2012-13 Catalog [ARCHIVED CATALOG]
Department of Mathematics
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Central 227
541-552-6141
Sherry Ettlich, Chair
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Associate Professor |
Assistant Professor |
Instructor |
Emeritus Faculty |
| Sherry Ettlich |
Lisa Ciasullo |
Francie Bostwick |
Jim Hatton |
John J. Engelhardt |
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Curtis Feist
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Irving Lubliner
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Larry Shrewsbury
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John D. Whitesitt
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Daniel Kim
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Brian Stonelake
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| Dusty E. Sabo |
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| Kemble Yates |
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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.
Mathematics Placement Testing
Prerequisites and Mathematics Placement Testing
The SOU 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 an appropriate SOU mathematics placement level to register. On rare occasions, a student may have a reasonable substitution for the stated prerequisite that is not recognized by the computer system. In those situations, the student should see the Mathematics Department Chair for clearance before trying to register for the course.
Placement Based on Transfer Coursework
Transfer coursework in mathematics is regularly reviewed and used for placement. Placement levels based on transfer coursework never expire. However, if several years have elapsed since completing the transfer course, students may need to review the material before continuing their studies. Students are encouraged to talk with a mathematics faculty member about options for refreshing prior coursework.
Placement Based on Testing
A variety of testing options are available. Students are encouraged to complete their first mathematics course during their first year at SOU. Waiting too long can be problematic since placement levels based on testing will expire two years from the date of the test.
• SOU offers an adaptive, computerized mathematics placement test. Testing is available in conjunction with registration and orientation activities throughout the year. Students may retake the placement test to improve their scores. Contact Academic Support Programs to find out when upcoming placement testing sessions are scheduled in Ashland or contact the Higher Education Center to see when testing is available in Medford.
• Students may be placed into entry-level courses based on recent SATM or ACTM test scores. This option will not place a student higher than Precalculus I (Mth 111). If a student has a strong mathematics background from high school, s/he is encouraged to take the SOU mathematics placement test to assure placement at the appropriate level.
• Recent placement test results from other accredited colleges and universities are also accepted, provided the Mathematics Department can interpret and apply those results to SOU’s offerings. Students interested in this option should arrange for the institution to send the Mathematics Department Chair notification of (1) the placement test used, (2) the date of the test, (3) the score(s) earned, and (4) where that institution would place the student based on his/her scores.
If there are questions about placement or testing options, the Mathematics Department encourages students to meet with a mathematics faculty member for individual advising.
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.
Students wanting a solid statistics core should consider MTH 243 and MTH 244 or the Statistics Minor .
Liberal arts majors wanting a solid mathematics core should consider MTH 251 , MTH 252 , MTH 261 , MTH 290 , and MTH 311 .
Prospective elementary, and middle school teachers should take MTH 211 , 212 , 213 .
Prospective elementary, middle school, and high school teachers who want to explore additional topics in mathematics education should consider MTH 481 and MTH 581 courses.
Physical science majors should consult their advisors and consider MTH 251 , 252 , 253 , 261 , 281 , 290 , 321 , 361 , 421 , and 461 .
For majors with no specific math requirement, recommendations include MTH 105 , 158 , or 243 . Students interested in exploring the basis of calculus should take MTH 111 , 112 , then 251 , 252 , and 290 .
Majors in any discipline who would like substantial training in applied mathematics can choose from blocks of courses in applied mathematics (MTH 321 , and 421 ) and probability and statistics (MTH 361 , and 461 ).
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 will have full junior standing in the mathematics major if they transfer in the following courses: an introductory statistics course, a full year of single-variable calculus, and one term of linear algebra.
Academic Support for Mathematics Students
Mathematics Tutoring Center
The Mathematics Department offers tutoring in the Hannon Library as part of the Learning Commons. The Mathematics Tutoring Center is a great place to work on mathematics homework. Tutors circulate among the students in the center, assisting students as questions arise.
