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**Mathematics**

The department offers two calculus sequences to meet students’ needs. MTH 251, 252 is the standard sequence recommended to most students in the physical sciences and mathematics. MTH 241, 242 is designed to serve the mathematical needs of students in the business, managerial and social sciences. The choice between these two sequences is an important one; the choice of MTH 241, 242 effectively closes the door to most advanced mathematics courses.

**MTH 070 Introductory Algebra**

Linear equations, linear systems, linear inequalities, and quadratic equations verbally, numerically, graphically and symbolically. Explores topics using a graphic calculator as well as traditional approaches. Credits earned apply for enrollment (eligibility) but do not apply toward a degree; satisfies no university or college requirement. Additional fee applies.

**MTH 095 Intermediate Algebra** (4)

Basics of algebra, including arithmetic of signed numbers, order of operations, arithmetic of polynomials, linear equations, problem solving, factoring techniques, graphing lines, exponents, radicals, and quadratic equations. Credits earned apply for enrollment (eligibility) but do not apply toward a degree; satisfies no university or college requirement. Additional fee applies. Prerequisite: Math 070 with a grade of C- or better, or satisfactory score on WOU’s math placement test

**MTH 105 Introduction to Contemporary Mathematics** (4)

Use of mathematical problem solving activities from real world situations designed to convey the application of mathematics. Extensive use of computer and graphics calculator required. The class is intended only for those students obtaining a B.A. degree.

**MTH 111 College Algebra** (4)

Polynomial equations and inequalities, functions and graphs, inverse functions, rational functions, exponential and logarithmic functions. Prerequisite: MTH 095 with grade of C- or better, or satisfactory score on WOU’s math placement test

**MTH 112 Elementary Functions** (4)

Triangle trigonometry, trigonometric equations and identities, circular functions and graphs, complex numbers, polar coordinates. Prerequisite: MTH 111 with grade of C- or better, or satisfactory score on WOU’s math placement test

**MTH 199 Special Studies: Mathematics** (1-6)

**MTH 211 Foundations of Elementary Mathematics I** (4)

Intended for prospective elementary or middle school teachers. Introduction to problem solving, set theory, whole number operations, number theory, and integer operations. Three hours lecture plus two hours lab. Does not apply toward a math major/minor. Prerequisite: MTH 095 with grade of C- or better, or satisfactory score on WOU’s math placement test

**MTH 212 Foundations of Elementary Mathematics II** (4)

Intended for prospective elementary or middle school teachers. Operations with fractions and decimals, percents, ratio and proportion, real numbers. Introduction to probability and statistics. Three hours lecture plus two hours lab. Does not apply toward a math major/minor. Prerequisite: MTH 211 with a grade of C- or better

**MTH 213 Foundations of Elementary Mathematics III** (4)

Intended for prospective elementary or middle school teachers. Introduction to geometric figures, congruence and similarity, measurement (area, perimeter, volume and surface area). Three hours lecture plus two hours lab. Does not apply toward a math major/minor. Prerequisite: MTH 212 with a grade of C- or better

**MTH 231 Elements of Discrete Mathematics** (3)

Includes sets, set operations, sequences, elementary symbolic logic, induction, division in integers, matrices, functions, order of growth, relations. Does not apply toward a math major/minor. Prerequisite: MTH 111 with grade of C- or better, or satisfactory score on WOU’s math placement test

**MTH 241 Calculus for Social Science I **(4)

Differential calculus with emphasis on applications and model building in business and social science. Does not apply toward a math major/minor. Prerequisite: MTH 111 with grade of C- or better

**MTH 242 Calculus for Social Sciences II** (4)

Integral and multivariate calculus with emphasis on applications and model building in business and social science. Does not apply toward a math major/minor. Prerequisite: MTH 241 with grade of C- or better

**MTH 243 Introduction to Probability and Statistics** (4)

Descriptive statistics, discrete and continuous probability models including binomial and normal distributions, sampling distributions; hypothesis testing, point and interval estimation. Does not apply toward a math major/minor. Prerequisite: MTH 111 with grade of C- or better, or satisfactory score on WOU’s math placement test

**MTH 251 Calculus I** (5)

Differential calculus of functions of a single variable, including transcendental functions. Prerequisite: MTH 112 with grade of C- or better, or satisfactory score on WOU’s math placement test

**MTH 252 Calculus II** (5)

Integral calculus of functions of a single variable. The Fundamental Theorem of Calculus.

