# Course Descriptions

**MTH 060 Preliminaries to Algebra (4)**

Provides pre-algebraic preparation with a focus on algebraic concepts and processes. Provides a solid background in signed numbers, manipulation of elementary algebraic expressions and equation solving. Applications, graphs, functions, formulas, and proper mathematical notation are emphasized throughout the course. Describes concepts using verbal, numerical, graphic, and symbolic forms. Credits earned apply for enrollment (eligibility) but do not apply toward a degree; satisfies no university or college requirement. Additional fee applies.

**MTH 070** **Introductory Algebra (4)**

Basics of algebra, including arithmetic of signed numbers, order of operations, problem solving; linear equations verbally, numerically, graphically and symbolically; linear modeling, regression, inequalities, and systems; and an introduction to functions. Explores topics using a graphing 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.

**MTH 095** **Intermediate Algebra (4)**

Arithmetic of polynomials; quadratic equations verbally, numerically, graphically and symbolically; problem solving, factoring techniques, graphing linear, exponential, radical, and quadratic functions; and solving rational, and radical 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**** Math in Society (4) ****
**Use of mathematical problem-solving activities from real-world situations designed to convey the application of mathematics. Emphasis on basic probability and statistics, formulas related to personal finance and methods of problem-solving. Completion of this course does not serve as a prerequisite for any other mathematics course. Three hours lecture plus two hours lab.

Prerequisite: none

**MTH 110 Applied College Mathematics (4)
**Study of rates, proportions and percent in applications; investigation into various types of data and ways to describe, represent and analyze data; and study of polynomial, exponential, logarithmic and power families of functions for use in modeling real-world data. Prerequisite: none

**MTH 111**** College Algebra (4)
**Study of linear, polynomial, rational, exponential, logarithmic, and power families of functions; representation of these functions symbolically, numerically, graphically, and verbally; develop regression and modeling for these function families; use of inverse functions symbolically, numerically, graphically, and verbally; and a rudimentary study of complex numbers. 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 a 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). 3 hours of lecture plus 2 hours of lab. Prerequisite: MTH 212 with a grade of C- or better. Does not apply toward a math major.

**MTH 231**** Elements of Discrete Mathematics I (3)
**Topics include sets, set operations, elementary symbolic logic, proof techniques, and study of polynomial, rational, and power functions. Does not apply toward a math major/minor.

**MTH 232**** Elements of Discrete Mathematics II (3)
**Topics include study of exponential, logarithmic, and discrete functions, analysis of algorithms, sequences and strings, enumeration, matrix algebra and systems of linear equations. Does not apply toward a math major/minor. Prerequisite: MTH 231 with a grade of C- or better.

**MTH 241**** Calculus for Social Science I (4)
**Differential calculus with emphasis on applications and model building in business and social science. Prerequisite: MTH 111 with a grade of C- or better. This course does not apply to a math major/minor. (Not offered regularly)

** MTH 242 Calculus for Social Science II (4)
**Integral and multivariate calculus with emphasis on applications and model building in business and social science. Prerequisite: MTH 241 with a grade of C- or better. This course does not apply to a math major/minor. (Not offered regularly)

**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 095 with a grade of C- or better, or satisfactory score on WOU’s placement exam.

**MTH 251**** Calculus I (4)
**Differential calculus of functions of a single variable, including transcendental functions. Prerequisite: MTH 112 with a grade of C- or better, or satisfactory score on WOU’s math placement test.

**MTH 252**** Calculus II (4)
**Integral calculus of functions of a single variable, with applications. The Fundamental Theorem of Calculus. Prerequisite: MTH 251 with a grade of C- or better.

**MTH 253**** Calculus III: Sequences and Series (4)
**Convergence and divergence of sequences, L’Hopital’s rule, infinite series, convergence tests, Taylor’s Theorem with remainder, power series, binomial series, applications. Prerequisite: MTH 252 with grade of C- or better.

**MTH 254**** Multivariate Calculus (4)
**Elementary vector algebra. Curves in space. Differential and integral calculus of functions of several variables and applications. 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. MTH 341 and at least one of the following: MTH 337, MTH 346, MTH 355, or MTH 441 with a grade of C- or better. (MTH 344 is strongly recommended.)

