Mathematics Course Descriptions

**MTH 067 Math Prep A (2)**

Computer based self-paced course, offered under the guided instruction of a Mathematics instructor. Students will focus on studying the mathematical topics they need to place into a higher level mathematics course. Offered weeks 1 - 5.

**MTH 068 Math Prep B (2)**

Computer based self-paced course, offered under the guided instruction of a Mathematics instructor. Students will focus on studying the mathematical topics they need to place into a higher level mathematics course. Offered weeks 6 - 10.

**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**** Introduction
to Contemporary Mathematics
(4)
**Use of mathematical problem
solving activities from real
world situations designed to
convey the application on mathematics.
Extensive use of computer and
graphics calculator required.
The class is intended only for
those students obtaining a BA
degree.

**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. Prerequisite: MTH 95 or higher with a grade of C- or better, or satisfactory score on WOU's math placement test.

**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 111 with minimum grade of C-, or MTH 112 with minimum grade of C-, or MTH 251 with minimum grade of C-, 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 a 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 a 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 344 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. 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.
Prerequisite: MTH 253 or MTH 254 with
grade of C- or better or consent
of instructor.

**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)
**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
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 253 or MTH 254 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 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, 2cm. Cubes, geoboards,
and multi-base blocks. Three
lectures, one laboratory. 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 213 with grade of C- or better in MTH 211, 212, 213.

**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 213 with a grade of C- or better in MTH 211, 212 and 21.

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

**MTH
403**** Senior Project
I (2)
**Terms to be arranged during final year of
study. Eligible for the RP grade option.

**MTH
404 Senior Project II (2)
**Continuation of MTH 403. Eligible for the RP
grade option.

**MTH
407/507 Seminar (1-6)
**Terms and hours to be arranged; may be repeated for credit.

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

**MTH
410**** Special
Topics: Analysis (3)
**Topics in analysis for advanced
undergraduate students. Prerequisite: MTH 312 with
grade of C- or better.

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

**MTH 412**** Capstone Experience for Mathematics Education (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**** Special Topics: Applied Mathematics
(3)
**Topics in applied mathematics
for undergraduate students.

**MTH
430**** Special
Topics: Geometry (3)
**Topics in geometry for advanced
undergraduate students. Prerequisite: Consent of
instructor.

**MTH
440**** Special Topics:
Algebra** **(3)
**Topics in modern algebra
for advanced undergraduate students.
Prerequisite: Consent of instructor.

**MTH
441**** Linear Algebra II (4)
**Complex vector spaces, linear
transformations, canonical forms,
the spectral theorem and eigenvalue
problems, applications. 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 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 it's 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 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 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 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

Mathematics Department **(503) 838-8465** | or **e-mail:** pricesl@wou.edu