MTH 065 ELEMENTARY ALGEBRA (3)
Arithmetic of signed numbers, order of operations, simplifying algebraic expressions, solution of linear equations, and inequalities. Rules of exponents, addition, subtraction, and multiplication of polynomials, factoring, solution of quadratic equations by factoring, reducing rational expressions. Word problems involving linear equations, graphing of linear equations, inequalities.
PREREQS:
Placement Test or Placement Test

MTH 095 INTERMEDIATE ALGEBRA (3)
Addition, subtraction, multiplication, and division of rational expressions, long division of polynomials, solution of fractional equations, applications involving linear equations. Fractional equations, inequalities, literal equations, and variations. Negative and fractional exponents, radicals, solution of quadratic equations, and complex numbers. Cartesian coordinates, graphs of linear equations and inequalities, distance formula, slope, equations of lines, solutions of systems of linear equations in two unknowns and inequalities.
PREREQS:
MTH 065 or Placement Test or Placement Test
and
MTH 065

MTH 102 ALGEBRAIC FOUNDATIONS (3)
This course is designed primarily for EOP students. They will use various computing technologies to explore realistic and interesting situations in which algebra is used. As they work through explorations, they will work with many of the fundamental ideas of algebra, ideas they will find important in their daily lives.

MTH 103 ALGEBRAIC REASONING (4)
A combination of cooperative learning and individual instruction is used to promote student development of algebraic reasoning processes and skills.
PREREQS:
MTH 065 or Placement Test or Placement Test
and
Previous algebra course.

MTH 105 INTRODUCTION TO CONTEMPORARY MATHEMATICS (3)
Elementary linear programming, combinatorics, descriptive statistics, elementary probability, exponential growth and decay, examples of major mathematical ideas and models. Lec/rec. (Bacc Core Course)
PREREQS:
MTH 095 or equivalent high school preparation.

MTH 111 COLLEGE ALGEBRA (4)
Polynomial equations and inequalities, polynomial functions and graphs, inverse functions, exponential and logarithmic functions, elementary mathematical modeling and applications. Lec/rec. (Bacc Core Course)
PREREQS:
MTH 095 or MTH 103 or Placement Test or Placement Test
and
MTH 095 or equivalent high school preparation.

MTH 112 ELEMENTARY FUNCTIONS (4)
Triangle trigonometry, circular functions and graphs, trigonometric equations and identities, inverse trigonometric functions, polar coordinates, vectors and applications. Lec/rec. (Bacc Core Course)
PREREQS:
MTH 111 or Placement Test or Placement Test
and
MTH 111

MTH 199 SPECIAL TOPICS (116)
Maximum 3 credits per term, 9 credits total. Does not meet university group requirement in physical science.
This course is repeatable for a maximum of 9 credits.

MTH 211 FOUNDATIONS OF ELEMENTARY MATHEMATICS (4)
Introduction to problem solving, sets, whole numbers, number theory, fractions, decimals, percent, ratio and proportion, integers. Intended primarily for prospective elementary teachers. (Bacc Core Course)
PREREQS:
(MTH 095 or MTH 103 or MTH 111 or MTH 112) or Placement Test or Placement Test

MTH 212 FOUNDATIONS OF ELEMENTARY MATHEMATICS (4)
Rational and real numbers, probability, statistics, and informal geometry.
PREREQS:
MTH 211

MTH 231 ELEMENTS OF DISCRETE MATHEMATICS (4)
Elementary logic and set theory, functions, direct proof techniques, contradiction and contraposition, mathematical induction and recursion, elementary combinatorics, basic graph theory, minimal spanning trees.
PREREQS:
MTH 112 or Placement Test or Placement Test
and
Placement in MTH 251

MTH 232 ELEMENTS OF DISCRETE MATHEMATICS (4)
Combinatorics, algorithms and complexity, graphs and trees. Lec/rec.
PREREQS:
MTH 231

MTH 241 CALCULUS FOR MANAGEMENT AND SOCIAL SCIENCE (4)
Elementary differential and integral calculus of polynomial, logarithmic, and exponential functions and their applications to business, management and social sciences. Lec/rec. (Bacc Core Course)
PREREQS:
(MTH 111 or MTH 112) or Placement Test
and
MTH 111

MTH 245 MATHEMATICS FOR MANAGEMENT, LIFE, AND SOCIAL SCIENCES (4)
Techniques of counting, probability and elements of statistics including binomial and normal distributions. Introductory matrix algebra. Elements of linear programming. Lec/rec. (Bacc Core Course)
PREREQS:
MTH 111 or Placement Test or Placement Test
and
MTH 111

MTH 251 DIFFERENTIAL CALCULUS (4)
Differential calculus for engineers and scientists. Rates of change: the derivative, velocity, and acceleration. The algebraic rules of differential calculus and derivatives of polynomial, rational, and trigonometric functions. Maximumminimum problems, curve sketching, and other applications. Antiderivatives and simple motion problems. (Bacc Core Course)
PREREQS:
MTH 112 or Placement Test or Placement Test
and
MTH 112

MTH 251H DIFFERENTIAL CALCULUS (4)
Differential calculus for engineers and scientists. Rates of change: the derivative, velocity, and acceleration. The algebraic rules of differential calculus and derivatives of polynomial, rational, and trigonometric functions. Maximumminimum problems, curve sketching, and other applications. Antiderivatives and simple motion problems. (Bacc Core Course)
PREREQS:
MTH 112 or Placement Test or Placement Test
and
MTH 112 and Honors College approval required.