**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. 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. (Not offered regularly)

**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 252 with grade of C- or better

**MTH 337**** Geometry (4)
**Rigorous treatment of geometry with topics selected from Euclidean, non-Euclidean, spherical, analytic, or transformational geometry. Prerequisite: MTH 280 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: MTH 280 with grade of C- or better (MTH 280 can be taken concurrently)

**MTH 344**** Group Theory (4)
**An introduction to the theory of groups. Lagrange’s Theorem, normal subgroups, homomorphisms, the isomorphism theorems. Prerequisite: MTH 341 and at least one of MTH 337, MTH 346, MTH 355, or MTH 441 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**** Applied Discrete Mathematics (4)
**Topics include recurrence relations, graph theory, network models, and combinatorial circuits. Prerequisite: MTH 232 or MTH 252 with a grade of C or better.

**MTH 355**** Discrete Mathematics (4)
** Sets, relations, functions, enumeration, mathematical induction, graph theory. Prerequisite: MTH 280 with grade of C- or better.

**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 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 252 with grade of C- or better. Recommended: MTH 253 or MTH 254.

**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. Prerequisite: MTH 213 with a grade of C- or better in MTH 211, 212 and 213 or consent of instructor. Does not apply toward math major/minor. (Not offered regularly)

**MTH 392**** College Algebra for Elementary and Middle School 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 212 with grade of C- or better in MTH 211, 212

**MTH 393**** Probability and Statistics for Elementary and Middle School 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 212 with a grade of C- or better in MTH 211, 212.

**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 will be used to gain an understanding of the underlying mathematics and an appreciation of the utility and value of mathematics. Prerequisite: MTH 213 with a grade of C- or better in Math 211, 212 and 213. (Not offered regularly)

**MTH 396**** Elementary Problem Solving (3)
**Mathematical problem solving, techniques and materials helpful in improving student problem solving abilities, mentoring of elementary and middle school students 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 MTH 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. Prerequisite: MTH 341, 337, or consent of instructor. Does not apply to a math major/minor. (Not offered regularly)

**MTH 398**** Discrete Mathematics for Elementary and Middle School 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 213 with a grade of C- or better in MTH 211, 212 and 213.

**MTH 401 Introduction to Senior Project (1**)

Terms to be arranged during final year of study. Eligible for the RP grade option.

**MTH 402/502 Independent Study (1-3)
**Terms and hours to be arranged; may be repeated for credit.

**MTH 403**** Senior Project I (4)
**Terms to be arranged during final year of study. Eligible for the RP grade option. Prerequisite: MTH 401 with a grade of C- or better

**MTH 404 Senior Project II (3)
**Continuation of MTH 403. Eligible for the RP grade option.

**MTH 409/509 Practicum; Work Experience; Internship (1 – 6)
**Terms and hours to be arranged.

**MTH 410/510**** Special Topics: Analysis (4)
**Topics in analysis for advanced undergraduate students. Students enrolled in MTH 510 will be expected to complete a graduate project. Prerequisite: Consent of instructor

**MTH 411**** Mathematics Education Capstone Experience I (2)
**Terms to be arranged before entering the Education Program. May be taken concurrently with MTH 412. (Typically a by arrangement course)

**MTH 412**** Mathematics Education Capstone Experience II (2)
**Terms to be arranged before entering the Education program. May be taken concurrently with MTH 411. (Typically a by arrangement course)

**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 expansion of analytic functions. Prerequisite: MTH 344 with a grade of C- or better, or consent of instructor.

**MTH 420/520**** Special Topics: Applied Mathematics (4)
**Topics in applied mathematics for advanced 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 (4)
**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 440/540**** Special Topics: Algebra** **(4)
**Topics in modern algebra for advanced undergraduate students. Students enrolled in MTH 540 will be expected to complete a graduate project. 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 liner algebra, elements of approximation theory including data fitting. Theoretical foundations of numerical analysis. Prerequisite: MTH 311 and MTH 351. (Not offered regularly)

**MTH 460**** Special Topics: Probability and Statistics (3)
**Topics in probability and statistics for advanced undergraduate students. Prerequisite: Consent of instructor. (Not offered regularly)

**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 481 Research (1-12)**

Terms and hours to be arranged. May be repeated for credit.

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

The 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 and materials) to the NCTM standards with extensive use of group activities and hands-on models.

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

A 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. Applications to middle school mathematics. (Not offered regularly)

**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. Prerequisite: MTH 396 with a grade of C- or better or consent of instructor. Does not apply toward math major.

**MTH 493/593**** Experimental Probability & 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. Prerequisite: MTH 212 with a grade of C- or better or consent of instructor. Does not apply toward a math major/minor.

