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Course Criteria
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3.00 Credits
This course is an introduction of some of the techniques of applied mathematics, with emphases on applications in the biological and physical sciences and the use of computers in modeling and solving problems. Topics include linear differential and difference equations, linear systems, matrix algebra, algebra of complex numbers, linear transforms, and introductions to partial differential equations and non-linear dynamical systems.
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3.00 Credits
The goal of this course is to introduce students to the theory, techniques, and applications of linear algebra. Some of the topics include systems of linear equations, matrix algebra, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, orthogonality, and the Gram-Schmidt process. Applications include predator-prey models, economic system equilibrium, Markov chains, traffic flow, balancing chemical equations, and least-squares approximations. Technology will be used to investigate concepts and solve problems.
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3.00 Credits
This course focuses on the fundamental concepts of computer programming and the development of computer programs using MATLAB programming environment. The overall objectives are to learn essential computer programming concepts and to apply these concepts in computer-based problem solving. The course includes the fundamentals of flow-charting, decision structures, sequential execution, repetition, subroutines, functions, user interface design, and data structures. There will be some emphasis on the development of computer programs that handle numerical data. The course incorporates mathematical topics such as matrix algebra, polynomial interpolation, linear and non-linear algebraic systems, correlation and regression, time series, gradient vectors, and contour plots to illustrate programming concepts. This course progresses from the development of simple concept-driven programs to more complicated programs that read, manipulate, display, and store data. MAT 225 is appropriate for mathematics and science majors and minors; MAT 525 includes advanced programming work for graduate students.
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3.00 Credits
This course provides an introduction to abstract mathematical thinking and the fundamental concepts of higher mathematics. The primary goal is to develop students' abilities to read, critique, construct, and write mathematical proofs. Topics, generally chosen from discrete mathematics, include logic, set theory, relations, graph theory, recursion and combinatorics.
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3.00 Credits
This course provides a survey of modern approaches to Euclidean and non-Euclidean geometries in two dimensions. The axiomatic foundations of metric and transformational geometries, isometries, similarities, symmetric figures, scaling, measurement, geometric construction, and projective geometry are topics that may be examined. Topics of interest to preservice secondary teachers include tessellation and connections between geometry and other areas of mathematics, including linear and abstract algebra. Technology is used extensively to investigate concepts.
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3.00 Credits
This course is an introduction to algebraic structures, including groups, rings, integral domains, and fields. Properties of these structures will be illustrated with numerous examples. An important component of this course is the reading and writing of mathematical proofs.
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3.00 Credits
This calculus-based course provides a foundation in the conceptual and mathematical underpinnings of probability and statistics. Topics include probability properties, discrete and continuous probability distributions, combinatorics, random variables, estimation, and hypothesis testing. The emphasis is on mathematical theory and communication of results, with applications serving as examples to illustrate concepts. Students will use mathematical or statitical software to explore and validate solutions.
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3.00 Credits
This course begins with a study of properties of real numbers and the topology of the real line, and uses these concepts to develop a rigorous treatment of topics from Calculus, including limits, continuity, uniform continuity, differentiation, sequences and series, and convergence. Additional topics may include numerical analysis of convergent phenomena. Emphasis will be placed on rigor, clarity, and elegance of proofs.
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3.00 Credits
The goal of this course is to engage students in investigation and discussion related to pertinent topics in mathematics education philosophy and research and the ways in which these can inform and be applied to classroom teaching. Topics may include research on: approaches to mathematics teaching, learning, and assessment; teaching methods related to particular areas of mathematics such as algebra, geometry, representations, data analysis, or mathematical proof; philosophies or theories of mathematics curriculum, teaching, and learning; historical and current perspectives on equity, gender, or crosscultural issues; other topics selected by the instructor and students. Prerequisite: Permission of the instructor and four MAT courses numbered 190 or higher. Does not fulfill core curriculum mathematics requirement.
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3.00 Credits
This course is designed to create a scholarly atmosphere in which students and faculty engage in discussions and explorations of interesting mathematical topics. Students will present the results of their research in seminar talks and critique talks of their classmates. Topics vary by semester, depending upon the expertise of the instructor and the interest of participants.
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