2007 - 2008 Catalog

All mathematics courses are designed to improve students’ abilities to think, analyze, and communicate, and, in particular, to use mathematics to express, define, and answer questions about the world. The bachelor’s degree program nurtures these abilities while building a solid base in mathematics—a combination highly valued by business, government, industry, and graduate programs in a variety of fields.

The department’s primary concern is the development of each student’s confidence in using mathematical ideas, approaches, and exposition. Key coursework hones the learner’s abilities to critically understand and use mathematics. One of the program goals is to make direct connections between mathematics and the contemporary environment.

Degrees

BA or BS in Mathematics
BA or BS in Mathematics with Honors in Mathematics

Co-Majors

Business-Mathematics
Mathematics-Computer Science

Minors

Mathematics
Mathematics Education

Accelerated Baccalaureate Degree Program

Mathematics majors may participate in the Accelerated Baccalaureate Degree Program.

Accelerated Baccalaureate Degree Program

Mathematics Placement Testing

To help students determine the mathematics courses that best meet their needs, the Mathematics Department uses a computerized placement test and encourages students to meet with a mathematics faculty member for individual advising. New students are required to take the mathematics placement test. Please contact the ACCESS Center to find out when upcoming placement testing sessions are scheduled.

Some students, however, may qualify for a transfer placement waiver. Students with prior college mathematics coursework should meet with the department chair to determine whether a waiver is appropriate.

The computer system checks prerequisites when processing a student’s request to register for a mathematics course. Students must have a C- or better in the prerequisite course or the appropriate SOU mathematics placement level to register. On rare occasions, a student may have a reasonable substitution for the stated prerequisite. In those situations, the student should see the department chair for clearance before trying to register for the course.

Curriculum for Nonmajors

The lower division curriculum offers a variety of choices for nonmajors. Consult your advisor or the Mathematics Department to select courses that match your background and goals. Possibilities include:

Liberal arts majors wanting a solid mathematics core should consider MTH 251, 252, 261, and 311.

Prospective elementary and middle school teachers should take MTH 211, 212, 213.

Physical science majors should consult their advisors and consider MTH 251, 252, 253, 261, 281, 321, 361, 421, and 461.

For breadth, others should consider MTH 105, 158, or 243; for more depth, consider MTH 111, 112, and 251, 252.

Majors in any discipline who would like substantial training in applied mathematics can choose from blocks of courses in applied mathematics (MTH 321, 421) and probability and statistics (MTH 361, 461).

Many upper division courses also serve nonmajors.

Prospective elementary, middle school, and high school teachers may select topics in mathematics education (MTH 481/581).

Enrichment Courses

All students are encouraged to take advantage of the available enrichment courses.

Mathematical Perspectives (MTH 290) presents mathematics as a way of thinking and a body of knowledge important to the development of civilization and the concerns of modern society.

The Mathematical Contest in Modeling is an opportunity for students with suitable backgrounds to compete in a nationwide competition. Teams of three students prepare several weeks in advance for the weekend contest. The contest involves writing up a solution to an open-ended problem to which mathematics may be applied.

Choosing a Major

Students who wish to major in mathematics should see the department chair to sign up for the major and be assigned an advisor for help with academic and career planning.

All majors take a common core of courses that includes two important coordinating courses: Mathematical Perspectives (MTH 290), which introduces prospective majors to the scope and role of mathematics in the world, and the Senior Colloquium (MTH 490), which helps graduating seniors integrate the diverse elements of their mathematics studies. Majors develop a common knowledge base and maturity in the study of mathematics, with topics courses providing senior-level studies in important areas of mathematics.

Transfer Students

Transfer students will have full junior standing in the mathematics major if they transfer in the following courses: an approved computer science language (such as Visual BASIC, C++, or Java), a full year of single-variable calculus, and one term of linear algebra. One term of lower division statistics is also recommended.

Requirements for the Major

1. Fulfill baccalaureate degree requirements as stated beginning on page 21.
   
   1. Students meeting the core curriculum requirements and the mathematics major requirements automatically meet the BS requirements.
      
