 100 with a grade of C- or better or placement test. Modeling and regression with algebraic, exponential, logarithmic, and trigonometric functions; systems of equations and matrices. These topics will be enhanced by the use of CAS. | ||
| 240 | MATH FOUND FOR EARLY CHLD EDUC | 3 credits |
| Prerequisite: Completion of 140 with a grade of C- or better. A problem-solving and inquiry-based approach to functions and algebra, coordinate and Euclidean geometry, and elementary data analysis. | ||
| 289 | SEL T: MATHEMATICS | 1-3 credits |
| Prerequisite: permission. Selected topics of interest in mathematics. | ||
| 307 | FUND: ADVANCED MATHEMATICS | 3 credits |
| Prerequisite: Completion of 222 with a grade of C- or better. Logic, solving problems, and doing proofs in mathematics. Sets, extended set operations, and indexed family sets, induction. Binary relations. Functions, cardinality. Introductory concepts of algebra and analysis. | ||
| 312 | LINEAR ALGEBRA | 3 credits |
| Prerequisite: Completion of 223 with a grade of C- or better or permission of instructor. Study of vector spaces, linear transformations, matrices, determinants, inner products, the eigenvalue problem, quadratic forms and canonical forms. | ||
| 331 | MODELING WITH CALCULUS | 4 credits |
| Prerequisite: Completion of 231 with a grade of C- or better. Introduction to limits, continuity, differentiation with applications, integration with applications, sequences and series. These topics will be enhanced by the use of CAS. | ||
| 335 | INTRO TO ORDINARY DIFF EQUATNS | 3 credits |
| Prerequisite: Completion of 223 with a grade of C- or better or permission of instructor. Basic techniques for solving ODEs and systems of ODEs. Analysis of models involving differential equations of first order and simple equations of second order. | ||
| 341 | GEOMETRY AND MEASUREMENT | 3 credits |
| Prerequisites: Completion of 209 with a grade of C- or better, or 307 with a grade of C- or better and be admitted to the College of Education. Basic Constructions, Polygons, Similarity, Pythagorean Theorem, Circles, Congruence, Perimeters and Areas of Plane Figures, Surface and Volume of Solids, Rigid Motions and Symmetry, Coordinate geometry. | ||
| 401 | HISTORY OF MATHEMATICS | 3 credits |
| Prerequisite : Completion of 307 with a grade of C- or better. Origin and development of mathematical ideas. | ||
| 410 | ADVANCED LINEAR ALGEBRA | 3 credits |
| Prerequisite: Completion of 312 with a grade of C- or better. Study of vector spaces, linear transformation, canonical and quadratic forms, inner product spaces. | ||
| 411 | ABSTRACT ALGEBRA I | 3 credits |
| Prerequisite: Completion of 307 with a grade of C- or better or permission of instructor. Study of groups, rings, fields, integral domains. | ||
| 412 | ABSTRACT ALGEBRA II | 3 credits |
| Prerequisite: Completion of 411 with a grade of C- or better or permission of instructor. Study of groups, rings, fields, integral domains, vector spaces, field extensions, Galois theory. | ||
| 413 | THEORY OF NUMBERS | 3 credits |
| Prerequisite: Completion of 222 with a grade of C- or better or permission. Euclidean algorithm, unique factorization theorem, congruences, primitive roots, indices, quadratic residues, number-theoretic functions, Gaussian integers and continued fractions. | ||
| 415 | COMBINATORICS & GRAPH THEORY | 3 credits |
| Prerequisite: Completion of 222 with a grade of C- or better or permission. Introduction to basic ideas and techniques of mathematical counting; properties of structure of systems. | ||
| 420 | MATH TECH AND COMMUNICATION | 3 credits |
| Prerequisites: Completion of 222 and 312 with grades of C- or better, or permission. Graphical, numerical, and algebraic computation with applications using a variety of mathematical hardware and software: symbolic manipulators, dynamic geometry software, programs, scripts and web-browsers. | ||
| 421 | ADVANCED CALCULUS I | 3 credits |
| Sequential. Prerequisite: Completion of 223 with a grade of C- or better; 307 is highly recommended. Real number system, sequences, series, set theory, continuity, differentiation, integration, partial derivatives, multiple integration, maxima and minima, convergence and uniform convergence, power series, improper integrals, transformations, line and surface integrals. | ||