MTH 252 INTEGRAL CALCULUS (4)
Definite integrals, elementary applications to area, force, and work. Integral tables and basic techniques of integration, calculus of logarithmic and exponential functions, polar coordinates, applications to areas, volumes, force, work, and growth and decay problems. Lec/rec.
PREREQS:
MTH 251 or MTH 251H
and
MTH 251 or MTH 251H

MTH 252H INTEGRAL CALCULUS (4)
Definite integrals, elementary applications to area, force, and work. Integral tables and basic techniques of integration, calculus of logarithmic and exponential functions, polar coordinates, applications to areas, volumes, force, work, and growth and decay problems.
PREREQS:
MTH 251 or MTH 251H
and
(MTH 251 or MTH 251H) and Honors College approval required.

MTH 253 INFINITE SERIES AND SEQUENCES (4)
Indeterminate forms. Improper integrals. Sequences and series, especially Taylor's formula and power series. Applications to numerical estimation with error analysis. Series with complex terms and the Euler identities. Lec/rec.
PREREQS:
MTH 252 or MTH 252H
and
MTH 252 or MTH 252H

MTH 254 VECTOR CALCULUS I (4)
Vectors, vector functions, and curves in two and three dimensions. Surfaces, partial derivatives, gradients, and directional derivatives. Multiple integrals in rectangular, polar, cylindrical, and spherical coordinates. Physical and geometric applications. Lec/rec.
PREREQS:
MTH 252 or MTH 252H
and
MTH 252 or MTH 252H

MTH 254H VECTOR CALCULUS I (4)
Vectors, vector functions, and curves in two and three dimensions. Surfaces, partial derivatives, gradients, and directional derivatives. Multiple integrals in rectangular, polar, cylindrical, and spherical coordinates. Physical and geometric applications. Lec/rec.
PREREQS:
MTH 252 or MTH 252H
and
(MTH 252 or MTH 252H) and Honors College approval required.

MTH 255 VECTOR CALCULUS II (4)
Brief review of vector functions, space curves, gradients, and directional derivatives. Introduction to vector analysis: vector fields, divergence, curl, line integrals, surface integrals, conservative fields, and the theorems of Gauss and Stokes with applications to force, work, mass, and charge. Lec/rec.
PREREQS:
MTH 254 or MTH 254H
and
MTH 254 or MTH 254H

MTH 255H VECTOR CALCULUS II (4)
Brief review of vector functions, space curves, gradients, and directional derivatives. Introduction to vector analysis: vector fields, divergence, curl, line integrals, surface integrals, conservative fields, and the theorems of Gauss and Stokes with applications to force, work, mass, and charge.
PREREQS:
MTH 254 or MTH 254H
and
(MTH 254 or MTH 254H) and Honors College approval required.

MTH 256 APPLIED DIFFERENTIAL EQUATIONS (4)
First order linear and nonlinear equations, and second order linear equations. Applications to electric circuits and mechanical oscillators. Introduction to the Laplace transform and higher order equations. Solution methods and applications appropriate for science and engineering. (Familiarity with complex numbers and Euler's identities is highly desirable.) Lec/rec.
PREREQS:
MTH 254 or MTH 254H
and
(MTH 254 or MTH 254H) or instructor approval required.

MTH 256H APPLIED DIFFERENTIAL EQUATIONS (4)
First order linear and nonlinear equations, and second order linear equations. Applications to electric circuits and mechanical oscillators. Introduction to the Laplace transform and higher order equations. Solution methods and applications appropriate for science and engineering. (Familiarity with complex numbers and Euler's identities is highly desirable.)
PREREQS:
MTH 254 or MTH 254H
and
(MTH 254 or MTH 254H) or instructor approval required. Honors College approval required.

MTH 268 MATHEMATICAL IDEAS IN BIOLOGY (4)
Mathematical models of biological systems, with emphasis on population dynamics and ecology. Integral calculus with applications to biology.
PREREQS:
MTH 251 or MTH 251H
and
MTH 251

MTH 299 SPECIAL TOPICS (116)
Maximum 3 credits per term, 9 credits total.
This course is repeatable for a maximum of 9 credits.

MTH 306 MATRIX AND POWER SERIES METHODS (4)
Introduction to matrix algebra, determinants, systematic solution to linear systems, and eigenvalue problems. Convergence and divergence of series with emphasis on power series, Taylor series expansions, convergence tests for power series, and error estimates for truncated series used in practical approximations. Lec/rec.
PREREQS:
MTH 252 or MTH 252H
and
(MTH 252 or MTH 252H)

MTH 306H MATRIX AND POWER SERIES METHODS (4)
Introduction to matrix algebra, determinants, systematic solution to linear systems, and eigenvalue problems. Convergence and divergence of series with emphasis on power series, Taylor series expansions, convergence tests for power series, and error estimates for truncated series used in practical approximations. Lec/rec.
PREREQS:
MTH 252 or MTH 252H
and
(MTH 252 or MTH 252H) and Honors College approval required.

MTH 311 ADVANCED CALCULUS (4)
Rigorous development of calculus, axiomatic properties of R, topology of the real line, convergence of sequences and series of real numbers, functions, limits of functions, basic properties of continuity and derivatives. Brief treatment of Riemann integration, improper integrals, sequences of functions, pointwise and uniform convergence, introductory aspects of multivariable calculus.
PREREQS:
(MTH 255 or MTH 255H) and MTH 355
and
Completion of lowerdivision calculus sequence (MTH 251 through MTH 255) and MTH 355, Discrete Mathematics.

MTH 312 ADVANCED CALCULUS (4)
Rigorous development of calculus, axiomatic properties of R, topology of the real line, convergence of sequences and series of real numbers, functions, limits of functions, basic properties of continuity and derivatives. Brief treatment of Riemann integration, improper integrals, sequences of functions, pointwise and uniform convergence, introductory aspects of multivariable calculus.
PREREQS:
MTH 311 and MTH 342*
and
MTH 311. Concurrent enrollment in MTH 342.