Mathematics tutoring is free of charge to any student enrolled in an SOU mathematics course. Tutors are available weekdays, evenings and weekends during the academic year, and weekdays during the 8-week summer session. The tutoring schedule varies from term to term. See Academic Support Programs for the current term’s schedule.
Career Counseling
What do you do with a mathematics degree? What kind of jobs can you get? These questions an more can be answered in a one-on-one career counseling session. Sign up at the Mathematics Department Office.
Jobs for Mathematics Students
The Mathematics Department hires tutors and graders for a variety of mathematics courses. Students interested in tutoring should pick up an application from the reception desk in Academic Support Programs. Students interested in grading should pick up an application in the Mathematics Department Office. Students do not need to be mathematics majors, but should have a good mathematics background in the areas they wish to tutor or grade. Normally some coursework beyond the course(s) they will tutor or grade is expected.
In addition, Academic Support Programs provides a tutor-for-hire list for individuals interested in private tutors. Students and community members interested in advertising on this list should contact the Mathematics Department Office.
Affiliations
The Mathematics Department is a member of 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. The Mathematics Department is also a member of the National Council of Teachers of Mathematics, the Oregon Council of Teachers of Mathematics, and the Teachers of Teachers of Mathematics. These organizations are actively committed to the improvement of mathematics education in the schools.
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, pre-professional 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, printer, study tables, white boards, reference books, couch, refrigerator, microwave and a variety of other items.
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/or volunteer experiences working with students 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 an Advanced Mathematics Endorsement (described above) or a Basic Mathematics Endorsement. The specific course requirements for the Basic Mathematics Endorsement include 27 credits in mathematics and coursework applicable to both intermediate and middle school teaching. The elementary/middle school licensure requires 12 of these credits (MTH 211 , 212 , and 213 ). The SOU Basic Mathematics Endorsement requires an additional 15 credits (MTH 481 /581 courses). 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.
Program Requirements
Major
Graduate Major
Co-Major
Minor
Mathematics
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MTH 60 - Beginning Algebra
4 credits
Builds an understanding of the language of mathematics. Topics include studying the real number system including operations, exponents, absolute value, and the number line; simplifying algebraic expressions; solving linear equations and inequalities, and applying these concepts to geometric and algebraic formulas; and exploring linear equations in two variables including slope, graphing and modeling data. Does not apply toward graduation requirements.
Prerequisite(s): Appropriate SOU placement level. -
MTH 65 - Elementary Algebra
4 credits
Builds on the skills developed in Math 60. Topics include the use of graphical and algebraic methods to solve linear equations in two variables, operations with polynomials, factoring polynomials, and simplifying rational expressions. Does not apply toward graduation requirements.Prerequisite(s): MTH 60 or appropriate SOU placement level. -
MTH 95 - Intermediate Algebra
4 credits
Builds on the skills developed in Math 60 and Math 65. Prepares for courses that satisfy the Quantitative Reasoning University Studies requirement and courses leading up to the calculus track. Focuses on quadratic equations. Other topics include rational expressions and equations and manipulation of expressions with exponents and square roots. Real-world applications include use of projectile formulas and the Pythagorean theorem. Includes the use of a graphing calculator. Does not apply toward graduation requirements.Prerequisite(s): MTH 65 or appropriate SOU placement level. -
MTH 105 - Contemporary Mathematics
4 credits