**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. Two hours of lecture plus two hours lab. Prerequisite: MTH 396 with a grade of C- or better, 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. Does not apply to math major/minor. Prerequisite: MTH 392 or MTH 111 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 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)**

In this course we will explore the topics of logical operators and sets, experimental vs. theoretical probability, the multiplication rule, permutations and combinations, and an introduction to graph theory. Prerequisite: MTH 213 with a grade of C- or better in MTH 211, 212 and 213, 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. (Not offered regularly)

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

Terms and hours to be arranged.

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

Terms and hours to be arranged

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

Terms and hours to be arranged.

**MTH 611 Counting and Whole Number Operations: K – 8 Learning and Teacher Practices (3)**

This course is a deep exploration into the teaching and learning of counting, whole numbers, and whole number operations. Investigation of the learning trajectory of number and operations throughout the K-8 curriculum, and instruction and activities based on effective standards for mathematical practice will be emphasized. Attention will also be given to deepening the candidates understanding of the mathematics and specialized content knowledge related to the teaching of number and operations as outlined in the Common Core State Standards for grades K-8.

**MTH 612 Fractions and Proportions: K – 8 Learning and Teacher Practices (3)
** This course is a deep exploration into the teaching and learning of number and operations with fractions and proportions. Investigation of the learning trajectory of fractions and proportions throughout the K-8 curriculum, and instruction and activities based on effective standards for mathematical practice will be emphasized. Attention will also be given to deepening the candidates understanding of the mathematics and specialized content knowledge related to the teaching of fractions and proportions as outlined in the Common Core State Standards for grades K-8.

**MTH 613 Geometry and Measurement: K – 8 Learning and Teacher Practices (3)**

This course is a deep exploration into the teaching and learning of geometry and measurement in grades K-8. Investigation of the learning trajectory of geometry and measurement throughout the K-8 curriculum, and instruction and activities based on effective standards for mathematical practice will be emphasized. Attention will also be given to deepening the candidates understanding of the mathematics and specialized content knowledge related to the teaching of geometry and measurement as outlined in the Common Core State Standards for grades K-8.

**MTH 614 Statistics and Probability: K – 8 Learning and Teacher Practices (3)**

This course is a deep exploration into the teaching and learning of elementary statistics and probability in grades K-8. Investigation of the learning trajectory of elementary statistics and probability throughout the K-8 curriculum, and instruction and activities based on effective standards for mathematical practice will be emphasized. Attention will also be given to deepening the candidates understanding of the mathematics and specialized content knowledge related to the teaching of statistics and probability as outlined in the Common Core State Standards for grades K-8.

**MTH 615 Patterns and Algebraic Thinking: K – 8 Learning and Teacher Practices (3)**

This course is a deep exploration into the teaching and learning of patterns and algebraic thinking in grades K-8. Investigation of the learning trajectory of patterns and algebraic thinking throughout the K-8 curriculum, and instruction and activities based on effective standards for mathematical practice will be emphasized. Attention will also be given to deepening the candidates understanding of the mathematics and specialized content knowledge related to the teaching of algebraic thinking as outlined in the Common Core State Standards for grades K-8.

**MTH 616 Algebra and Functions: K – 8 Learning and Teacher Practices (3)**

This course is a deep exploration into the teaching and learning of algebraic thinking with an emphasis on functions in grades K-8. Investigation of the learning trajectory of algebra and functions throughout the K-8 curriculum, and instruction and activities based on effective standards for mathematical practice will be emphasized. Attention will also be given to deepening the candidates understanding of the mathematics and specialized content knowledge related to the teaching of algebra and functions as outlined in the Common Core State Standards for grades K-8.

**MTH 621 Number and Operations for K – 8 Teachers (3)**

Exploring and understanding the foundations and properties of arithmetic operations, place value, number comparisons and equivalences. Math 095 (with grade C- or better, satisfied by B.S. or AAOT), appropriate placement on the Math Assessment Exam

**MTH 622 Measurement and Data for K – 8 Teachers**

Exploring and understanding measurement (length, area and volume) and the foundations of data collection and display.Math 095 (with grade C- or better, satisfied by B.S. or AAOT), appropriate placement on the Math Assessment Exam

**MTH 623 Geometry for K – 8 Teachers**

Exploring and understanding the structure and composition of two-dimensional and three-dimensional geometry. Math 095 (with grade C- or better, satisfied by B.S. or AAOT), appropriate placement on the Math Assessment Exam

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

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