MTH 323 MATHEMATICAL MODELING (3)
A variety of mathematical modeling techniques will be introduced. Students will formulate models in response to practical problems drawn from the literature of ecology, environmental sciences, engineering or other fields. Informal writing assignments in class and formal written presentation of the models will be required. (Writing Intensive Course)
PREREQS:
(MTH 256 or MTH 256H) and MTH 341
and
MTH 256 and MTH 341 or instructor approval.

MTH 333 FUNDAMENTAL CONCEPTS OF TOPOLOGY (3)
Open and closed sets, continuity, compactness, connectedness, winding number, fixed point theorems in the plane. (Writing Intensive Course)
PREREQS:
MTH 341 or MTH 355
and
MTH 341 or MTH 355

MTH 338 NONEUCLIDEAN GEOMETRY (3)
Introduction to nonEuclidean geometries. Selected topics such as hyperbolic and elliptic geometry, spherical geometry, projective geometry, geometries arising from alternative metrics. (Writing Intensive Course)
PREREQS:
MTH 252 or MTH 252H
and
MTH 252

MTH 341 LINEAR ALGEBRA I (3)
Matrix algebra, determinants, systems of linear equations, computational aspects of eigenvalues and eigenvectors.
PREREQS:
MTH 254 or MTH 254H
and
MTH 254

MTH 342 LINEAR ALGEBRA II (4)
Vector spaces, linear transformations, inner product spaces, orthogonality, eigenvalues, diagonalization.
PREREQS:
MTH 341
and
MTH 341

MTH 343 INTRODUCTION TO MODERN ALGEBRA (3)
Introduction to rings and fields with an emphasis on the integers and polynomial rings; selected applications.
PREREQS:
MTH 341 and MTH 355

MTH 351 INTRODUCTION TO NUMERICAL ANALYSIS (3)
Introduction to the computation of approximate solutions to mathematical problems that cannot be solved by hand: analysis of errors; rootfinding for nonlinear equations in one variable; interpolation of functions; numerical integration.
PREREQS:
MTH 253 or MTH 306
and
MTH 253 or MTH 306 and programming experience.

MTH 355 DISCRETE MATHEMATICS (3)
For mathematics majors beginning upperdivision mathematics course work. Topics include elementary combinatories and basic counting principles such as the sum, product, pigeonhole, and bijection principles; mathematical induction; equivalence relations; introductory aspects of graph theory; generating functions; and the inclusionexclusion principle.
PREREQS:
MTH 253
and
MTH 253 required and MTH 341 recommended.

MTH 361 INTRODUCTION TO PROBABILITY (3)
Probability problem solving using concepts developed in calculus. Topics include probability models, discrete and continuous random variables, expectation and variance, the law of large numbers, and the central limit theorem.
PREREQS:
MTH 253 or MTH 306 or MTH 306H
and
MTH 253 or MTH 306

MTH 361H INTRODUCTION TO PROBABILITY (3)
Probability problem solving using concepts developed in calculus. Topics include probability models, discrete and continuous random variables, expectation and variance, the law of large numbers, and the central limit theorem.
PREREQS:
MTH 253 or MTH 306 or MTH 306H
and
MTH 253 or MTH 306 and Honors College approval required.

MTH 390 FOUNDATIONS OF ELEMENTARY MATHEMATICS (4)
Measurement, congruence, similarity, coordinate and transformational geometry.
PREREQS:
MTH 212
and
MTH 212

MTH 399 SPECIAL TOPICS (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 399H SPECIAL TOPICS (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Honors College approval required.

MTH 401 RESEARCH (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 403 THESIS (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 405 READING AND CONFERENCE (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 406 PROJECTS (13)
Graded P/N.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 407 SEMINAR (3)
This course is repeatable for a maximum of 99 credits.
PREREQS:
Departmental approval required.

MTH 410 OCCUPATIONAL INTERNSHIP (312)
Planned and supervised training experience at selected government, industrial, or business placement sites. Must be followed by a onehour postinternship seminar. Consult departmental head advisor. Graded P/N.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Junior standing in mathematics, cumulative 3.00 GPA in mathematics, head advisor/departmental approval required.

MTH 411 REAL ANALYSIS (3)
Topological concepts in metric, normed, and innerproduct spaces. Properties of continuous functions, including the StoneWeierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini's theorem, and applications to Fourier transforms and probability.
PREREQS:
MTH 312 and MTH 341
and
MTH 312 and MTH 341

MTH 412 REAL ANALYSIS (3)
Topological concepts in metric, normed, and innerproduct spaces. Properties of continuous functions, including the StoneWeierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini's theorem, and applications to Fourier transforms and probability.
PREREQS:
MTH 411 or MTH 511
and
MTH 411 or MTH 511

MTH 413 REAL ANALYSIS (3)
Topological concepts in metric, normed, and innerproduct spaces. Properties of continuous functions, including the StoneWeierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini's theorem, and applications to Fourier transforms and probability.
PREREQS:
MTH 412 or MTH 512
and
MTH 412 or MTH 512

MTH 420 MODELS AND METHODS OF APPLIED MATHEMATICS (3)
Discrete and continuous mathematical models and methods for analysis, including linear analysis, equilibrium and minimum principles, calculus of variations, principal component analysis and orthogonal expansions, asymptotic and Fourier analysis, least squares, constrained and unconstrained optimization, inverse problems, and Monte Carlo techniques. Particular models and methods covered may vary annually.
PREREQS:
(MTH 256 or MTH 256H) and MTH 341
and
junior standing or above.