   2. Students wishing to receive a BA should pay careful attention to the additional requirements listed on page 22.
      
2. Complete core curriculum requirements beginning on page 22 or, if qualified, the University Studies requirements for transfer students beginning on page 25. Mathematics majors meet the writing and research requirements by successfully completing three required courses: Mathematical Perspectives (MTH 290), Number Structures (MTH 311), and Senior Colloquium (MTH 490).
   
3. Complete the required courses specified below.
   
4. All courses required for the major must be taken for a grade. No more than two of the upper division requirements may be met with a grade below C-.
   
5. Complete the capstone.
   

Required Courses

Computer Science

(3–4 credits)

Must complete by the end of the sophomore year with a grade of C- or better. Select one course from:

Computer Science I (CS 200)	4
Computer Science II (CS 257)	4
Computer Applications in Chemistry (CH 371)	3
Computer Methods (PH 380/ENGR 373)	3

Lower Division Core Courses

(22 credits)

Calculus I, II, III, IV (MTH 251, 252, 253, and 281)	16
Linear Algebra (MTH 261)	4
Mathematical Perspectives (MTH 290)	2

Upper Division Sequences

(39–41 credits)

1. Foundations: Number Structures (MTH 311) and Geometry (MTH 411)	9
2. Analysis: Introduction to Real Analysis (MTH 331) and one term of Topics in Analysis (MTH 431)	8
3. Abstract Algebra: Introduction to Algebraic Systems (MTH 341) and one term of Topics in Abstract Algebra (MTH 441)	8
4. Probability and Statistics: Probability (MTH 361) and Statistics (MTH 461)	8
5a. Differential Equations (MTH 321) and one term of Topics in Applied Mathematics (MTH 421)	8

or

5b. Any two distinct topics of Topics in Middle School and High School Mathematics (MTH 481)

6

Capstone Experience

(4 credits)

The capstone project is completed by taking the Senior Colloquium (MTH 490) over three terms, usually the fall, winter, and spring terms prior to graduation. The Senior Colloquium allows students to draw on their mathematical background while investigating a topic not readily available in the curriculum. Students research the topic in conjunction with a faculty mentor. As part of the capstone, students produce a final paper and make an oral presentation to a general audience of faculty and mathematics students. One outstanding student is selected to present his or her capstone project at the School of Sciences Undergraduate Research Symposium.

Mathematics Honors Program

Graduation with honors in mathematics is attained by completing the department’s honors program. In their junior year, students must successfully petition the Honors Committee for admission to the honors program. Honors students work with a faculty mentor while independently studying an advanced mathematical topic and preparing an expository thesis (MTH 401 for 8 credits and MTH 403 for 4 credits). In addition, students must complete differential equations (MTH 321), as well as two topics from both abstract algebra (MTH 441) and analysis (MTH 431). Honors graduates must have a 3.25 GPA in mathematics and a 3.00 overall GPA. Students completing the honors program may have their projects accepted in lieu of the Senior Colloquium (MTH 490).

Minors

Mathematics

(26–28 credits) ¹

Calculus I, II (MTH 251, 252)	8
Linear Algebra (MTH 261)	4
Mathematical Perspectives (MTH 290)	2
Upper division mathematics2	12–14

Mathematics Education

(27 credits) ¹

Fundamentals of Elementary Mathematics I, II, III (MTH 211, 212, 213)3	12
Any five distinct MTH 481 Topics in Middle School and High School Mathematics	15

--- Footnotes ---

1	Only one of the upper division requirements may be met with a grade below C-.
2	Must include three upper division courses of 4 credits or more. Students may substitute two MTH 481 courses for one of those courses.
3	Students who have taken at least one of the following courses—MTH 251, 252, 253, 261, or 281—may apply for the alternative 12-credit package: 1) substitute a MTH 409 Practicum in which the student assists an instructor in planning and delivering a MTH 211, 212, or 213 course, and 2) additionally substitute one or two courses taken from MTH 251, 252, 253, 261, or 281.