| 422 | ADVANCED CALCULUS II | 3 credits |
| Sequential. Prerequisite: Completion of 223 with a grade of C- or better; 307 is highly recommended. Real number system, sequences, series, set theory, continuity, differentiation, integration, partial derivatives, multiple integration, maxima and minima, convergence and uniform convergence, power series, improper integrals, transformations, line and surface integrals. | ||
| 425 | COMPLEX VARIABLES | 3 credits |
| Prerequisite: Completion of 223 with a grade of C- or better. Complex variables; elementary functions, differentiation and analytic functions; integration and Cauchy's theorem; power series and Laurent series; residue theorem; applications such as conformal mappings, inversion of integral transform. | ||
| 427 | APPLIED NUMERICAL METHODS I | 3 credits |
| Prerequisites: Completion of 222 and 3460:209 with grades of C- or better or permission. Numerical methods in polynomial interpolation, rootfinding, numerical integration, and numerical linear algebra. | ||
| 428 | APPLIED NUMERICAL METHODS II | 3 credits |
| Prerequisites: Completion of 335 and 427 with grades of C- or better or permission. Numerical methods in the solution of ordinary and partial differential equations. Numerical differentiation, Runge-Kutta methods, and iterative methods for ODEs, finite differences for PDEs. | ||
| 430 | NUM SOLUT FOR PARTL DIFF EQUA | 3 credits |
| Prerequisite: Completion of 428 with a grade of C- or better or equivalent. For advanced undergraduate and graduate students. The study of finite difference and finite element methods for partial differential equations consistency, stability, convergence and computer implementation. | ||
| 432 | PARTIAL DIFFERENTIAL EQUATIONS | 4 credits |
| Prerequisite: Completion of 335 with a grade of C- or better. The classical initial value and boundary value problems of mathematical physics developed and solved using Fourier series and integral transforms. | ||
| 435 | SYSTEMS OF ORD DIFF EQUATIONS | 3 credits |
| Prerequisites: Completion of 335 and either 312 or 428 with grades of C- or better or permission. Analysis, solution of systems of equations, linear, nonlinear. Topics: stability theory, perturbation methods, asymptotic methods, applications from physical, social sciences. | ||
| 436 | MATHEMATICAL MODELS | 3 credits |
| Prerequisite: Completion of 335 with a grade of C- or better, and a six-hour sequence in an approved applied area, or permission. Formulation and analysis of mathematical models in social and physical sciences. Analysis of deterministic and stochastic models. Topics may include stochastic processes, linear programming, graph theory, theory of measurement. | ||
| 438 | ADVANCED ENGINEERING MATH I | 3 credits |
| Prerequisites: Completion of 335 and 312 with grades of C- or better or permission. Matrices, eigenvalue problems, systems of ODEs, vector analysis, complex variables. | ||
| 439 | ADVANCED ENGINEERING MATH II | 3 credits |
| Prerequisites: Completion of 335 and 312 with grades of C- or better or permission. Special functions, Fourier series and transforms, PDEs. | ||
| 441 | CONCEPTS IN GEOMETRY | 4 credits |
| Prerequisite: 307 with a grade of C- or better or permission of instructor. Axiomatic treatment of both Euclidean and non-Euclidean geometries. Other concepts included are finite geometry, transformations, constructions and inversions. | ||
| 445 | INTRODUCTION TO TOPOLOGY | 3 credits |
| Prerequisite: Completion of 307 with a grade of C- or better or permission of instructor. Introduction to topological spaces and topologies, mappings, cardinality, homeomorphisms, connected spaces, metric spaces. | ||
| 489 | T: MATHEMATICS | 1-4 credits |
| (May be repeated for a total of 12 credits) Prerequisite : permission of instructor. Selected topics in mathematics and applied mathematics at an advanced level. | ||
| 491 | W: MATHEMATICS | 1-4 credits |
| (May be repeated) Group studies of special topics in mathematics and applied mathematics. May not be used to meet undergraduate or graduate major requirements. May be used for elective credit. | ||
| 497 | INDIV READING: MATH | 1-2 credits |