Surveys various practical areas of mathematics. Topics include finance, combinatorics and discrete probability, and modern geometry. Additional topics selected from logic, number theory, voting and apportionment, exponential and logarithmic functions, and mathematics in arts and music. Emphasizes real-world applications, critical thinking, and the effective communication of mathematical ideas. Approved for University Studies (Quantitative Reasoning-Strand D).Prerequisite(s): 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. Intended for students continuing to Precalculus II (MTH 112 ) and Calculus MTH 251 . Approved for University Studies (Quantitative Reasoning-Strand D).Prerequisite(s): MTH 95 or appropriate SOU placement level. -
MTH 112 - Precalculus II: Elementary Functions
4 credits
In-depth study of exponential, logarithmic, and trigonometric functions and their graphs and applications. Topics include Laws of Logarithms, triangle trigonometry, circular functions and graphs, inverse trigonometric functions, and trigonometric equations. Intended as preparation for Calculus I (MTH 251 ). Approved for University Studies (Quantitative Reasoning).Prerequisite(s): 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. Credit for MTH 158 is not given to students who have received credit for MTH 261 . Approved for University Studies (Quantitative Reasoning-Strand D).Prerequisite(s): MTH 95 or appropriate SOU placement level. -
MTH 199 - Special Studies
1 to 18 credits
Credits to be arranged. Repeatable. -
MTH 209 - Practicum
1 to 6 credits
Credits to be arranged. Repeatable. -
MTH 211 - Fundamentals of Elementary Mathematics I
4 credits
Introduces the theory of arithmetic for prospective teachers. Topics include problem-solving strategies, 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. 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-Strand D [met after completion of both MTH 211 and MTH 212 ]).Prerequisite(s): 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. 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-Strand D [met after completion of both MTH 211 and MTH 212]).Prerequisite(s): 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 figures, the metric system, measurement, estimation, perimeter, area, volume, surface area, congruence, similarity, constructions, coordinate geometry, and transformations. Content is taught within a problem-solving framework. 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(s): 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(s): MTH 251 . -
MTH 243 - Introduction to Statistical Methods
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- Strand D).Prerequisite(s): MTH 95 or an appropriate SOU placement level. -
MTH 244 - Applied Statistical Methods
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(s): MTH 243 or . -
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-Strand D).Prerequisite(s): 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(s): MTH 251 . -
MTH 253 - Calculus III
4 credits
Studies infinite sequences and series, convergence tests, power series expansion of functions, vectors and vector functions, and the geometry of functions in multidimensional space.Prerequisite(s): 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 linear systems of equations, vector algebra in Rn (including basis dimension and span), matrices, linear transformations, Eigenvalue problems, and an introduction to abstract vector spaces. Prerequisite(s): MTH 252 . -
MTH 271 - Computational Mathematics
4 credits
Introduces basic techniques of numerical analysis and their associated computer methods. Topics chosen from error analysis, root finding algorithms, linear and nonlinear equation solving, linear systems, interpolation, and numerical methods for integration and solving differential equations. Course content learned in a mathematical programming environment. Prerequisite or concurrent registration: MTH 252 . -
MTH 281 - Calculus IV
4 credits
Studies partial derivatives, multiple integrals, vector calculus including vector fields, line integrals, the fundamental theorem for line integrals, Green’s theorem, curl and divergence, and surface integrals.Prerequisite(s): MTH 253 . -
MTH 290 - Mathematical Perspectives
2 credits
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, expository, writing, and student discussion.Prerequisite(s): MTH 252 (may be taken concurrently). -
MTH 299 - Special Studies
1 to 18 credits
Credits to be arranged. Repeatable. -
MTH 311 - Number Structures
5 credits
A careful introduction to the process of constructing mathematical arguments, covering the basic ideas of logic, set theory, number theory, functions and relations. A substantial amount of time will be devoted to looking at important forms of mathematical argument such as direct proof, proof by contradiction, proof by contrapositive, proof by cases, and various forms of proof by induction, including use of the well-ordering axiom. Additional concepts from abstract algebra or analysis may be covered at the discretion of the instructor.Prerequisite(s): 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 include: first order linear and nonlinear equations, second order linear equations, introduction to systems of equations, Laplace Transforms, and power series solutions.Prerequisite(s): MTH 253 or PH 371 . -