MTH 430 METRIC SPACES AND TOPOLOGY (3)
Fundamental notions of metric space topology. Examples of Euclidean, nonEuclidean and other fundamental metric spaces including the Hilbert Cube and twodimensional surfaces. Characterization and classification results for metric spaces. Selected applications of topology, possibly including the structure of molecules and/or networks.
PREREQS:
MTH 342 or MTH 355
and
/or instructor approval. MTH 311 is recommended.

MTH 434 INTRODUCTION TO DIFFERENTIAL GEOMETRY (3)
Curves and surfaces in Euclidean space; geodesics; curvature; introduction to tensor algebra and differential forms; selected applications.
PREREQS:
MTH 312 and MTH 342
and
MTH 311 recommended.

MTH 435 DIFFERENTIAL GEOMETRY (3)
Differentiable 2manifolds; curvature; geodesics; tensor algebra and the algebra of exterior differential forms with emphasis on Euclidean space; differentiation of tensors and forms; integration of forms; selected applications.
PREREQS:
MTH 434 or MTH 534
and
(MTH 434 or MTH 534) or instructor approval required.

MTH 437 GENERAL RELATIVITY (3)
Geometry of special relativity. Tensor analysis, metrics, geodesics, curvature. Einstein field equations, cosmological models, black holes. Selected topics such as global structure, conserved quantities, spinors.
PREREQS:
MTH 311
and
MTH 311. MTH 434 or MTH 534 is recommended.

MTH 440 COMPUTATIONAL NUMBER THEORY (3)
Development of the number theory used in some basic tests of primality and methods of factoring integers. Applications to cryptology.
PREREQS:
MTH 231 or MTH 343 or MTH 355
and
MTH 231 or MTH 343 or MTH 355

MTH 441 APPLIED AND COMPUTATIONAL ALGEBRA (3)
Applications of fundamental algebraic systems to topics such as factorization of polynomials, finding roots of polynomials, error correcting codes.
PREREQS:
MTH 342 or MTH 440 or MTH 540
and
MTH 342 or (MTH 440 or MTH 540) or instructor approval required.

MTH 442 APPLIED AND COMPUTATIONAL ALGEBRA (3)
Applications of fundamental algebraic systems to topics such as factorization of polynomials, finding roots of polynomials, error correcting codes.
PREREQS:
MTH 441 or MTH 541
and
MTH 441 or MTH 541 or instructor approval required.

MTH 443 ABSTRACT LINEAR ALGEBRA (3)
Abstract vector spaces. Linear transformations, eigenvalues and eigenvectors, the Jordan canonical form, inner product spaces.
PREREQS:
MTH 342 or MTH 343
and
MTH 342 and MTH 343

MTH 451 NUMERICAL LINEAR ALGEBRA (3)
Computation of solutions of linear systems using direct and iterative methods; leastsquares solution of overdetermined systems; computation of eigenvalues and eigenvectors.
PREREQS:
MTH 341
and
MTH 341 and programming experience or instructor approval required. MTH 342 and MTH 351 are recommended.

MTH 452 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS (3)
Numerical solution of initialvalue problems using RungeKutta methods and linear multistep methods; introduction to boundaryvalue problems. Analysis of stability, accuracy, and implementation of methods.
PREREQS:
(MTH 256 or MTH 256H) and (MTH 451 or MTH 551)
and
MTH 256 and (MTH 451 or MTH 551) or instructor approval required.

MTH 453 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (3)
Numerical solution of boundary value problems and initialboundary value problems using finite difference and finite element methods. Analysis of stability, accuracy, and implementation of methods.
PREREQS:
MTH 452 or MTH 552
and
(MTH 452 or MTH 552) or instructor approval required.

MTH 463 PROBABILITY I (3)
An introduction to probability theory; topics covered include: the axioms of probability, probability spaces and models, independence, random variables; densities, distributions, expectation, and variance; probability inequalities, the law of large numbers, and the binomial central limit theorem.
PREREQS:
MTH 312
and
MTH 312 or instructor approval required.

MTH 464 PROBABILITY II (3)
Transformations of random variables; sums of independent random variables, generating functions, characteristic functions, the central limit theorem and other weak limit theorems.
PREREQS:
(MTH 463 or MTH 563) and MTH 341
and
(MTH 463 or MTH 563) and MTH 341 or instructor approval required.

MTH 465 PROBABILITY III (3)
Random variables, central limit theorem; distributions of standard statistics; Markov chains, continuous and discontinuous stochastic processes.
PREREQS:
MTH 464 or MTH 564
and
(MTH 464 or MTH 564) or instructor approval required.

MTH 467 ACTUARIAL MATHEMATICS (3)
Foundations of actuarial science from the point of view of mathematical models that arise in the design and management of insurance systems. Most models will be life insurance based.
PREREQS:
MTH 463 or MTH 563 or ST 421
and
(MTH 463 or MTH 563) or ST 421 or instructor approval required.

MTH 480 SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS (3)
Systems of two firstorder differential equations, phase portraits, linearization and the stability of equilibria, conservative systems, reversible systems, limit cycles and the PoincareBendixson Theorem. Additional topics selected from Hamiltonian systems, Hopf bifurcation or Lorenz equations and chaos. MTH 480 and MTH 481 cannot both be taken for credit.
PREREQS:
(MTH 256 or MTH 256H) and MTH 341

MTH 481 MATHEMATICAL METHODS FOR ENGINEERS AND SCIENTISTS (3)
Linear and nonlinear systems of ordinary differential equations, elementary stability theory, higher order equations, boundary value problems, series solution of ordinary differential equations.
PREREQS:
MTH 256 or MTH 256H
and
MTH 256

MTH 482 MATHEMATICAL METHODS FOR ENGINEERS AND SCIENTISTS (3)
Partial differential equations, Bessel's and Legendre's equations, Fourier analysis, separation of variables, transform methods.
PREREQS:
MTH 481
and
MTH 481 or consent of instructor.

