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MTH Undergraduate Courses, Corvallis Campus

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Top MTH 065 ELEMENTARY ALGEBRA (3) 
Arithmetic of signed numbers, order of operations, simplifying algebraic expressions, solutions 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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: Placement Test MPT(05) or Placement Test MPAL(015) and (MPT=Math Placement Test score of 05; MPAL=Math Placement Test-ALEKS score of 15%)

Top MTH 095 INTERMEDIATE ALGEBRA (3) 
Addition, subtraction, multiplication, and division of rational expressions, long division of polynomials, solutions of fractional equations, applications involving linear equations. Fractional equations, inequalities, literal equations, and variations. Negative and fractional exponents, radicals, solutions 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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 065 [C-] or Placement Test MPT(11) or Placement Test MPAL(030) and (MPT=Math Placement Test score of 11; MPAL=Math Placement Test-ALEKS score of 30%)

Top MTH 102 ALGEBRAIC FOUNDATIONS (3)  Offered in current or future terms
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.

Top MTH 103 ALGEBRAIC REASONING (4)  Offered in current or future terms Has Extra Fees
Graphing data, functions, rate of change, linear equations, systems of linear equations, linear inequalities, linear functions, absolute value functions, quadratic functions, exponential functions. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 065 [C-] or Placement Test MPT(11) or Placement Test MPAL(030) and (MPT=Math Placement Test score of 11; MPAL=Math Placement Test-ALEKS score of 30%)

Top MTH 105 INTRODUCTION TO CONTEMPORARY MATHEMATICS (3)  Offered in current or future terms Baccalaureate Core Course
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 MTH 103 or (MPT=Math Placement Test score of 17; MPAL=Math Placement Test-ALEKS score of 46%) recommended.

Top MTH 111 COLLEGE ALGEBRA (4)  Offered in current or future terms Baccalaureate Core Course Has Extra Fees
Polynomial equations and inequalities, polynomial functions and graphs, inverse functions, exponential and logarithmic functions, elementary mathematical modeling and applications. Lec/rec. All courses used to satisfy MTH prerequisites must be completed with a C- or better. (Bacc Core Course) PREREQS: MTH 095 [C-] or MTH 103 [C-] or Placement Test MPT(17) or Placement Test MPAL(046) and (MPT=Math Placement Test score of 17; MPAL=Math Placement Test-ALEKS score of 46%)

Top MTH 112 ELEMENTARY FUNCTIONS (4)  Offered in current or future terms Baccalaureate Core Course Has Extra Fees
Triangle trigonometry, circular functions and graphs, trigonometric equations and identities, inverse trigonometric functions, polar coordinates, vectors and applications. Lec/rec. All courses used to satisfy MTH prerequisites must be completed with C- or better. (Bacc Core Course) PREREQS: MTH 111 [C-] or Placement Test MPT(24) or Placement Test MPAL(060) and (MPT=Math Placement Test score of 24; MPAL=Math Placement Test-ALEKS score of 60%)

Top MTH 150X PRECALCULUS (4)  Offered in current or future terms
Trigonometry. Exponential, logarithmic and trigonometric functions. Lec/rec. PREREQS: MTH 111 [C-] or Placement Test MPT(24) or Placement Test MPAL(060)

Top MTH 199 SPECIAL TOPICS (1-16)  Offered in current or future terms
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.

Top MTH 211 FOUNDATIONS OF ELEMENTARY MATHEMATICS (4)  Offered in current or future terms Baccalaureate Core Course Has Extra Fees
Introduction to problem solving, sets, whole numbers, number theory, fractions, decimals, percent, ratio and proportion, integers. Intended primarily for prospective elementary teachers. All courses used to satisfy MTH prerequisites must be completed with C- or better. (Bacc Core Course) PREREQS: MTH 095 [C-] or MTH 103 [C-] or MTH 111 [C-] or MTH 112 [C-] or Placement Test MPT(17) or Placement Test MPAL(046)