MTH 331 - Introduction to Real Analysis
4 credits
Studies the basic analytic structure of real numbers. Topics include sequences and functions; continuity, differentiation, and their applications; and an introduction to Riemann integration.Prerequisite(s): MTH 253 and MTH 311 -
MTH 341 - Introduction to Algebraic Systems
4 credits
Demonstrates the fundamental strategies used to study algebraic structures, including subsystems, morphisms, and cosets. Emphasizes groups, rings, and fields.Prerequisite(s): MTH 311 . -
MTH 361 - Probability
4 credits
Covers the theory and applications of probability. Topics include laws of probability, principles of counting, probability distributions of discrete and continuous random variables, expected values and varianes, and multivariate probability distributions. Prerequisites must be completed with a C- or better. Prerequisite(s): MTH 243 or SOC 327 , and MTH 252 . -
MTH 399 - Special Studies
1 to 18 credits
Credits to be arranged. Repeatable. -
MTH 401 - Research
1 to 4 credits
Credits to be arranged. Repeatable. -
MTH 403 - Thesis
1 to 4 credits
Credits to be arranged. Repeatable. -
MTH 405 - Reading and Conference
1 to 4 credits
Credits to be arranged. Repeatable. -
MTH 407 - Seminar
1 to 4 credits
Credits to be arranged. Repeatable. -
MTH 409 - Practicum
1 to 15 credits
Credits to be arranged. Repeatable for a maximum of 15 credits. -
MTH 411 - Topics in Foundations and Geometry
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 411A (Geometry). -
MTH 411A - Geometry
4 credits
An axiomatic development of a variety of geometries, with special attention given to Hyperbolic Geometry.Prerequisite(s): MTH 311 . -
MTH 421 - Topics in Applied Mathematics
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 421A (Applied Complex Variables), MTH 421B (Optimization), MTH 421C (Partial Differential Equations), MTH 421D (Mathematical Modeling), MTH 421E (Numerical Linear Algebra), MTH 421F (Adaptive Signal Analysis and Processing).
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MTH 421A - Applied Complex Variables
4 credits
Studies the algebra of complex numbers; analytic and harmonic functions; complex integration, including Cauchy’s Integral Formula; Taylor and Laurent series; Residue theory; and Möbius transformations. Prerequisite(s): MTH 281 . -
MTH 421B - Optimization
4 credits
Introduces linear programming and nonlinear optimization. Prerequisite(s): MTH 261 is required. CS 200 and CS 257 are recommended. -
MTH 421C - Partial Differential Equations
4 credits
Introduces diffusion, wave, and Laplace equations; separation of variables; and Fourier series.Prerequisite(s): MTH 281 and MTH 321 . -
MTH 421D - Mathematical Modeling
4 credits
Applies a variety of continuous and discrete modeling techniques to real-world phenomena. Includes dimensional analysis, parameter estimation, model fitting and testing, and simulation. Prerequisite(s): MTH 261 and MTH 321 . -
MTH 421E - Numerical Linear Algebra
4 credits
Develops computational methods in linear algebra. Topics include direct solution methods for linear systems, matrix decompositions (Cholesky, LU,QR, Schur, singular value), least-squares problems, eigenvalues and eigenvectors, and sensitivity. Other topics might include: special linear systems and iterative methods.Prerequisite(s): MTH 261 . -
MTH 421F - Adaptive Signal Analysis and Processing
4 credits
Investigates the mathematics of signal processing. Topics include Fourier Transforms of both discrete and continuous domains, filters, frequency responses, sampling, compression, and modulation.Prerequisite(s): MTH 261 and MTH 321 . -
MTH 431 - Topics in Analysis
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 431A (Integration), MTH 431B (Metric Spaces), MTH 431C (Infinite Series).
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MTH 431A - Integration
4 credits
Introduces Lebesque and Riemann integration.Prerequisite(s): MTH 331 . -
MTH 431B - Metric Spaces
4 credits
Extends analytic concepts to general metric spaces and mappings. Includes metric topology, convergence, continuity, and compactness.Prerequisite(s): MTH 331 . -
MTH 431C - Infinite Series
4 credits
Extends the analysis of infinite series to series of functions. Topics include uniform convergence, power series, and trigonometric series.Prerequisite(s): MTH 331 . -
MTH 441 - Topics in Abstract Algebra
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 441A (Groups), MTH 441B (Rings).