| Prerequisites: senior standing and permission. Mathematics or applied mathematics majors only. Directed studies designed as an introduction to research problems, under guidance of selected faculty member. | ||
| 498 | SENIOR HONORS PROJECT: MATH | 1-3 credits |
| Prerequisite: Permission of Instructor. Directed study for senior student in the Honors Program. An introduction to research problems in mathematics and applied mathematics under the guidance of selected faculty. May be repeated for up to six credits. | ||
| 501 | HISTORY OF MATHEMATICS | 3 credits |
| Prerequisite: departmental permission. Origin and development of mathematical ideas. Course does not meet degree requirements in the department. | ||
| 510 | ADVANCED LINEAR ALGEBRA | 3 credits |
| Prerequisite: departmental permission. Study of vector spaces, linear transformation, canonical and quadratic forms, inner product spaces. | ||
| 511 | ABSTRACT ALGEBRA I | 3 credits |
| Prerequisite: Departmental permission. Study of groups, rings, fields, integral domains, vector spaces, field extensions. Galois theory. May not be used to meet master's degree requirements in mathematics. | ||
| 512 | ABSTRACT ALGEBRA II | 3 credits |
| Prerequisite: 511or departmental permission. Study of groups, rings, fields, integral domains, vector spaces, field extensions, Galois theory. | ||
| 513 | THEORY OF NUMBERS | 3 credits |
| Prerequisite: departmental permission. Euclidean algorithm, unique factorization theorem, congruences, primitive roots, indices, quadratic residues, number-theoretic functions, Gaussian integers and continued fractions. | ||
| 515 | COMBINATORICS & GRAPH THEORY | 3 credits |
| Prerequisite: departmental permission. Introduction to basic ideas and techniques of mathematical counting; properties of structure of systems. | ||
| 520 | MATH TECH AND COMMUNICATION | 3 credits |
| Prerequisites: departmental permission. Graphical, numerical, and algebraic computation with applications using a variety of mathematical hardware and software: symbolic manipulators, dynamic geometry software, programs, scripts and web-browsers. | ||
| 521 | ADVANCED CALCULUS I | 3 credits |
| Sequential. Prerequisite: Departmental permission. Real number system, sequences, series, set theory, continuity, differentiation, integration, partial derivatives, multiple integration, maxima and minima, convergences and uniform convergences, power series, improper integrals, transformations, line and surface integrals. May not be used to meet master's degree requirements for mathematics or applied mathematics. | ||
| 522 | ADVANCED CALCULUS II | 3 credits |
| Sequential. Prerequisite: departmental permission. Real number system, sequences, series, set theory, continuity, differentiation, integration, partial derivatives, multiple integration, maxima and minima, convergence and uniform convergence, power series, improper integrals, transformations, line and surface integrals. | ||
| 525 | COMPLEX VARIABLES | 3 credits |
| Prerequisite: departmental permission. Complex variables; elementary functions, differentiation and analytic functions; integration and Cauchy's theorem; power series and Laurent series; residue theorem; applications such as conformal mappings, inversion of integral transform. | ||
| 527 | APPLIED NUMERICAL METHODS I | 3 credits |
| Prerequisite: departmental permission. Numerical methods in polynomial interpolation, root finding, numerical integration, and numerical linear algebra. May not be used to meet master's degree requirements for applied mathematics. | ||
| 528 | APPLIED NUMERICAL METHODS II | 3 credits |
| Prerequisite: departmental permission. Numerical methods in the solution of ordinary and partial differential equations. Numerical differentiation, Runge-Kutta methods, and iterative methods for ODEs, finite differences for PDEs. | ||
| 532 | PARTIAL DIFFERENTIAL EQUATIONS | 4 credits |
| Prerequisite: departmental permission. The classical initial value and boundary value problems of mathematical physics developed and solved using Fourier series and integral transforms. | ||
| 535 | SYSTEMS OF ORD DIFF EQUATIONS | 3 credits |
| Prerequisites: departmental permission. Analysis, solution of systems of equations, linear, nonlinear. Topics: stability theory, perturbation methods, asymptotic methods, applications from physical, social sciences. | ||