Top MTH 212 FOUNDATIONS OF ELEMENTARY MATHEMATICS (4)  Offered in current or future terms Has Extra Fees
Rational and real numbers, probability, statistics, and informal geometry. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 211 [C-]

Top MTH 227X CALCULUS AND PROBABILITY FOR LIFE SCIENCES I (4)  Offered in current or future terms
Review of exponential and trigonometric functions, including examples of exponential and periodic behavior; discrete probability; examples of biologically motivated difference equations; differentiation of polynomials, exponential and trigonometric functions with applications to optimization. PREREQS: MTH 112 [C-] or MTH 150X [C-] or Placement Test MPT(33) or Placement Test MPAL(75)

Top MTH 228 CALCULUS AND PROBABILTITY FOR THE LIFE SCIENCES II (4)  Offered in current or future terms
Continuation of MTH 227 with more general population growth models. Antidifferentiation; The Fundamental Theorem of Calculus applied to solving continuous growth models. Continuous random variables. Basic linear algebra of small systems sufficient to calculate eigenvalues and eigenvectors and appreciate their use in life science applications. Lec/rec. PREREQS: MTH 227 [C-] or MTH 251 [C-] or MTH 251H [C-]

Top MTH 231 ELEMENTS OF DISCRETE MATHEMATICS (4)  Offered in current or future terms
Elementary logic and set theory, functions, direct proof techniques, contradiction and contraposition, mathematical induction and recursion, elementary combinatorics, basic graph theory, minimal spanning trees. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 112 [C-] or Placement Test MPT(33) or Placement Test MPAL(075) and (MPT=Math Placement Test score of 33; MPAL=Math Placement Test-ALEKS score of 75%)

Top MTH 232 ELEMENTS OF DISCRETE MATHEMATICS (4) 
Combinatorics, algorithms and complexity, graphs and trees. Lec/rec. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 231

Top MTH 241 CALCULUS FOR MANAGEMENT AND SOCIAL SCIENCE (4)  Offered in current or future terms Baccalaureate Core Course Has Extra Fees
Elementary differential and integral calculus of polynomial, logarithmic, and exponential functions and their applications to business, management and social sciences. Lec/rec. All courses used to satisfy MTH prerequisites must be completed with C- or better. (Bacc Core Course) PREREQS: MTH 111 [C-] or Placement Test MPT(24) or Placement Test MPAL(060) and (MPT=Math Placement Test score of 24; MPAL=Math Placement Test-ALEKS score of 60%)

Top MTH 245 MATHEMATICS FOR MANAGEMENT, LIFE, AND SOCIAL SCIENCES (4)  Offered in current or future terms Baccalaureate Core Course
Techniques of counting, probability and elements of statistics including binomial and normal distributions. Introductory matrix algebra. Elements of linear programming. Lec/rec. All courses used to satisfy MTH prerequisites must be completed with C- or better. (Bacc Core Course) PREREQS: MTH 111 [C-] or Placement Test MPT(24) or Placement Test MPAL(060) and (MPT=Math Placement Test score of 24; MPAL=Math Placement Test-ALEKS score of 60%)

Top MTH 251 DIFFERENTIAL CALCULUS (4)  Offered in current or future terms Baccalaureate Core Course Has Extra Fees
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. Maximum-minimum problems, curve sketching, and other applications. Antiderivatives and simple motion problems. Lec/rec. All courses used to satisfy MTH prerequisites must be completed with a C- or better. (Bacc Core Course) PREREQS: MTH 112 [C-] or MTH 150X [C-] or Placement Test MPT(33) or Placement Test MPAL(075) and (MPT=Math Placement Test score of 33; MPAL=Math Placement Test-ALEKS score of 75%)

Top MTH 251H DIFFERENTIAL CALCULUS (4)  Offered in current or future terms Baccalaureate Core Course Has Extra Fees
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. Maximum-minimum problems, curve sketching, and other applications. Antiderivatives and simple motion problems. Lec/rec. All courses used to satisfy MTH prerequisites must be completed with C- or better. (Bacc Core Course) PREREQS: MTH 112 [C-] or MTH 150X [C-] or Placement Test MPT(33) or Placement Test MPAL(075) and (MPT=Math Placement Test score of 33; MPAL=Math Placement Test-ALEKS score of 75%). Honors College approval required.