Prerequisite: MTH 251 with grade of C- or better

**MTH 253 Calculus III: Sequences and Series** (3)

Convergence and divergence of sequences, L’Hopital’s rule, improper integrals, infinite series, convergence tests, Taylor’s Theorem with remainder, power series. Prerequisite: MTH 252 with grade of C- or better

**MTH 254 Multivariate Calculus** (5)

Elementary vector algebra. Curves in space. Differential and integral calculus of functions of several variables and applications. Line integrals, Green’s Theorem. Prerequisite:
MTH 252 with grade of C- or better

**MTH 280 Introduction to Proof** (4)

An introduction to basic proof strategies and elementary logic. Elementary set and function theory. Prerequisite: MTH 252 with grade of C- or better

**MTH 311 Advanced Calculus I **(4)

A rigorous introduction to analysis. The topology of Euclidean spaces. Completeness, compactness. The Bolzano-Weierstrass Theorem. Limits of sequences and functions. Continuity, uniform continuity. Uniform convergence.
Prerequisites: MTH 253, 254, and 280 with grade of C- or better

**MTH 312 Advanced Calculus II** (4)

A rigorous introduction to differential and integral analysis of functions of one variable. The Mean Value Theorem, Taylor’s Theorem, the Riemann integral, and the Fundamental Theorem of Calculus. Prerequisite: MTH 311 with grade of C- or better

**MTH 313 Advanced Calculus III** (4)

A rigorous treatment of the differential and integral calculus of functions of several variables. The Inverse Function Theorem, the Implicit Function Theorem, Lagrange’s method of constrained optimization. Representation of functions by infinite series, power series and integrals. Prerequisite: MTH 312 with grade of C- or better

**MTH 314 Differential Equations** (4)

Introduction to methods of solutions of first and second order differential equations. Linear and nonlinear equations, series solutions, applications. Prerequisites: MTH 253 and 254 with grade of C- or better

**MTH 337 Geometry** (4)

Selected topics from advanced plane or solid Euclidean, analytic, transformational, spherical geometry. Prerequisite: MTH 254 with grade of C- or better; recommended: MTH 280

**MTH 338 Axiomatic Geometry** (4)

A formal development of Euclidean and non-Euclidean geometry from axioms. History of geometry. Prerequisites: MTH 280 and either MTH 341 or MTH 337 with grade of C- or better

**MTH 341 Linear Algebra** I (4)

Vector algebra and geometry of 3-space, systems of linear equations, Gaussian elimination, real vector spaces, determinants, linear transformations. Prerequisite: concurrent enrollment in MTH 254; recommended: MTH 280

**MTH 344 Group Theory** (4)

An introduction to the theory of groups. Lagrange’s Theorem, normal subgroups, homomorphisms and the isomorphism theorems. Prerequisites: MTH 280 and MTH 341 with grade of C- or better

**MTH 345 Ring Theory** (4)

An introduction to the theory of rings and fields. Prerequisite: MTH 344 with grade of C- or better

**MTH 346 Number Theory** (4)

Properties of integers. The division and Euclidean algorithms, Diophantine equations, prime numbers, congruencies and residues. Prerequisite: MTH 280 with grade of C- or better

**MTH 351 Introduction to Numerical Analysis** (4)

Computer representation of numbers, error analysis, root finding, interpolation, approximation of functions, numerical integration and differentiation. Prerequisite: MTH 341 with grade of C- or better

**MTH 354 Discrete Mathematics for Computer Science** (3)

Enumeration relations, digraphs, trees, graph theory, and related topics for computer science students. Does not apply toward a math major/minor. Prerequisite: MTH 231