Affiliations

The Mathematics Department is a member of the American Mathematics Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. These organizations are actively committed to advancing mathematics and maintaining the currency of college mathematics programs.

Facilities

The department is committed to using technology to enhance student learning. The Computing Services lab is equipped with software specific to mathematics coursework.

The Harry S. Kieval Memorial Mathematics Education Laboratory is well-stocked with materials available for use by regional educators, preprofessional education students, and students in mathematics education courses.

Located near faculty offices, the Mathematics Study Room provides a space where students may gather regularly to study and socialize. It is equipped with lockers, three computer stations, and a variety of other supplies.

Teacher Licensing

Students who would like to teach math at the middle school or high school level in Oregon public schools must complete specific course requirements in mathematics before applying for admission to the Master of Arts in Teaching (MAT) program at SOU. Interested students should consult the department chair regarding mathematics requirements and the assignment of an advisor and the School of Education regarding admission requirements for the MAT program.

Students must prepare in advance to increase their chances of acceptance into this competitive program. Practica, internships, and volunteer experiences working with children in the public schools are required prior to application to the MAT program.

Students who wish to teach mathematics at the high school level in Oregon public schools need an Advanced Mathematics Endorsement. The specific course requirements in mathematics are roughly equivalent to the mathematics major at SOU, with three 300-level courses and four 400-level courses. These courses should be completed before applying for admission to the MAT program at SOU. Contact the Mathematics Department chair to obtain the current course listing and a mathematics advisor. All SOU mathematics majors meet these requirements, provided they select the MTH 481 courses for their applied area.

Students who would like to teach mathematics at the middle school level in Oregon public schools should pursue a Basic Mathematics Endorsement. The specific course requirements in mathematics total 27 credits and comprise coursework applicable to both intermediate and middle school teaching. The elementary/middle school licensure requires 12 of these credits, plus an additional 15 credits to add the Basic Mathematics Endorsement. These courses should be completed before applying for admission to the MAT program. Students completing these courses as part of the undergraduate degree at SOU are eligible for a minor in mathematics education. Contact the Mathematics Department chair to obtain the current course listing and a mathematics advisor.

Mathematics Courses

See Course Prerequisites Policy

All math course prerequisites must be met with a grade of C- or better.

Lower Division Courses

MTH 60 Beginning Algebra

4 credits

Builds an understanding of the language of mathematics. Provides exercises in simplifying, graphing, and evaluating expressions involving fractions, negatives, exponents, and variables. Other concepts and topics include absolute value, scientific notation, simple interest, area, and volume. Introduces translation of textual statements into algebraic statements, as well as graphing and the creation of algebraic tables. Includes the use of a graphing calculator. Does not apply toward graduation requirements. Prerequisite: Appropriate SOU placement level.

MTH 65 Elementary Algebra

4 credits

Uses graphical, algebraic, and numeric methods to solve linear equations and inequalities in one and two variables. Applies mathematics to real-world settings. Includes the use of a graphing calculator. Does not apply toward graduation requirements. Prerequisite: MTH 60 or appropriate SOU placement level.

MTH 95 Intermediate Algebra

4 credits

Bridges courses that satisfy the Quantitative Reasoning University Studies requirement with courses leading up to the calculus track. Focuses on simplifying, evaluating, and solving quadratic equations. Other topics include rational expressions and equations and manipulation of expressions with exponents and square roots. Real-world applications include use of the vertical position formula and the Pythagorean Theorem. Includes the use of a graphing calculator. Does not apply toward graduation requirements. Prerequisite: MTH 65 or appropriate SOU placement level.

MTH 105 Contemporary Mathematics

4 credits

Surveys various practical areas of mathematics. Topics include logic, probability and statistics, finance, and dimensional analysis. Emphasizes real-world applications, critical thinking, and the effective communication of mathematical ideas. Approved for University Studies (Quantitative Reasoning). Prerequisite: MTH 95 or appropriate SOU placement level.