MTH 483 MATHEMATICAL METHODS FOR ENGINEERS AND SCIENTISTS (3)
Introduction to the complex differential and integral calculus: Cauchy's theorem and formula, the residue calculus, power series and Laurent series, harmonic functions, conformal mapping, and applications.
PREREQS:
MTH 256 or MTH 256H

MTH 490 INTENSIVE SUMMER RESEARCH IN MATHEMATICS (12)
Combination of seminar, lectures, and individual research projects designed to introduce students to research mathematics.
This course is repeatable for a maximum of 99 credits.
PREREQS:
Open to participants in the OSU Undergraduate Summer Research Program in Mathematics (REU program).

MTH 491 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)
Ordered fields, number systems (natural, integer, rational, real, and complex), fundamental theorems of arithmetic and algebra, algebraic and transcendental numbers, constructible points and numbers and the classical geometric constructions, Polya's problem solving heuristics and strategies. Intended primarily for prospective mathematics teachers.
PREREQS:
MTH 341
and
MTH 341

MTH 492 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)
Major results of Euclidean geometry, axiom systems for Euclidean geometry, dependency tree of Euclidean theorems, groups of geometric transformations with applications to symmetries of plane and solid objects, Euler's formula, tilings and tesselations, isometries and similitudes of the plane (translations, rotations, reflections, glide reflections, dilations). Intended primarily for prospective mathematics teachers.
PREREQS:
MTH 491 or MTH 591
and
MTH 491 or MTH 591

MTH 493 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)
Geometric transformations as real, complex, and matrix functions, invariants and genealogy of geometric transformations, extensions to transformations of the sphere and of threedimensional space, selected applications chosen from fractals, analysis of frieze and crystallographic patterns, problem solving, groups of symmetries, computer graphics, and the use of dynamic geometry software. Intended primarily for prospective mathematics teachers.
PREREQS:
MTH 492 or MTH 592
and
MTH 492 or MTH 592

MTH 499 SPECIAL TOPICS (016)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 501 RESEARCH (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 503 THESIS (116)
This course is repeatable for a maximum of 999 credits.
PREREQS:
Departmental approval required.

MTH 505 READING AND CONFERENCE (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 506 PROJECTS (116)
Graded P/N.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 507 SEMINAR (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 508 WORKSHOP (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 510 OCCUPATIONAL INTERNSHIP (312)
Planned and supervised training experience at selected government, industrial, or business placement sites. Must be followed by a onehour postinternship seminar. Consult departmental head advisor. Graded P/N.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 511 REAL ANALYSIS (3)
Topological concepts in metric, normed, and innerproduct spaces. Properties of continuous functions, including the StoneWeierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini's theorem, and applications to Fourier transforms and probability.
PREREQS:
MTH 312 and MTH 341

MTH 512 REAL ANALYSIS (3)
Topological concepts in metric, normed, and innerproduct spaces. Properties of continuous functions, including the StoneWeierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini's theorem, and applications to Fourier transforms and probability.
PREREQS:
MTH 411 or MTH 511

MTH 513 REAL ANALYSIS (3)
Topological concepts in metric, normed, and innerproduct spaces. Properties of continuous functions, including StoneWeierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini's theorem, and applications to Fourier transforms and probability.
PREREQS:
MTH 412 or MTH 512

MTH 520 MODELS AND METHODS OF APPLIED MATHEMATICS (3)
Discrete and continuous mathematical models and methods for analysis, including linear analysis, equilibrium and minimum principles, calculus of variations, principal component analysis and orthogonal expansions, asymptotic and Fourier analysis, least squares, constrained and unconstrained optimization, inverse problems, and Monte Carlo techniques. Particular models and methods covered may vary annually.
PREREQS:
(MTH 256 or MTH 256H) and MTH 341 and junior standing or above.

MTH 524 DYNAMICAL SYSTEMS THEORY AND APPLICATIONS (3)
Theory, models, and problems for discrete and/or continuous dynamical systems. Depending on term, the emphasis may be toward deterministic or stochastic systems. Topics generally include stability theory, periodic behavior, and chaotic systems. Models selected from biology, economics, fluid dynamics, and electrical and mechanical systems. May be repeated once for credit with a different topic.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 341MTH 342, MTH 311MTH 312, MTH 361 or consent of instructor.

MTH 525 DYNAMICAL SYSTEMS THEORY AND APPLICATIONS (3)
Theory, models, and problems for discrete and/or continuous dynamical systems. Depending on term, the emphasis may be toward deterministic or stochastic systems. Topics generally include stability theory, periodic behavior, and chaotic systems. Models selected from biology, economics, fluid dynamics, and electrical and mechanical systems. May be repeated once for credit with a different topic.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 341 and MTH 342 and MTH 311 and MTH 312 and MTH 361 or consent of instructor.

MTH 531 GENERAL TOPOLOGY AND FUNDAMENTAL GROUPS (3)
Topological spaces and maps. Separation axioms, compactness, convergence, extension theorems, metrizability and compactification. Product spaces and simplicial complexes. Definition and basic properties of the fundamental group functor, with applications to the theory of covering spaces. Selected topics from dimension theory, manifold theory, and other areas of topology.
PREREQS:
MTH 531 and MTH 532 must be taken in order.

MTH 532 GENERAL TOPOLOGY AND FUNDAMENTAL GROUPS (3)
Topological spaces and maps. Separation axioms, compactness, convergence, extension theorems, metrizability and compactification. Product spaces and simplicial complexes. Definition and basic properties of the fundamental group functor, with applications to the theory of covering spaces. Selected topics from dimension theory, manifold theory, and other areas of topology.
PREREQS:
MTH 531 and MTH 532 must be taken in order.