**MTH 355 Discrete Mathematics** (4)

Sets, relations, functions, enumeration, mathematical induction, graph theory. Prerequisite: MTH 253 with grade of C- or better; recommended: MTH 280

**MTH 358 Mathematical Modeling** (4)

Construction, analysis, and interpretation of a variety of mathematical models that arise from real-world problems. Prerequisite: MTH 254 and MTH 341 with a grade of C- or better

**MTH 363 Operations Research** (4)

Optimization of functions with linear constraints, convex sets, the simplex method and applications, duality; two person matrix games.
Prerequisite: MTH 341 with grade of C- or better

**MTH 365 Mathematical Probability** (4)

Probability theory developed through moment generating functions. Random variables, classical probability distributions. Prerequisite: MTH 253 or MTH 254 with grade of C- or better

**MTH 366 Mathematical Statistics** (4)

Theory of point and interval estimation, hypothesis and significance testing. Prerequisite: MTH 365 with grade of C- or better

**MTH 391 Manipulatives in Mathematics** (3)

Using concrete models to teach mathematics. Learning theory from concrete to abstract. Models include Cuisenaire rods, bean sticks, 2 cm. cubes, geoboards, and multi-base blocks. Two hours of lecture plus two hours of lab. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better in MTH 211, 212 and 213 or consent of instructor

**MTH 392 College Algebra for Elementary Teachers** (3)

Enhancement of algebraic skills via problem solving and the visual representation and use of algebraic methods. Integer arrays, algebraic patterns, linear equations, quadratic equations, and graphing. Two hours of lecture plus two hours of lab. Does not apply toward a math major/minor. Prerequisite: MTH 213 with grade of C- or better in MTH 211, 212, 213

**MTH 393 Probability and Statistics for Elementary Teachers** (3)

Using basic elements of probability and statistics to solve problems involving the organization, description and interpretation of data. Concrete application will be explored. Two hours of lecture plus two hours of lab. Students may not take both MTH 393 and MTH 493 for their undergraduate program. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better in MTH 211, 212 and 213

**MTH 394 Introduction to Geometry for Elementary Teachers** (3)

Examination of intuitive geometry including construction, basic Euclidean geometry, proof, and measure. Two hours of lecture plus two hours of lab. Students may not take both MTH 394 and MTH 494 for their undergraduate program. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better in MTH 211, 212 and 213

**MTH 395 Elementary Integrated Mathematics** (3)

The study of computational skills, geometry, probability and statistics, data collection, and number theory in applied problem solving. Extensive use of group activities, technology, and real-world applications are used to gain an understanding of the underlying mathematics and an appreciation of the utility and value of mathematics. Two hours of lecture plus two hours of lab. Does not apply toward a math major/minor. Prerequisite: MTH 396 with a grade of C- or better or consent of instructor

**MTH 396 Elementary Problem Solving** (3)

Mathematical problem solving, techniques and materials helpful in improving student problem solving abilities, student mentoring in problem solving processes. Two hours lecture plus two hours lab. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better in Math 211, 212 and 213

**MTH 397 Secondary Problem Solving** (3)

Techniques for posing and solving mathematical problems. Critical analysis of student solutions. Intended for secondary mathematics teachers. Does not apply toward a math major/minor. Prerequisites: MTH 341, 337

**MTH 398 Discrete Mathematics for Elementary Teachers** (3)

Explores topics in discrete mathematics including set theory, enumeration and graph theory. Techniques in enumeration include the multiplication rule, combinations and permutations. Topics in graph theory include coloring, the traveling salesman problem and spanning trees. Two hours of lecture plus two hours lab. Prerequisites: MTH 211, 212 and 213 with a grade of C- or better

**MTH 401 Research** (1-9)

Terms and hours to be arranged.

**MTH 402 Independent Study** (1-3)

Terms and hours to be arranged.

