School of Graduate Studies > Graduate Catalogs > 2010-2012 > College of Letters & Sciences > Mathematical and Computer Sciences Courses

Mathematical and Computer Sciences Department

Laurentide 2223

Phone: (262) 472-1313

Email: mathcmpsci@uww.edu

**Applied Statistics 3 u **

This course will cover the basics of statistical testing, regression analysis, experimental design, analysis of variance, the use of computers to analyze statistical problems.

Prerequisite: MATH 253 or MATH 250 or consent of instructor.

**Infinite Processes for the Elementary Teacher 3 u**

This course is primarily for pre-service elementary and middle school teachers. Students will be introduced to the concepts of calculus, which include infinite processes, limits, and continuity. In addition, derivatives and integrals, and their relationship to area and change will be covered.

Prerequisite: MATH 152

**Matrices and Linear Algebra 3 u **

Systems of linear equations, vector spaces, linear dependence, bases, dimension, linear mappings, matrices, determinants, quadratic forms, orthogonal reduction to diagonal form, eigenvalues, geometric applications.

Prerequisite: MATH 253 or MATH 250, MATH 254 or concurrent registration or consent of instructor.

**Problem Solving for the Elementary Teacher 3 u **

This course is primarily for pre-service elementary and middle school teachers. Students will learn a variety of problem solving strategies applicable in elementary and middle school. The applications will cover many different areas of mathematics.

Prerequisite: MATH 149

**Development of Mathematics 3 u **

A study of the development of mathematical notation and ideas from prehistoric times to the present, periods and topics will be chosen corresponding to the backgrounds and interests of the students.

Prerequisite: Consent of instructor.

**Modern Algebra and Number Theory for the Elementary Teacher 3 u**

An introduction to modern algebra with special emphasis on the number systems and algorithms which underlie the mathematics curriculum of the elementary school. Topics include sets, rings, integral domains, rational numbers, real numbers, complex numbers and polynomials. Students may not receive credit for both MATH 615 and MATH 652.

Prerequisite: MATH 149 and MATH 152

**Geometry for the Elementary Teacher 3 u **

A study of the intuitive, informal geometry of sets of points in space. Topics include elementary constructions, coordinates and graphs, tessellations, transformations, problem solving, and symmetries of polygons and polyhedra and use of geometry computer software.

Prerequisite: MATH 149 and MATH 152

**Theory of Numbers 3 u**

A study of the properties of integers, representation of integers in a given base, properties of primes, arithmetic functions, modulo arithmetic. Diophantine equations and quadratic residues. Consideration is also given to some famous problems in number theory.

Prerequisite: MATH 615 or MATH 652 or consent of instructor

**Mathematics for High School Teachers I 3 u**

The course revisits the high school curriculum from an advanced perspective. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes number systems, functions, equations, integers, and polynomials. Connections to geometry are emphasized throughout the course.

Prerequisite: Math 280, Math 301, and at least an additional 3 credits in upper level math

**Mathematics for High School Teachers II 3 u**

The course continues the explorations of the high school curriculum from an advanced perspective that was started in Math 421. The focus is on deepening understanding of concepts, highlighting connections and solving challenging problems. The mathematical content includes congruence, distance, similarity, trigonometry, area, and volume. Connections to algebra are emphasized throughout the course.

Prerequisite: Math 353 and Math 421

**Topology 3 u **

An introduction to point-set topology, including such topics as topological spaces, mappings, connectedness, compactness, separation axioms, metric spaces, complete spaces, product paces and function spaces.

**Probability Theory 3 u **

Probability spaces, discrete and continuous random variables, mathematical expectation, discrete and continuous distributions.

Prerequisite: MATH 255 or MATH 280 or consent of instructor.

**Mathematical Statistics 4 u **

This course will cover moment generating functions, moment of linear combinations of random variables, conditional expectation, functions of random variables, sampling distributions, the theory of estimation, Bayesian estimation, hypothesis testing, nonparametric tests, and linear models.

Prerequisite: MATH 641 and either MATH 555 or consent of instructor.

**Abstract Algebra 3 u **

This course is a continuation of MATH 452/652 with emphasis on ring and field theory. Topics include a review of group theory, polynomial rings, divisibility in integral domains, vector spaces, extension fields, algebraic extension fields, etc.

Prerequisite: MATH 555 and MATH 652.

**Partial Differential Equations 3 u **

Fourier analysis, partial differential equations and boundary value problems, complex variables, and its potential theory.

**Advanced Calculus 3 u **

This course presents a rigorous treatment of the differential and integral calculus of single variable functions, convergence theory of numerical sequences and series, uniform convergence theory of sequences and series of functions, metric spaces, function of several real variables, and the inverse function theorem. This course contains a written component.

**Workshop 1-3 u **

**Seminar 2 u **

Special Studies 1-3 u

Prerequisite: Consent of instructor.

**Workshop 1-6 u **

**Seminar 1-3 u **

**Special Studies 1-3 u**

**Individual Studies 1-3 u **

In addition to allowing students to carry on independent studies in a wide variety of graduate level topics, students may take many of the departmentâ€™s upper level undergraduate courses supplemented with graduate components. These courses include advanced calculus, complex variables, differential equations, abstract algebra, number theory, probability, statistics, and more.

**Thesis Research 1-6 u **

Students must complete a Thesis Proposal Form in the Graduate Studies Office before registering for this course.

**Workshop 1-3 u **

Repeatable.

**Special Studies 1-3 u **

Repeatable.

**Workshop 1-3 u **

**Seminar 1-3 u **

**Individual Studies 1-3 u**