Top MTH 252 INTEGRAL CALCULUS (4)  Offered in current or future terms Has Extra Fees
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 251 [C-] or MTH 251H [C-]

Top MTH 252H INTEGRAL CALCULUS (4)  Offered in current or future terms Has Extra Fees
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 251 [C-] or MTH 251H [C-] and Honors College approval required.

Top MTH 253 INFINITE SERIES AND SEQUENCES (4)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 252 [C-] or MTH 252H [C-]

Top MTH 254 VECTOR CALCULUS I (4)  Offered in current or future terms Has Extra Fees
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 252 [C-] or MTH 252H [C-]

Top MTH 254H VECTOR CALCULUS I (4)  Offered in current or future terms Has Extra Fees
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 252 [C-] or MTH 252H [C-] and Honors College approval required.

Top MTH 255 VECTOR CALCULUS II (4)  Offered in current or future terms Has Extra Fees
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 254 [C-] or MTH 254H [C-]

Top MTH 255H VECTOR CALCULUS II (4)  Offered in current or future terms Has Extra Fees
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 254 [C-] or MTH 254H [C-] and Honors College approval required.

Top MTH 256 APPLIED DIFFERENTIAL EQUATIONS (4)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 254 [C-] or MTH 254H [C-] and /or instructor approval required.

Top MTH 256H APPLIED DIFFERENTIAL EQUATIONS (4)  Offered in current or future terms
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.) All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 254 [C-] or MTH 254H [C-] and /or instructor approval required. Honors College approval required.

Top 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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 251 [D-] or MTH 251H [D-]

Top MTH 299 SPECIAL TOPICS (0-16)  Offered in current or future terms
Maximum 3 credits per term, 9 credits total. This course is repeatable for a maximum of 9 credits.

Top MTH 306 MATRIX AND POWER SERIES METHODS (4)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 252 [C-] or MTH 252H [C-]

Top MTH 306H MATRIX AND POWER SERIES METHODS (4)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 252 [C-] or MTH 252H [C-] and Honors College approval required.

Top MTH 311 ADVANCED CALCULUS (4)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: (MTH 255 [C-] or MTH 255H [C-] ) and MTH 355 [C-]

Top MTH 312 ADVANCED CALCULUS (4)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 311 [C-] and MTH 342* [C-]

Top MTH 321 INTRODUCTORY APPLICATIONS OF MATHEMATICAL SOFTWARE (3)  Offered in current or future terms
An introduction to select mathematical software packages to support problem solving and applications. Topics include using computational resources to solve basic numerical and symbolic problems in mathematics, visualization and presentation of data, creation of simple programming scripts, and applications of basic programming techniques to promote mathematical understanding. The scientific typesetting language LaTeX will also be covered. All courses used to satisfy MTH prerequisites must be completed with a C- or better. PREREQS: (MTH 252 [C-] or MTH 252H [C-] ) and (MTH 341 [C-] or MTH 306 [C-] or MTH 306H [C-] )

Top MTH 323 MATHEMATICAL MODELING (3)  Offered in current or future terms WIC Core Course
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. (Writing Intensive Course) PREREQS: (MTH 256 [C-] or MTH 256H [C-] ) and MTH 341 [C-] and /or instructor approval.