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MTH 441A - Groups
4 credits
Rigorous study of groups, including normal subgroups, quotient groups, isomorphism theorems, and the Sylow or the equivalent structure theorems. Prerequisite(s): MTH 341 . -
MTH 441B - Rings
4 credits
Rigorous study of rings, including ideals, quotient rings, isomorphism theorems, polynomial rings, factorization and related results.Prerequisite(s): MTH 341 . -
MTH 461 - Topics in Probability and Statistics
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 461A (Multivariate Statistical Analysis), MTH 461B (Regression Analysis), MTH 461C (Financial Mathematics), MTH 461D (Actuarial Mathematics).
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MTH 461A - Multivariate Statistical Analysis
4 credits
Explores probability distribution of random vectors, covariance matrix, multivariate normal distributions, inferences about a mean vector and several multivariate mean vectors, principal component analysis, and discriminant analysis.Prerequisite(s): MTH 361 . -
MTH 461B - Regression Analysis
4 credits
Explores linear and nonlinear regression, multiple regression, model diagnostics, variable selection procedures, logistic regression, and applications to biostatistics. Prerequisite(s): MTH 361 . -
MTH 461C - Financial Mathematics
4 credits
Studies the theory, computational methods, and practical applications of financial models. Topics include derivatives pricing and theory of portfolio management.Prerequisite(s): MTH 253 , MTH 321 , and MTH 361 are required. MTH 281 is recommended. -
MTH 461D - Actuarial Mathematics
4 credits
Studies the construction and analysis of actuarial models that describe the process by which funds flow into and out of an insurance system. Includes moments, quantiles, measures of risk, continuous and discrete actuarial models, and aggregate loss models.Prerequisite(s): MTH 361 is required. MTH 281 and MTH 321 are recommended. -
MTH 481 - Topics in Middle School and High School Mathematics
3 to 5 credits
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 481A (Arithmetic and Algebraic Structures), MTH 481B (Concepts of Calculus), MTH 481C , (Informal Geometry), MTH 481D (Math and History: Connections), MTH 481E (Measurement), MTH 481F (Problem Solving), MTH 481G (Experimental Probability and Statistics), MTH 481I (Curriculum: Conceptual Depth in the K-12 Curriculum). -
MTH 481A - Arithmetic and Algebraic Structures
3 credits
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(s): MTH 212 or MTH 251 . -
MTH 481B - Concepts of Calculus
3 credits
Introduces students to the limit concept and its role in defining the derivative and the integral. Investigations will demonstrate how concepts taught in middle school serve as the foundations for the study of calculus.