MTH 534 INTRODUCTION TO DIFFERENTIAL GEOMETRY (3)
Curves and surfaces in Euclidean space; geodesics; curvature; introduction to tensor algebra and differential forms; selected applications.
PREREQS:
MTH 312 and MTH 342 or instructor approval required.

MTH 535 DIFFERENTIAL GEOMETRY (3)
Differentiable 2manifolds; curvature; geodesics; tensor algebra and the algebra of exterior differential forms with emphasis on Euclidean space; differentiation of tensors and forms; integration of forms; selected applications.
PREREQS:
(MTH 434 or MTH 534) or instructor approval required.

MTH 537 GENERAL RELATIVITY (3)
Geometry of special relativity. Tensor analysis, metrics, geodesics, curvature. Einstein field equations, cosmological models, black holes. Selected topics such as global structure, conserved quantities, spinors.
PREREQS:
MTH 434 or MTH 534
and
MTH 311. (MTH 434 or MTH 534) is recommended.

MTH 540 COMPUTATIONAL NUMBER THEORY (3)
Development of the number theory used in some basic tests of primality and methods of factoring integers. Applications to cryptology.
PREREQS:
MTH 231 or MTH 343 or MTH 355

MTH 541 APPLIED AND COMPUTATIONAL ALGEBRA (3)
Applications of fundamental algebraic systems to topics such as factorization of polynomials, finding roots of polynomials, error correcting codes.
PREREQS:
MTH 342 or (MTH 440 or MTH 540) or instructor approval required.

MTH 542 APPLIED AND COMPUTATIONAL ALGEBRA (3)
Applications of fundamental algebraic systems to topics such as factorization of polynomials, finding roots of polynomials, error correcting codes.
PREREQS:
(MTH 441 or MTH 541) or instructor approval required.

MTH 543 ABSTRACT LINEAR ALGEBRA (3)
Abstract vector spaces. Linear transformations, eigenvalues and eigenvectors, the Jordan canonical form, inner product spaces.
PREREQS:
MTH 342 and MTH 343

MTH 551 NUMERICAL LINEAR ALGEBRA (3)
Computation of solutions of linear systems using direct and iterative methods; leastsquares solution of overdetermined systems; computation of eigenvalues and eigenvectors.
PREREQS:
MTH 341 and programming experience or instructor approval required. MTH 342 are MTH 351 are recommended.

MTH 552 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS (3)
Numerical solution of initialvalue problems using RungeKutta methods and linear multistep methods; introduction to boundaryvalue problems. Analysis of stability, accuracy, and implementation of methods.
PREREQS:
MTH 256 and (MTH 451 or MTH 551) or instructor approval required.

MTH 553 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (3)
Numerical solution of boundary value problems and initialboundary value problems using finite difference and finite element methods. Analysis of stability, accuracy, and implementation of methods.
PREREQS:
(MTH 452 or MTH 552) or instructor approval required.

MTH 563 PROBABILITY I (3)
An introduction to probability theory; topics covered include: the axioms of probability, probability spaces and models, independence, random variables; densities, distributions, expectation, and variance; probability inequalities, the law of large numbers, and the binomial central limit theorem.
PREREQS:
MTH 312 or instructor approval required.

MTH 564 PROBABILITY II (3)
Transformations of random variables; sums of independent random variables, generating functions, characteristic functions, the central limit theorem and other weak limit theorems.
PREREQS:
(MTH 463 or MTH 563) and MTH 341 or instructor approval required.

MTH 565 PROBABILITY III (3)
Random variables, central limit theorem; distributions of standard statistics; Markov chains, continuous and discontinuous stochastic processes.
PREREQS:
(MTH 464 or MTH 564) or instructor approval required.

MTH 567 ACTUARIAL MATHEMATICS (3)
Foundations of actuarial science from the point of view of mathematical models that arise in the design and management of insurance systems. Most models will be life insurance based.
PREREQS:
(MTH 463 or MTH 563) or ST 421.

MTH 574 NUMBER SYSTEMS AND OPERATIONS IN K8 MATHEMATICS (3)
Key ideas and topics in number systems, operations, place value, and algorithms critical for the mathematics content knowledge of elementary teachers in grades K8. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences.
PREREQS:
MTH 390 or instructor approval required.

MTH 575 COMPARING GEOMETRIES IN K8 MATHEMATICS (3)
Key ideas and topics in Euclidean and nonEuclidean geometries critical for the mathematics content knowledge of elementary teachers in grades K8. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences.
PREREQS:
MTH 390 or instructor approval required.

MTH 576 ALGEBRA AND FUNCTION IN K8 MATHEMATICS (3)
Key ideas and topics in algebra and function concepts critical for the mathematics content knowledge of elementary teachers in grades K8. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences.
PREREQS:
MTH 390 or instructor approval required.

MTH 578 PROBABILITY AND DATA ANALYSIS IN K8 MATHEMATICS (3)
Key ideas and topics in probability, data analysis, and statistics critical for the mathematics content knowledge of elementary teachers in grades K8. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences.
PREREQS:
MTH 390 or instructor approval required.

MTH 581 MATHEMATICAL METHODS FOR ENGINEERS AND SCIENTISTS (3)
Linear and nonlinear systems of ordinary differential equations, elementary stability theory, higher order equations, boundary value problems, series solution of ordinary differential equations.
PREREQS:
MTH 256

MTH 582 MATHEMATICAL METHODS FOR ENGINEERS AND SCIENTISTS (3)
Partial differential equations, Bessel's and Legendre's equations, Fourier analysis, separation of variables, transform methods.
PREREQS:
MTH 481 or consent of instructor.