Top MTH 333 FUNDAMENTAL CONCEPTS OF TOPOLOGY (3)  Offered in current or future terms WIC Core Course
Open and closed sets, continuity, compactness, connectedness, winding number, fixed point theorems in the plane. All courses used to satisfy MTH prerequisites must be completed with C- or better. (Writing Intensive Course) PREREQS: MTH 341 [C-] or MTH 355 [C-]

Top MTH 338 NON-EUCLIDEAN GEOMETRY (3)  Offered in current or future terms WIC Core Course
Introduction to non-Euclidean geometries. Selected topics such as hyperbolic and elliptic geometry, spherical geometry, projective geometry, geometries arising from alternative metrics. All courses used to satisfy MTH prerequisites must be completed with C- or better. (Writing Intensive Course) PREREQS: MTH 252 [C-] or MTH 252H [C-]

Top MTH 341 LINEAR ALGEBRA I (3)  Offered in current or future terms
Matrix algebra, determinants, systems of linear equations, subspaces, an introductory study of eigenvalues and eigenvectors.All courses used to satisfy MTH prerequisites must be completed with C- or better PREREQS: MTH 254 [C-] or MTH 254H [C-]

Top MTH 342 LINEAR ALGEBRA II (4)  Offered in current or future terms
Abstract (real or complex) vector spaces, linear transformations, inner product spaces, orthogonality, eigenspaces and diagonalization, spectral theorems, singular value decomposition. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 341 [C-]

Top MTH 343 INTRODUCTION TO MODERN ALGEBRA (3)  Offered in current or future terms
Introduction to rings and fields with an emphasis on the integers and polynomial rings; selected applications. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 341 [C-] and MTH 355 [C-]

Top MTH 351 INTRODUCTION TO NUMERICAL ANALYSIS (3)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: (MTH 253 [C-] or MTH 306 [C-] or MTH 306H [C-] ) and programming experience.

Top MTH 355 DISCRETE MATHEMATICS (3)  Offered in current or future terms
Proof analysis and development in the context of discrete mathematics for math majors transitioning to upper-division course work. Topics include elementary logic and set theory, quantifiers, basic counting principles, elementary combinatorics, equivalence relations, the binomial theorem, and mathematical induction. Additional topics may include recurrence relations, generating functions, and introductory graph theory. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 253 [C-] and MTH 341 recommended.

Top MTH 361 INTRODUCTION TO PROBABILITY (3)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 253 [C-] or MTH 306 [C-] or MTH 306H [C-]

Top MTH 390 FOUNDATIONS OF ELEMENTARY MATHEMATICS (4)  Offered in current or future terms Has Extra Fees
Measurement, congruence, similarity, coordinate and transformational geometry. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 212 [C-]

Top MTH 399 SPECIAL TOPICS (1-16) 
This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 399H SPECIAL TOPICS (1-16) 
This course is repeatable for a maximum of 16 credits. PREREQS: Honors College approval required.

Top MTH 401 RESEARCH (1-16)  Offered in current or future terms
This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 403 THESIS (1-16)  Offered in current or future terms
This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 405 READING AND CONFERENCE (1-16)  Offered in current or future terms
This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 406 PROJECTS (1-3)  Offered in current or future terms
Graded P/N. This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 407 SEMINAR (3)  Offered in current or future terms
This course is repeatable for a maximum of 99 credits. PREREQS: Departmental approval required.

Top MTH 410 OCCUPATIONAL INTERNSHIP (3-12)  Offered in current or future terms
Planned and supervised training experience at selected government, industrial, or business placement sites. Must be followed by a one-hour post-internship 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.

Top MTH 411 REAL ANALYSIS (3)  Offered in current or future terms
Topological concepts in metric, normed, and inner-product spaces. Properties of continuous functions, including the Stone-Weierstrass 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. All courses used to satisfy MTH 411 prerequisites must be completed with B+ or better. PREREQS: MTH 312 [B+] and MTH 341 [B+]

Top MTH 412 REAL ANALYSIS (3)  Offered in current or future terms
Topological concepts in metric, normed, and inner-product spaces. Properties of continuous functions, including the Stone-Weierstrass 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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 411 [C-] or MTH 511 [C-]

Top MTH 413 REAL ANALYSIS (3)  Offered in current or future terms
Topological concepts in metric, normed, and inner-product spaces. Properties of continuous functions, including the Stone-Weierstrass 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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 412 [C-] or MTH 512 [C-]

Top MTH 419 MULTIVARIABLE ADVANCED CALCULUS (3) 
A rigorous development of multivariable advanced calculus, including continuity and compactness in multivariable Euclidean spaces, differentiation and approximation of multivariable functions, the inverse function theorem and the implicit function theorem, integration in several variables. PREREQS: MTH 312 [B]

Top MTH 420 MODELS AND METHODS OF APPLIED MATHEMATICS (3)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: (MTH 256 [C-] or MTH 256H [C-] ) and MTH 341 [C-] and junior standing or above.