MTH 111 Precalculus I: College Algebra

4 credits

Develops skills in algebra and deductive thinking in the real-number setting. Uses algebraic and function concepts to solve problems and analyze applications. Topics include real number properties, absolute value, theory of equations, inequalities, graphs, polynomial and rational functions, and an introduction to complex numbers. Recommended as preparation for Precalculus II (MTH 112). Approved for University Studies (Quantitative Reasoning). Prerequisite: MTH 95 or appropriate SOU placement level.

MTH 112 Precalculus II: Elementary Functions

4 credits

Examines exponential, logarithmic, and trigonometric functions and their graphs and applications. Intended as preparation for Calculus I (MTH 251). Approved for University Studies (Quantitative Reasoning). Prerequisite: MTH 111 or appropriate SOU placement level.

MTH 158 Elementary Linear Mathematics with Applications

4 credits

Introduces analytic geometry, with an emphasis on linear functions of one or more variables and their graphs. Applications are drawn primarily from the social and management sciences. Topics include lines, planes, systems of linear equations, matrix algebra, and linear programming problems. Credit for MTH 158 is not given to students who have received credit for MTH 261. Approved for University Studies (Quantitative Reasoning). Prerequisite: MTH 95 or appropriate SOU placement level.

MTH 199 Special Studies

1 to 4 credits

MTH 209 Practicum

Credits to be arranged

MTH 211 Fundamentals of Elementary Mathematics I

4 credits

Introduces the theory of arithmetic for prospective teachers. Topics include set theory, numeration, place value, computational algorithms for whole numbers and integers, computational estimation, mental arithmetic, relations and functions, and number theory. Content is taught within a problem-solving framework using calculators and computers as aids. Three hours of lecture and three hours of laboratory. Students entering the next MAT cohort have enrollment priority over other registered and waitlisted students. Approved for University Studies (Quantitative Reasoning (met after completion of both MTH 211 and 212)). Prerequisite: MTH 95 or appropriate SOU placement level.

MTH 212 Fundamentals of Elementary Mathematics II

4 credits

Covers rational number arithmetic for prospective teachers. Topics include theory and modeling of fractions, decimals, and percentages; rational and irrational numbers; mental arithmetic and computational estimation; graphing linear and nonlinear functions; and probability and statistics. Content is taught within a problem-solving framework using calculators and computers as aids. Three hours of lecture and three hours of laboratory. Students entering the next MAT cohort have enrollment priority over other registered and waitlisted students. Approved for University Studies (Quantitative Reasoning (met after completion of both MTH 211 and 212)). Prerequisite: MTH 211.

MTH 213 Fundamentals of Elementary Mathematics III

4 credits

Covers informal geometry and measurement for prospective teachers. Topics include properties of two- and three-dimensional space, the metric system, measurement, estimation, perimeter, area, volume, surface area, congruence motions, similarity motions, and topological motions. Content is taught within a problem-solving framework using calculators and computers as aids. Three hours of lecture and three hours of laboratory. Students entering the next MAT cohort have enrollment priority over other registered and waitlisted students. Prerequisite: MTH 211.

MTH 235 Discrete Structures

4 credits

Introduces the mathematical structures fundamental to the study of computer science. Topics selected from sets, functions, combinatorics, statistics, coding theory, logic networks, and Boolean expressions. Prerequisite: MTH 251.

MTH 243 Elementary Statistics

4 credits

Emphasizes the basic concepts and techniques of probability, descriptive, and inferential statistics. Topics include describing the distribution of data graphically and numerically, standard scores, normal distribution, empirical rule, sampling distributions, confidence intervals, hypothesis testing of both one and two populations, and linear regression. Introduces appropriate technology to display and analyze data. Appropriate calculators are required. Approved for University Studies (Quantitative Reasoning). Prerequisite: MTH 95 or an appropriate SOU placement level.