**MTH 403 Senior Project** (1-4)

Terms to be arranged during final year of study.

**MTH 404 Work Experience; Internship** (1-9)

Terms and hours to be arranged.

**MTH 405 Reading and Conference** (1-6)

Terms and hours to be arranged.

**MTH 406 Special Problems/Projects** (1-3)

Terms and hours to be arranged.

**MTH 407/507 Seminar** (1-3)

Terms and hours to be arranged.

**MTH 408 Workshop** (1-9)

Terms and hours to be arranged.

**MTH 409 Practicum** (1-4)

Terms and hours to be arranged.

**MTH 410/510 Special Topics: Analysis** (3)

Topics in analysis for advanced undergraduate students. Students enrolled in MTH 510 will be expected to complete a graduate project.
Prerequisite: MTH 312 with grade of C- or better

**MTH 411 Mathematics Education Capstone** (4)

Terms to be arranged before entering the Education Program.

**MTH 416 Complex Analysis** (4)

The analysis of functions of a single complex variable. Conformal mappings, Cauchy’s Theorem, Cauchy’s Integral Formula, power series expansions of analytic functions. Prerequisite: MTH 312 with a grade of C- or better

**MTH 420/520 Special Topics: Applied Mathematics** (3)

Topics in applied mathematics for undergraduate students. Students enrolled in MTH 520 will be expected to complete a graduate project. Prerequisite: consent of instructor

**MTH 430/530 Special Topics: Geometry** (3)

Topics in geometry for advanced undergraduate students. Students enrolled in MTH 530 will be expected to complete a graduate project.
Prerequisite: consent of instructor

**MTH 440 Special Topics: Algebra** (3)

Topics in modern algebra for advanced undergraduate students. Prerequisite: consent of instructor

**MTH 441/541 Linear Algebra II** (4)

Complex vector spaces, linear transformations, canonical forms, the spectral theorem and eigenvalue problems, applications. Students enrolled in MTH 541 will be expected to complete a graduate project. Prerequisite: MTH 341 with a grade of C- or better

**MTH 451 Numerical Analysis** (4)

Introduction to numerical linear algebra, elements of approximation theory including data fitting. Theoretical foundations of numerical analysis. Prerequisites: MTH 311, 351 with a grade of C- or better

**MTH 460 Special Topics: Probability and Statistics** (3)

Topics in probability and statistics for advanced undergraduate students. Prerequisite: consent of instructor

**MTH 472 History of Mathematics** (4)

The history of mathematics from ancient to modern times. The effect of mathematics on the development of science. The interaction of mathematics with other fields of human endeavor such as philosophy, arts and social values. Prerequisite: consent of instructor

**MTH 489/589 Algebraic Structures for Middle School Teachers** (3)

Study of integers and algebraic skills; solving linear and quadratic equations, inequalities, functions, graphing and complex numbers. Connection of visual methods (using Math in the Mind’s Eye curriculum) to the NCTM standards with extensive use of group activities and hands-on models. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better, or consent of instructor

**MTH 491/591 Historical Topics In Mathematics for Middle School Teachers** (3)

Survey of the historical development of topics In mathematics from ancient to modern times, with special emphasis on topics in arithmetic, algebra and informal geometry. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better, or consent of instructor

**MTH 492/592 Abstract Algebra for Middle School Teachers** (3)

An introduction to abstract mathematics as a structured mathematical systems. This course will explore number sets and properties, and beginning group theory with concrete applications for the elementary and middle school classroom. Two hours of lecture plus two hours of lab. Does not apply toward a math major/minor. Prerequisite: MTH 396 with a grade of C- or better, or consent of instructor

**MTH 493/593 Experimental Probability and Statistics for Middle School Teachers **(3)

The study of data collection and hypothesis testing through laboratory experiments, simulations and applications. The use of technology will be an important part of the data collection and analysis. Students may not take both MTH 393 and MTH 493 for their undergraduate program. Does not apply toward a math major/minor. Prerequisite: MTH 212 with a grade of C- or better in MTH 211 and MTH 212, or consent of instructor