| 536 | MATHEMATICAL MODELS | 3 credits |
| Prerequisite: departmental permission. Formulation and analysis of mathematical models in social and physical sciences. Analysis of deterministic and stochastic models. Topics may include stochastic processes, linear programming, graph theory, theory of measurement. | ||
| 538 | ADVANCED ENGINEERING MATH I | 3 credits |
| Prerequisite: Departmental permission. Matrices, eigenvalue problems, systems of ODEs, vector analysis, complex variables. May not be used to meet master's requirements for applied mathematics. | ||
| 539 | ADVANCED ENGINEERING MATH II | 3 credits |
| Prerequisite: departmental permission. Special functions, fourier series and transforms, PDEs. | ||
| 541 | CONCEPTS IN GEOMETRY | 4 credits |
| Prerequisite: departmental permission. Axiomatic treatment of both Euclidean and non-Euclidean geometries. Other concepts included are finite geometry, transformations, constructions and inversions. | ||
| 545 | INTRODUCTION TO TOPOLOGY | 3 credits |
| Prerequisite: departmental permission. Introduction to topological spaces and topologies, mapping, cardinality, homeomorphisms, connected spaces, metric spaces. | ||
| 589 | T: MATHEMATICS | 1-4 credits |
| (May be repeated for a total of 12 credits) Prerequisite : permission of instructor. Selected topics in mathematics and applied mathematics at an advanced level. | ||
| 591 | W: MATHEMATICS | 1-4 credits |
| (May be repeated) Group studies of special topics in mathematics and applied mathematics. May not be used to meet undergraduate or graduate credit requirements in mathematics. May be used for elective credit only. | ||
| 611 | T: ALGEBRA | 3 credits |
| Prerequisite: 512 or departmental permission. Advanced study of selected topics in some of the following areas: semigroups, groups, rings, modules and fields. | ||
| 621 | REAL ANALYSIS | 3 credits |
| Prerequisite: 522 or departmental permission. In-depth study of real analysis - metric spaces, normed vector spaces, integration theory, Hilbert spaces. | ||
| 625 | ANALYTIC FUNCTION THEORY | 3 credits |
| Prerequisite: 522 or departmental permission. Complex number system, holomorphic functions, continuity, differentiability, power series complex integration, residue theory, singularities, analytic continuation, asymptotic expansion. | ||
| 627 | ADVANCED NUMERICAL ANALYSIS I | 3 credits |
| Prerequisites: 522 (grade C- or better) and knowledge of C++, FORTRAN, or MATLAB or departmental permission. Error propagation; theoretical analysis of numerical methods in interpolation, integration and ordinary differential equations. | ||
| 628 | ADVANCED NUMERICAL ANALYSIS II | 3 credits |
| Prerequisites: 522 (grade C- or better) and knowledge of C++, FORTRAN, or MATLAB or departmental permission. Theoretical analysis of numerical methods in linear algebra. | ||
| 631 | CALCULUS OF VARIATIONS | 3 credits |
| Prerequisite: departmental permission. Problems with fixed and movable endpoints, problems with constraints, generalization to several variables, the maximality principle, linear time-optional problems, the connective between classical theory and the maximality principle. | ||
| 632 | ADVANCED PARTIAL DIFF EQUA | 3 credits |
| Prerequisite: 532 or departmental permission. Existence, uniqueness and stability of solutions to general classes of partial differential equations. Methods for solving these classes introduced, emphasizing both analytical and numerical techniques. | ||
| 633 | METHODS OF APPLIED MATH I | 3 credits |
| Prerequisite: 539 or departmental permission. Methods of applied mathematics concentrating on techniques for analysis of differential and integral equations - applied complex analysis, integral transforms, partial differential equations, and integral equations. | ||
| 634 | METHODS OF APPLIED MATH II | 3 credits |
| Prerequisite: 539 or departmental permission. Methods of applied mathematics concentrating on techniques for analysis of differential and integral equations - applied complex analysis, integral transforms, partial differential equations, and integral equations. | ||
| 635 | OPTIMIZATION | 3 credits |
| Prerequisite: 522 or departmental permission. Unconstrained and constrained optimization theory and methods in applied problems. | ||
| 636 | ADV COMBINATORICS & GRAPH THRY | 3 credits |