Prerequisite(s): MTH 212 or MTH 251 . -
MTH 481C - Informal Geometry
3 credits
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(s): MTH 213 or MTH 251 . -
MTH 481D - Math and History: Connections
3 credits
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(s): MTH 211 or MTH 251 . -
MTH 481E - Measurement
3 credits
Explores quantification of various attributes, direct and indirect measurement, approximations, development of standard units, and connections to other mathematical concepts. Prerequisite(s): MTH 213 or MTH 251 . -
MTH 481F - Problem Solving
3 credits
Introduces a variety of techniques for solving mathematical problems within the framework of Pólya’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(s): MTH 211 or MTH 251 . -
MTH 481G - Experimental Probability and Statistics
3 credits
Examines probability and statistics through lab experiments, simulations, and applications. Includes applications to middle school and high school general mathematics curricula.Prerequisite(s): MTH 212 , MTH 243 , or MTH 251 . -
MTH 481I - Curriculum: Conceptual Depth in the K-12 Math Curriculum
3 credits
Examines the cognitive demand of tasks, questioning strategies to increase cognitive demand, and the role student discourse plays in connecting and extending understanding of mathematical concepts.Prerequisite(s): MTH 211 or MTH 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 major writing and oral presentation components. Repeatable for a maximum of 8 credits.Prerequisite(s): Senior standing in the mathematics major, MTH 311 , and completion of at least two of the upper division sequences required for the major. -
MTH 501 - Research
1 to 4 credits
Credits to be arranged. Repeatable. -
MTH 503 - Thesis
1 to 4 credits
Credits to be arranged. Repeatable. -
MTH 505 - Reading and Conference
1 to 4 credits
Credits to be arranged. Repeatable. -
MTH 507 - Seminar
1 to 4 credits
Credits to be arranged. Repeatable. -
MTH 509 - Practicum
1 to 9 credits
Credits to be arranged. Repeatable for a maximum of 15 credits. -
MTH 511 - Topics in Foundations and Geometry
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 511A (Geometry). -
MTH 511A - Geometry
4 credits
An axiomatic development of a variety of geometries, with special attention given to Hyperbolic Geometry.Prerequisite(s): MTH 311 . -
MTH 521 - Topics in Applied Mathematics
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 521A (Applied Complex Variables), MTH 521B (Optimization), MTH 521C (Partial Differential Equations), MTH 521D (Mathematical Modeling), MTH 521E (Numerical Linear Algebra) MTH 521F (Adaptive Signal Analysis and Processing). -
MTH 521A - Applied Complex Variables
4 credits
Studies the algebra of complex numbers; analytic and harmonic functions; complex integration, including Cauchy’s Integral Formula; Taylor and Laurent series; Residue theory; and Möbius transformations. Prerequisite(s): MTH 281 . -
MTH 521B - Optimization
4 credits
Introduces linear programming and nonlinear optimization. Prerequisite(s): MTH 261 is required. CS 200 and CS 257 are recommended. -
MTH 521C - Partial Differential Equations
4 credits
Introduces diffusion, wave, and Laplace equations; separation of variables; and Fourier series.Prerequisite(s): MTH 281 and MTH 321 . -
MTH 521D - Mathematical Modeling
4 credits
Applies a variety of continuous and discrete modeling techniques to real-world phenomena. Includes dimensional analysis, parameter estimation, model fitting and testing, and simulation.Prerequisite(s): MTH 261 and MTH 321 . -
MTH 521E - Numerical Linear Algebra
4 credits
Develops computational methods in linear algebra. Topics include direct solution methods for linear systems, matrix decompositions (Cholesky, LU,QR, Schur, singular value), least-squares problems, eigenvalues and eigenvectors, and sensitivity. Other topics might include: special linear systems and iterative methods.Prerequisite(s): MTH 261 . -
MTH 521F - Adaptive Signal Analysis and Processing
4 credits
Investigates the mathematics of signal processing. Topics include Fourier Transforms of both discrete and continuous domains, filters, frequency responses, sampling, compression, and modulation.Prerequisite(s): MTH 261 and MTH 321 . -
MTH 531 - Topics in Analysis
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 531A (Integration), MTH 531B (Metric Spaces), MTH 531C (Infinite Series).