Top MTH 427 INTRODUCTION TO MATHEMATICAL BIOLOGY (3)  Offered in current or future terms
Modeling and mathematical analysis of biological processes using first principles at scales ranging from the molecular to the population level. Deterministic models are studied in both discrete and continuous time and analyzed using linearization principles, linear and nonlinear stability techniques, phase plane methods, and methods from partial differential equations. Results obtained from mathematical analysis will be qualitatively interpreted and applied to the biological process under investigation. All courses used to satisfy MTH prerequisites must be completed with a C- or better. PREREQS: (MTH 256 [C-] or MTH 256H [C-] ) and MTH 341 [C-]

Top MTH 428 STOCHASTIC ELEMENTS IN MATHEMATICAL BIOLOGY (3)  Offered in current or future terms
An introduction to stochastic modeling of biological processes. The stochastic models covered may include Markov processes in both continuous and discrete time, urn models, branching processes, and coalescent processes. The biological applications may include genetic drift, population dynamics, genealogy, demography, and epidemiology. Mathematical results will be qualitatively interpreted and applied to the biological process under investigation. PREREQS: MTH 341 [C] and (MTH 361 [C] or MTH 463 [C] or MTH 563 [C] )

Top MTH 430 METRIC SPACES AND TOPOLOGY (3)  Offered in current or future terms
Fundamental notions of metric space topology. Examples of Euclidean, non-Euclidean and other fundamental metric spaces including the Hilbert Cube and two-dimensional surfaces. Characterization and classification results for metric spaces. Selected applications of topology, possibly including the structure of molecules and/or networks. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 342 [C-] or MTH 355 [C-] and /or instructor approval. MTH 311 is recommended.

Top MTH 434 INTRODUCTION TO DIFFERENTIAL GEOMETRY (3)  Offered in current or future terms
Curves and surfaces in Euclidean space; geodesics; curvature; introduction to tensor algebra and differential forms; selected applications. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: (MTH 255 [C-] or MTH 255H [C-] ) and MTH 342 [C-] and (MTH 311 recommended)

Top MTH 435 DIFFERENTIAL GEOMETRY (3)  Offered in current or future terms
Differentiable 2-manifolds; 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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 434 [C-] or MTH 534 [C-] and /or instructor approval required.

Top 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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: (MTH 434 [C-] or MTH 534 [C-] ) and MTH 311 is recommended.

Top MTH 440 COMPUTATIONAL NUMBER THEORY (3)  Offered in current or future terms
Development of the number theory used in some basic tests of primality and methods of factoring integers. Applications to cryptology. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 231 [C-] or MTH 343 [C-] or MTH 355 [C-]

Top MTH 441 APPLIED AND COMPUTATIONAL ALGEBRA (3)  Offered in current or future terms
Applications of fundamental algebraic systems to topics such as factorization of polynomials, finding roots of polynomials, error correcting codes. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 343 [C-] and (MTH 342 [C-] or MTH 440 [C-] or MTH 540 [C-] ) and /or instructor approval required.

Top MTH 442 APPLIED AND COMPUTATIONAL ALGEBRA (3)  Offered in current or future terms
Applications of fundamental algebraic systems to topics such as factorization of polynomials, finding roots of polynomials, error correcting codes. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 441 [C-] or MTH 541 [C-] and /or instructor approval required.