MTH 244 Applied Inferential Statistics

4 credits

Presents an assortment of tools from inferential statistics with an emphasis on applications. Reviews the concepts of hypothesis testing and confidence intervals. Introduces probability distributions of test statistics for various inferential statistical problems. Includes Analysis of Categorical Data (Chi-Square Goodness of Fit Test), Analysis of Variance (ANOVA), Nonparametric Statistics, and a brief introduction to Multiple Linear Regression. Applies the concepts and procedures with appropriate software tools for data analysis. Prerequisite: MTH 243.

MTH 251 Calculus I

4 credits

Introduces limits, continuity, and differentiation. Applications include linear approximation, graphing techniques, and maximum/minimum problems. Students are introduced to writing precise mathematical arguments. Approved for University Studies (Quantitative Reasoning). Prerequisite: MTH 112 or appropriate SOU placement level.

MTH 252 Calculus II

4 credits

Introduces integration, developed as a limit of Riemann sums. Covers the first and second forms of the Fundamental Theorem of Calculus, techniques of integration, and numerical integration. Applications are selected from length, area, volume, work, and motion. Students are expected to understand and reproduce precise mathematical arguments. Prerequisite: MTH 251.

MTH 253 Calculus III

4 credits

Introduces differential equations, including separation of variables. Other topics include sequences and series, power series representations of functions, and improper integrals. Prerequisite: MTH 252.

MTH 261 Linear Algebra

4 credits

Provides the basic linear algebra necessary for multivariable calculus, differential equations, and abstract algebra. Develops skills for constructing rigorous mathematical proofs. Topics include finite dimensional vector spaces, matrices, linear transformations, and eigenvalue problems. Prerequisite: MTH 252.

MTH 281 Calculus IV

4 credits

Applies the concepts of limit, continuity, differentiability, and integrability to multivariate and vector-valued functions. Topics include the study of motion, partial derivatives, and multiple and line integrals. Prerequisites: MTH 252; MTH 261 or PH 221.

MTH 290 Mathematical Perspectives

2 credits

Seminar that presents mathematics as a way of thinking and a body of knowledge important to the development of civilizations. Explores a variety of mathematical topics and history through guest lectures, reading, writing, and student discussion. Prerequisite: MTH 252 (may be taken concurrently).

MTH 299 Special Studies

1 to 4 credits

Upper Division Courses

MTH 311 Number Structures

5 credits

Studies the essential features of the real number system and the organization of number systems in general. Stresses logical development, precise notation, and written exposition. Includes axiomatic developments, set and function theory, division algorithm, congruence, completeness, Archimedean Principle, denseness, and infinite sets. Prerequisites: MTH 261; WR 122 or USEM 103.

MTH 321 Differential Equations

4 credits

Introduces the theory and application of ordinary differential equations. Analyzes problems from the natural and physical sciences, with emphasis on finding and interpreting solutions. Topics selected from separable equations, linear equations, power series solutions, Laplace Transforms, and systems of linear equations. Prerequisite: MTH 253 or PH 371.

MTH 331 Introduction to Real Analysis

4 credits

Studies the basic analytic structure of real numbers. Topics include sequences; continuity; uniform continuity; properties of functions on closed, bounded sets; and an introduction to metric spaces. Prerequisites: MTH 253 and 311.

MTH 341 Introduction to Algebraic Systems

4 credits

Presents abstract groups to demonstrate the fundamental strategies used to study algebraic structures such as subsystems, morphisms, and quotient systems. Includes a brief overview of some alternative algebraic systems. Prerequisite: MTH 311.

MTH 361 Probability

4 credits

Covers the theory and applications of probability. Topics include laws of probability, Bayes theorem, principles of counting, combinatorics, random variables, discrete and continuous probability distributions, and expected values. MTH 243 recommended. Prerequisite: MTH 281.

MTH 399 Special Studies

1 to 4 credits

MTH 401/501 Research

1 to 4 credits

MTH 403/503 Thesis

1 to 4 credits

MTH 405/505 Reading and Conference

1 to 4 credits

MTH 407/507 Seminar

Credits to be arranged

MTH 409/509 Practicum

Credits to be arranged

MTH 411/511 Topics in Foundations and Geometry

4 credits each

The following and other topics are offered as needed. Repeat credit is offered for distinct topics.