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MTH 531A - Integration
4 credits
Introduces Lebesque and Riemann integration.Prerequisite(s): MTH 331 . -
MTH 531B - Metric Spaces
4 credits
Extends analytic concepts to general metric spaces and mappings. Includes metric topology, convergence, continuity, and compactness.Prerequisite(s): MTH 331 . -
MTH 531C - Infinite Series
4 credits
Extends the analysis of infinite series to series of functions. Topics include uniform convergence, power series, and trigonometric series.Prerequisite(s): MTH 331 . -
MTH 541 - Topics in Abstract Algebra
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 541A (Groups), MTH 541B (Rings). -
MTH 541A - Groups
4 credits
Rigorous study of groups, including normal subgroups, quotient groups, isomorphism theorems, and the Sylow or the equivalent structure theorems.Prerequisite(s): MTH 341 . -
MTH 541B - Rings
4 credits
Rigorous study of rings, including ideals, quotient rings, isomorphism theorems, polynomial rings, factorization and related results.Prerequisite(s): MTH 341 . -
MTH 561 - Topics in Probability and Statistics
4 credits each
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 561A (Multivariate Statistical Analysis), MTH 561B (Regression
Analysis), MTH 561C (Financial Mathematics), MTH 561D (Actuarial Mathematics). -
MTH 561A - Multivariate Statistical Analysis
4 credits
Explores probability distribution of random vectors, covariance matrix, multivariate normal distributions, inferences about a mean vector and several multivariate mean vectors, principal component analysis, and discriminant analysis.Prerequisite(s): MTH 361 . -
MTH 561B - Regression Analysis
4 credits
Explores linear and nonlinear regression, multiple regression, model diagnostics, variable selection procedures, logistic regression, and applications to biostatistics. Prerequisite(s): MTH 361 . -
MTH 561C - Financial Mathematics
4 credits
Studies the theory, computational methods, and practical applications of financial models. Topics include derivatives pricing and theory of portfolio management.Prerequisite(s): MTH 253 , MTH 321 and MTH 361 are required. MTH 281 is recommended. -
MTH 561D - Actuarial Mathematics
4 credits
Studies the construction and analysis of actuarial models that describe the process by which funds flow into and out of an insurance system. Includes moments, quantiles, measures of risk, continuous and discrete actuarial models, and aggregate loss models.Prerequisite(s): MTH 361 is required. MTH 281 and MTH 321 are recommended. -
MTH 571 - Applied Mathematics in Practice Seminar
2 credits
Focused on practical problem solving, appropriate blending of software and analysis, cultivation of teamwork skills, and effective written and oral business communication. Business partners provide specific real-world problems faced by their business or agency that require mathematical expertise. The business partner for any given term will participate in the seminar, which will typically be team-taught by SOU faculty member and a business representative. May be repeated for a maximum of 24 credits. -
MTH 581 - Topics in Middle School and High School Mathematics
3 to 5 credits
Topics are offered as needed. Prerequisites vary. Repeat credit is offered for distinct topics. Topics offered regularly are distinguished with an alpha character: MTH 581A (Arithmetic and Algebraic Structures), MTH 581B (Concepts of Calculus), MTH 581C (Informal Geometry), MTH 581D (Math and History: Connections), MTH 581E (Measurement), MTH 581F (Problem Solving), MTH 581G (Experimental Probability and Statistics), MTH 581I (Curriculum: Conceptual Depth in the K-12 Curriculum).
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MTH 581A - Arithmetic and Algebraic Structures
3 credits
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(s): MTH 212 or MTH 251 . -
MTH 581B - Concepts of Calculus
3 credits
Investigations will demonstrate how concepts taught in middle school serve as the foundations for the study of calculus.Prerequisite(s): MTH 212 or MTH 251 . -
MTH 581C - Informal Geometry
3 credits
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(s): MTH 213 or MTH 251 . -
MTH 581D - Math and History: Connections
3 credits
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(s): MTH 211 or MTH 251 . -
MTH 581E - Measurement
3 credits
Explores quantification of various attributes, direct and indirect measurement, approximations, development of standard units, and connections to other mathematical concepts. Prerequisite(s): MTH 213 or MTH 251 . -
MTH 581F - Problem Solving
3 credits
Introduces a variety of techniques for solving mathematical problems within the framework of Pólya’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(s): MTH 211 or MTH 251 . -
MTH 581G - Experimental Probability and Statistics
3 credits
Examines probability and statistics through lab experiments, simulations, and applications. Includes applications to middle school and high school general mathematics curricula.Prerequisite(s): MTH 212 , MTH 243 , or MTH 251 .
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