| Prerequisite: departmental permission. Theory and techniques of combinatorics as applied to network problems and graph theoretic problems. | ||
| 638 | THEORY & APPL OF WAVELETS | 3 credits |
| Prerequisite: permission of instructor. Theory of wavelets and applications to signal and image analysis. Topics include time-frequency representations, filter bands, discrete and continuous wavelet transforms, wavelet packets, and applications. | ||
| 689 | ADV T: MATHEMATICS | 1-3 credits |
| (May be repeated for a total of six credits) Prerequisite: permission of advisor. Seminar-type discussion on topics in mathematics leading to supervised research project. No more than 2 credits apply to major requirements. | ||
| 692 | SEM: MATHEMATICS | 3 credits |
| Prerequisite: permission of advisor. Seminar-type discussion on topics in mathematics leading to supervised research project. | ||
| 695 | PRACTICUM IN MATHEMATICS | 1-3 credits |
| (May be repeated) Prerequisite: graduate teaching assistant or permission. Training and experience in college teaching of mathematics. May not be used to meet degree requirements. Credit/noncredit. | ||
| 697 | INDIV READING: MATH | 1-3 credits |
| (May be repeated for a total of four credits) Prerequisites: graduate standing and permission. Directed studies in mathematics at graduate level under guidance of selected faculty member. | ||
| 698 | MASTERS RESEARCH | 1-6 credits |
| (May be repeated) Prerequisite: permission of advisor. Research in suitable topics in mathematics or applied mathematics culminating in a research paper. May not be used to meet master's degree requirements for mathematics or applied mathematics. | ||
| 699 | MASTERS THESIS | 3 credits |
| Prerequisite: permission. A properly qualified candidate for the master's degree may obtain three credits for research that culminates in a public oral presentation of the faculty-supervised thesis. | ||
| 721 | FUNCTIONAL ANALYSIS I | 3 credits |
| Prerequisites: 510 and 621 or departmental permission. These courses are sequential. Study of normed linear spaces and transformations between them with an emphasis on the formulation and analysis of differential and integral equations as operator equations on these spaces. | ||
| 722 | FUNCTIONAL ANALYSIS II | 3 credits |
| Prerequisites: 510 and 621 or departmental permission. These courses are sequential. Study of normed linear spaces and transformations between them with an emphasis on the formulation and analysis of differential and integral equations as operator equations on these spaces. | ||
| 728 | MATRIX ITERATIVE ANALYSIS | 3 credits |
| Prerequisite: departmental permission. Basic Iterative methods, Matrix Properties and Concepts, Linear and Nonlinear equation solver, Semi-iterative and conjugate-gradient methods. | ||
| 730 | ADVANCED NUM SOL PART DIFF EQU | 3 credits |
| Prerequisites: 522 and 528, or 628, or departmental permission. Derivation, analysis, and implementation of difference and variational-based methods for the solution of partial differential equations and systems of differential equations. | ||
| 732 | ADVANCED PART DIFF EQUATION II | 3 credits |
| Prerequisites: 522 and 532 or departmental permission. Well-posedness of elliptic, hyperbolic and parabolic problems. Variational Methods for Elliptic problems, Conservation Laws and numerical methods, potential theory and integral equations. | ||
| 733 | ASYMP METHODS & NONLIN ANAL I | 3 credits |
| Prerequisites: 633/634 or equivalent. Survey of asymptotic and perturbation methods as applied to integrals and differential equations. Topics: bifurcation and stability with applications from the physical sciences and engineering. | ||
| 734 | ASYM METH & NONLIN ANL II | 3 credits |
| Prerequisites: 633/634 or equivalent. Survey of asymptotic and perturbation methods as applied to integrals and differential equations. Topics: bifurcation and stability with applications from the physical sciences and engineering. | ||
| 735 | DYNAMICAL SYSTEMS | 3 credits |
| Prerequisite: 522 or departmental permission. The study of mathematical models of systems which evolve over time. An introduction to maps and applications to ordinary differential equations. | ||
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