Geometry. An axiomatic development of a variety of geometries. Prerequisite: MTH 311.

MTH 421/521 Topics in Applied Mathematics

4 credits each

The following and other topics are offered as needed. Repeat credit is offered for distinct topics.

Partial Differential Equations. Introduces diffusion, wave, and Laplace equations; separation of variables; and Fourier series. Prerequisites: MTH 281 and 321.

Optimization. Introduces linear programming and nonlinear optimization. Prerequisites: MTH 261; CS 200 or 257.

MTH 431/531 Topics in Analysis

4 credits each

The following and other topics are offered as needed. Repeat credit is offered for distinct topics.

Metric Spaces. Extends analytic concepts to general metric spaces and mappings. Includes metric topology, convergence, continuity, and compactness. Prerequisite: MTH 331.

Complex Analysis. Studies complex numbers, mappings, differentiation, and integration. Prerequisite: MTH 331.

Integration. Introduces Lebesque and Riemann integration.

Infinite Series. Extends the analysis of infinite series to series of functions. Topics include uniform convergence, power series, and trigonometric series. Prerequisites: MTH 253 and 331.

MTH 441/541 Topics in Abstract Algebra

4 credits each

The following and other topics are offered as needed. Repeat credit is offered for distinct topics.

Groups. Involves careful study of groups, including normal subgroups, group morphisms, isomorphism theorems, and the Sylow or the equivalent structure theorems. Prerequisite: MTH 341.

Rings. Involves careful study of rings, including integral domains, Euclidean domains, and other algebraically related structures. Uses quotient rings, ideals, and ring homomorphisms to establish the existence of solutions to certain polynomials. Prerequisite: MTH 341.

MTH 461/561 Topics in Probability and Statistics

4 credits each

The following and other topics are offered as needed. Repeat credit is offered for distinct topics.

Statistics. Explores the theory and applications of inferential statistical procedures. Topics include interval estimation and testing for means, variances, proportions, tests of independence and goodness-of-fit, linear regression and correlation, and nonparametric statistics. MTH 243 recommended. Prerequisite: MTH 361.

MTH 481/581 Topics in Middle School and High School Mathematics

3 to 5 credits eaach

The following and other topics are offered as needed. Repeat credit is offered for distinct topics.

Arithmetic and Algebraic Structures. Studies the real number system and its subsystems, which leads to the introduction of more general algebraic structures and their applications. Includes applications to middle school mathematics, high school general mathematics, and first-year algebra curriculum. Prerequisite: MTH 212 or 251.

Concepts of Calculus. Introduces students to the limit concept and its role in defining the derivative, the integral, and the finite series. Calculus background approved for middle school mathematics teachers. Prerequisites: MTH 212; MTH 213 or 251.

Experimental Probability and Statistics. Examines probability and statistics through lab experiments, simulations, and applications. Includes applications to middle school and high school general mathematics curricula. Prerequisite: MTH 212, 243, or 251.

Informal Geometry. Focuses on understanding the theory behind selected topics in the high school geometry curriculum. Attention is given to the informal background necessary for appreciation of formal development. Prerequisite: MTH 213 or 251.

Math and History: Connections. Explores interesting historical topics to introduce students to the background of important mathematical concepts. Includes applications for middle school and high school mathematics curricula. Prerequisite: MTH 212, 213, or 251.

Problem Solving. Introduces a variety of techniques for solving mathematical problems within the framework of Polya’s general strategy for problem solving. Problems are taken from many areas, including number theory, geometry, probability, combinatorics, and logic. Includes applications for middle school and high school mathematics curricula. Prerequisite: MTH 211 or 251.

MTH 490 Senior Colloquium

1 to 4 credits

A directed project organized around a theme that necessitates a synthesis of a variety of concepts in the undergraduate mathematics curriculum. Includes a major writing component. Prerequisites: Senior standing in the mathematics major, MTH 311, and completion of at least two of the upper division sequences required for the major.