MTH 583 MATHEMATICAL METHODS FOR ENGINEERS AND SCIENTISTS (3)
Introduction to the complex differential and integral calculus: Cauchy's theorem and formula, the residue calculus, power series and Laurent series, harmonic functions, conformal mapping, and applications.
PREREQS:
MTH 256

MTH 590 TOPICS IN SECONDARY MATHEMATICS (3)
Key ideas and topics in discrete mathematics critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences.
PREREQS:
MTH 390 or instructor approval required.

MTH 591 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)
Ordered fields, number systems (natural, integer, rational, real, and complex), fundamental theorems of arithmetic and algebra, algebraic and transcendental numbers, constructible points and numbers and the classical geometric constructions, Polya's problem solving heuristics and strategies. Intended primarily for prospective mathematics teachers.
PREREQS:
MTH 341

MTH 592 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)
Major results of Euclidean geometry, axiom systems for Euclidean geometry, dependency tree of Euclidean theorems, groups of geometric transformations with applications to symmetries of plane and solid objects, Euler's formula, tilings and tesselations, isometries and similitudes of the plane (translations, rotations, reflections, glide reflections, dilations). Intended primarily for prospective mathematics teachers.
PREREQS:
MTH 491 or MTH 591

MTH 593 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)
Geometric transformations as real, complex, and matrix functions, invariants and genealogy of geometric transformations, extensions to transformations of the sphere and of threedimensional space, selected applications chosen from fractals, analysis of frieze and crystallographic patterns, problem solving, groups of symmetries, computer graphics, and the use of dynamic geometry software. Intended primarily for prospective mathematics teachers.
PREREQS:
MTH 492 or MTH 592

MTH 594 NUMBER SYSTEMS AND OPERATIONS IN SECONDARY MATHEMATICS (3)
Key ideas and topics in number systems, operations, place value, and algorithms critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences.
PREREQS:
MTH 390 or instructor approval required.

MTH 595 COMPARING GEOMETRIES IN SECONDARY MATHEMATICS (3)
Key ideas and topics in Euclidean and nonEuclidean geometries critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences.
PREREQS:
MTH 390 or instructor approval required.

MTH 596 ALGEBRA AND FUNCTION IN SECONDARY MATHEMATICS (3)
Key ideas and topics in algebra and function concepts critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences.
PREREQS:
MTH 390 or instructor approval required.

MTH 598 PROBABILITY AND DATA ANALYSIS IN SECONDARY MATHEMATICS (3)
Key ideas and topics in probability, data analysis, and statistics critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences.
PREREQS:
MTH 390 or instructor approval required.

MTH 599 SPECIAL TOPICS (016)
Topics may vary.
This course is repeatable for a maximum of 18 credits.
PREREQS:
Instructor approval required.

MTH 601 RESEARCH (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 603 THESIS (116)
This course is repeatable for a maximum of 999 credits.
PREREQS:
Departmental approval required.

MTH 605 READING AND CONFERENCE (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 606 SPECIAL PROJECTS (116)
Graded P/N.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 607 SEMINAR (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 611 COMPLEX ANALYSIS (3)
Basic theory of analytic functions of a complex variable, including Cauchy's theorem, residue theorem, analytic continuation, conformal mappings, entire, and meromorphic functions.
PREREQS:
(MTH 411 or MTH 511). MTH 611 and MTH 612 must be taken in order.

MTH 612 COMPLEX ANALYSIS (3)
Basic theory of analytic functions of a complex variable, including Cauchy's theorem, residue theorem, analytic continuation, conformal mappings, entire, and meromorphic functions.
PREREQS:
MTH 611

MTH 614 FUNCTIONAL ANALYSIS (3)
Topological vector spaces, generalized functions, operator theory. Normally offered alternate years.
PREREQS:
MTH 513

MTH 619 TOPICS IN ANALYSIS (112)
This course is repeatable for a maximum of 12 credits.

MTH 621 DIFFERENTIAL AND INTEGRAL EQUATIONS OF MATHEMATICAL PHYSICS (3)
Partial differential equations of physics, including those of potential theory, wave propagation, and heat flow, treated by classical means, generalized functions and variational principles. Square summable function methods and integral equations.
This course is repeatable for a maximum of 6 credits.
PREREQS:
6 credits of seniorlevel analysis or instructor consent. MTH 621, MTH 622, MTH 623 must be taken in order.

MTH 622 DIFFERENTIAL AND INTEGRAL EQUATIONS OF MATHEMATICAL PHYSICS (3)
Partial differential equations of physics, including those of potential theory, wave propagation, and heat flow, treated by classical means, generalized functions and variational principles. Square summable function methods and integral equations.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 621 and 6 credits of seniorlevel analysis or instructor consent.

MTH 623 DIFFERENTIAL AND INTEGRAL EQUATIONS OF MATHEMATICAL PHYSICS (3)
Partial differential equations of physics, including those of potential theory, wave propagation, and heat flow, treated by classical means, generalized functions and variational principles. Square summable function methods and integral equations.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 622 and 6 credits of seniorlevel analysis or instructor consent.

MTH 627 PARTIAL DIFFERENTIAL EQUATIONS (3)
Advanced theory including existence proofs and distributional approach. Normally offered alternate years.
PREREQS:
MTH 413 or MTH 513 or instructor consent.

MTH 628 PARTIAL DIFFERENTIAL EQUATIONS (3)
Advanced theory including existence proofs and distributional approach. Normally offered alternate years.
PREREQS:
MTH 627 or consent of instructor.

MTH 634 ALGEBRAIC TOPOLOGY (3)
Simplicial and singular homology, products, and cohomology; applications to fixedpoint and separation theorems. Topics selected from homotopy, manifold and obstruction theory. Normally offered alternate years.
PREREQS:
MTH 532. MTH 634, MTH 635, MTH 636 must be taken in order.