**MTH 494/594 Geometry for Middle School Teachers** (3)

Selected topics in informal geometry through the use of discovery and technology. The studies in how students learn geometry will be used in the development of geometric ideas. Students may not take both MTH 394 and MTH 494 for their undergraduate program. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better in MTH 211, 212 and 213 or consent of instructor

**MTH 495/595 Calculus Concepts for Middle School Teachers** (3)

An introduction to the theory of functions of one real variable, the derivative and its applications to optimization, integration theory and its applications to areas and volumes, the Fundamental Theorem of Calculus and infinite series. A hands-on approach with applications to the middle school curriculum. Two hours of lecture plus two hours of lab. Does not apply toward a math major/minor. Prerequisite: MTH 111 or MTH 392 with a grade of C- or better, or consent of instructor

**MTH 496/596 Problem Solving for Middle School Teachers** (3)

Assists middle school teachers in becoming better mathematical problem solvers. Focuses on general problem solving techniques, introduces techniques and materials helpful in improving student problem solving abilities and suggests ways to organize the curriculum to achieve problem solving goals. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better in MTH 211, 212 and 213, or consent of instructor

**MTH 497/597 Discrete Mathematics for Middle School Teachers** (3)

Explores topics of logical operators and sets, experimental vs theoretical probability, the multiplication rule, permutations and combinations, and an introduction to graph theory. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better, or consent of instructor

**MTH 499/599 Algebraic Problem Solving for Middle School Teachers** (3)

Assists middle school teachers in becoming better mathematical problem solvers. Focuses on algebraic problem solving techniques, introduces materials helpful in improving student problem solving abilities, and suggests ways to organize the curriculum to achieve problem solving goals. Does not apply toward a math major/minor. Prerequisite: MTH 213 with a grade of C- or better in MTH 211, 212 and 213, or consent of instructor

**MTH 601 Research** (1-9)

Terms and hours to be arranged.

**MTH 602 Independent Study** (1-3)

Terms and hours to be arranged.

**MTH 603 Thesis** (1-9)

Terms and hours to be arranged.

**MTH 604 Work Experience Internship** (1-9)

Terms and hours to be arranged.

**MTH 605 Reading and Conference** (1-6)

Terms and hours to be arranged.

**MTH 606 Special Problems/Projects** (1-3)

Terms and hours to be arranged.

**MTH 608 Workshop** (1-9)

Terms and hours to be arranged.

**MTH 609 Practicum** (1-4)

Terms and hours to be arranged.

**MTH 617 Complex Analysis** (3)

The analysis of functions of a single complex variable. Conformal mappings, Cauchy’s Theorem, Cauchy’s Integral Formula, power series expansion of analytic functions. Prerequisite: consent of instructor

**MTH 638 Transformational Geometry** (3)

A study of transformations of the plane. Classification of the plane isometrics. Crystallographic and frieze groups. Prerequisite: consent of instructor

**MTH 647 Abstract Algebra** (3)

Advanced group theory or ring and field theory. Prerequisite: consent of instructor

**MTH 652 Numerical Analysis** (3)

Introduction to numerical linear algebra, elements of approximation theory including data fitting. Theoretical foundations of numerical analysis. Prerequisite: consent of instructor

**MTH 673 History of Mathematics** (3)

The history of mathematics from ancient to modern times. The effect of mathematics on the development of science. The interaction of mathematics with other fields of human endeavor such as philosophy, arts and social values. Prerequisite: consent of instructor

**MTH 681 Foundations of Mathematics** (3)

Selected topics from: axiomatic systems, consistency, completeness, set theory, cardinality. Construction of number systems. Prerequisite: consent of instructor

**MTH 690 Advanced Topics: Mathematics Education** (3)

A study of selected topics in the teaching of mathematics. Prerequisite: consent of instructor

Contact

Office of the Registrar **ph: 503-838-8327; fax: 503-838-9696** | or **e-mail:** registrar@wou.edu