Top MTH 443 ABSTRACT LINEAR ALGEBRA (3)  Offered in current or future terms
Abstract vector spaces. Linear transformations, eigenvalues and eigenvectors, the Jordan canonical form, inner product spaces. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 342 [C-] or MTH 343 [C-]

Top MTH 451 NUMERICAL LINEAR ALGEBRA (3)  Offered in current or future terms
Computation of solutions of linear systems using direct and iterative methods; least-squares solution of overdetermined systems; computation of eigenvalues and eigenvectors. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 341 [C-] and programming experience or instructor approval required. MTH 342 and MTH 351 are recommended.

Top MTH 452 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
Numerical solution of initial-value problems using Runge-Kutta methods and linear multistep methods; introduction to boundary-value problems. Analysis of stability, accuracy, and implementation of methods. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: (MTH 256 [C-] or MTH 256H [C-] ) and (MTH 306 [C-] or MTH 306H [C-] or MTH 341 [C-] ) and programming experience required and junior standing required. MTH 351 or MTH 451 or MTH 551 recommended.

Top MTH 453 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
Numerical solution of boundary value problems and initial-boundary value problems using finite difference and finite element methods. Analysis of stability, accuracy, and implementation of methods. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 452 [C-] or MTH 552 [C-] and /or instructor approval required.

Top MTH 463 PROBABILITY I (3)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 312 [C-] and /or instructor approval required.

Top MTH 464 PROBABILITY II (3)  Offered in current or future terms
Transformations of random variables; sums of independent random variables, generating functions, characteristic functions, the central limit theorem and other weak limit theorems. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: (MTH 463 [C-] or MTH 563 [C-] ) and MTH 341 [C-] and /or instructor approval required.

Top MTH 465 PROBABILITY III (3)  Offered in current or future terms
Random variables, central limit theorem; distributions of standard statistics; Markov chains, continuous and discontinuous stochastic processes. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 464 [C-] or MTH 564 [C-] and /or instructor approval required.

Top MTH 467 ACTUARIAL MATHEMATICS (3)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 463 [C-] or MTH 563 [C-] or ST 421 [C-] and /or instructor approval required.

Top MTH 480 SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
Systems of two first-order differential equations, phase portraits, linearization and the stability of equilibria, conservative systems, reversible systems, limit cycles and the Poincare-Bendixson 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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: (MTH 256 [C-] or MTH 256H [C-] ) and MTH 341 [C-]

Top MTH 481 APPLIED ORDINARY DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
Linear and nonlinear systems of ordinary differential equations, elementary stability theory, higher order equations, boundary value problems, series solution of ordinary differential equations. All courses used to satisfy MTH prerequisites must be completed with a C- or better. PREREQS: (MTH 256 [C-] or MTH 256H [C-] ) and ( ( (MTH 253 [C-] or MTH 253H [C-] ) and MTH 341 [C-] ) or (MTH 306 [C-] or MTH 306H [C-] ) )

Top MTH 482 APPLIED PARTIAL DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
Partial differential equations, Bessel's and Legendre's equations, Fourier analysis, separation of variables, transform methods. All courses used to satisfy MTH prerequisites must be completed with a C- or better. PREREQS: MTH 480 [C-] or MTH 481 [C-] or MTH 581 [C-] and /or instructor approval required.

Top MTH 483 COMPLEX VARIABLES (3)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with a C- or better. PREREQS: (MTH 256 [C-] or MTH 256H [C-] ) and (MTH 253 [C-] or MTH 306 [C-] or MTH 306H [C-] )

Top MTH 490 INTENSIVE SUMMER RESEARCH IN MATHEMATICS (12)  Offered in current or future terms
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).

Top MTH 491 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 341 [C-]

Top MTH 492 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)  Offered in current or future terms
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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 491 [C-] or MTH 591 [C-]

Top MTH 493 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)  Offered in current or future terms
Geometric transformations as real, complex, and matrix functions, invariants and genealogy of geometric transformations, extensions to transformations of the sphere and of three-dimensional 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. All courses used to satisfy MTH prerequisites must be completed with C- or better. PREREQS: MTH 492 [C-] or MTH 592 [C-]

Top MTH 499 SPECIAL TOPICS (0-16)  Offered in current or future terms
This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.



 
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