MTH 635 ALGEBRAIC TOPOLOGY (3)
Simplicial and singular homology, products, and cohomology; applications to fixedpoint and separation theorems. Topics selected from homotopy, manifold and obstruction theory. Normally offered alternate years.
PREREQS:
MTH 532 and MTH 634

MTH 636 ALGEBRAIC TOPOLOGY (3)
Simplicial and singular homology, products, and cohomology; applications to fixedpoint and separation theorems. Topics selected from homotopy, manifold and obstruction theory. Normally offered alternate years.
PREREQS:
MTH 532 and MTH 635

MTH 644 ABSTRACT ALGEBRA (3)
Group theory, rings and fields, Galois theory.
PREREQS:
Graduate standing in mathematics or a related field, or instructor approval required. MTH 443 or MTH 543 is recommended.

MTH 645 ABSTRACT ALGEBRA (3)
Group theory, rings and fields, Galois theory.
PREREQS:
Graduate standing in mathematics or a related field, or instructor approval required. MTH 644 is recommended.

MTH 649 TOPICS IN ALGEBRA AND NUMBER THEORY (3)
This course is repeatable for a maximum of 27 credits.

MTH 654 NUMERICAL ANALYSIS (3)
Advanced topics in numerical analysis, such as finite volume methods and finite element methods for partial differential equations, numerical methods for inverse problems, and image processing.
PREREQS:
(MTH 451 or MTH 551) and (MTH 452 or MTH 552) and (MTH 453 or MTH 553) or equivalent or instructor's consent.

MTH 655 NUMERICAL ANALYSIS (3)
Advanced topics in numerical analysis, such as finite volume methods and finite element methods for partial differential equations, numerical methods for inverse problems, and image processing.
PREREQS:
MTH 654 or instructor's consent.

MTH 656 NUMERICAL ANALYSIS (3)
Advanced topics in numerical analysis, such as finite volume methods and finite element methods for partial differential equations, numerical methods for inverse problems, and image processing.
PREREQS:
MTH 655 or instructor's consent.

MTH 657 TOPICS IN APPLIED MATHEMATICS (112)
Previous topics have included turbulence, financial mathematics and probability methods in partial differential equations.
This course is repeatable for a maximum of 12 credits.

MTH 658 TOPICS IN MATHEMATICAL MODELING (112)
Mathematical treatment of topics of current interest in the physical and biological sciences and technology. May be repeated for credit when topic varies.
This course is repeatable for a maximum of 12 credits.
PREREQS:
Instructor approval required.

MTH 659 TOPICS IN NUMERICAL ANALYSIS (112)
This course is repeatable for a maximum of 12 credits.

MTH 664 PROBABILITY THEORY (3)
General theory of probability measures and random variables, including weak convergence, characteristic functions, central limit theory, conditional expectations, martingales.
PREREQS:
MTH 411 or MTH 511 or equivalent.

MTH 665 PROBABILITY THEORY (3)
General theory of probability measures and random variables, including weak convergence, characteristic functions, the central limit theorem, and the Brownian motion process.
PREREQS:
MTH 664

MTH 669 TOPICS IN STOCHASTIC PROCESSES (112)
Previous topics have included Markov processes, martingales, branching processes, and stochastic differential equations.
This course is repeatable for a maximum of 12 credits.

MTH 674 DIFFERENTIAL GEOMETRY OF MANIFOLDS (3)
Differentiable manifolds, tangent bundles, vector fields and flows, submanifolds, Riemannian metrics, differential forms, integration on manifolds. Selected topics such as foliations, Lie groups, and de Rham cohomology.
PREREQS:
MTH 341 and (MTH 411 or MTH 511). MTH 674 or MTH 675 must be taken in order.

MTH 675 DIFFERENTIAL GEOMETRY OF MANIFOLDS (3)
Differentiable manifolds, connections in linear bundles, Riemannian manifolds and submanifolds. Selected topics such as variational theory of geodesics, harmonic forms, and characteristic classes. Normally offered alternate years.
PREREQS:
MTH 674

MTH 676 TOPICS IN TOPOLOGY (3)
This course is repeatable for a maximum of 27 credits.

MTH 679 TOPICS IN GEOMETRY (112)
This course is repeatable for a maximum of 12 credits.

MTH 680 MODERN APPROACHES TO CALCULUS (3)
Alternative approaches to calculus instruction based on the availability of computers and calculators. Applications of symbolicgraphical calculators, spreadsheets, symbolic algebra systems, and graphics packages to the teaching of calculus.
PREREQS:
MTH 253 and instructor approval required.

MTH 682 TEACHING AND LEARNING PROBABILITY AND STATISTICS (3)
Experimental, activitybased approaches to introductory probability and statistics are explored. Topics include computer simulations, exploratory data analysis, misuses of statistics, and misconceptions of probability.
PREREQS:
Instructor approval required.

MTH 684 COMPUTERS AND MATHEMATICS (3)
A variety of mathematical problems are investigated with a laboratory approach using microcomputers and a wide variety of software. Problems may be taken from number theory, calculus, geometry, probability, and elementary numerical analysis.
PREREQS:
Ability to program in either BASIC or PASCAL and instructor approval required.

MTH 685 ADVANCED PROBLEM SOLVING (3)
Mathematical problem solving using the heuristic approach of George Polya. Problems may be taken from a variety of areas, including number theory, calculus, geometry, probability, abstract and linear algebra.
PREREQS:
Instructor approval required.

MTH 689 TOPICS IN MATHEMATICS EDUCATION (112)
Topics may vary.
This course is repeatable for a maximum of 12 credits.

MTH 699 SPECIAL TOPICS (116)
This course is repeatable for a maximum of 16 credits.
