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5 Fermat s last theem, quadratic residues, primitive roots, Chinese Remainder theem. Prerequisites: Calculus II permission of the MED MED 553 Discrete Structures (3 An introduction to the basic concepts of discrete mathematics essential both to mathematics and many of its applications. Topics include logic, sets, relations, functions, recurrence equations, combinatics, graphs. Techniques of mathematical proof will be developed. Prerequisites: Calculus II permission of the MED MED 554 Geometry (3 Contempary topics in Euclidean and non- Euclidean geometry. Topics include motion geometry, affine transfmation, projective transfmations, axiomatic systems, and applications of geometry. Prerequisites: MED 552 MED 553 permission of the MED MED 555 Probability and Statistics (3 Descriptive statistics, random variables, discrete and continuous probability distributions, moments, crelations, sampling distributions, estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance. Additional topics as time permits may include fact analysis, contingency tables, multilinear regression and nonparametric methods. Prerequisites: Calculus II permission of the MED MED 556 Linear Algebra (3 Linear systems, vect spaces, dimension, linear transfmations, matrices, inner product, othogonality, characteristic polynomials, diagonalization, eigenvalues, eigenvects. Prerequisites: Calculus II permission of the MED MED 557 Modern Algebra (3 This course discusses modern topics in abstract algebra groups, rings, ideals, fields, vect spaces. Axiomatic systems are used to prove theems and discuss relationships such as homomphism and isomphism. Applications in elementary geometry and algebra are discusses. Prerequisites: Calculus II; and MED 552 MED 553 permission of the MED MED 559 Mathematical Problem Solving (3 Techniques of solving mathematical problems which draw on a wide mathematical background. Solutions may incpate concepts from linear algebra, analysis, modern algebra, combinatics, geometry and applied mathematics. Prerequisites: Calculus II; and MED 552 MED 553 permission of the MED MED 601 Communication and Technology in Mathematics (3 This course is designed to introduce pre-service teachers to the different types of technology available to the mathematics classroom. The use of manipulative devices, ptfolios journals, writing and verbal communication in the mathematics classroom will be discussed. Emphasis will be placed on the appropriate use of the graphing calculat, applications f the personal computer, and the internet in the mathematics classroom. Ethical and practical issues surrounding the use of technology will be discussed. MED 602 Secondary Mathematics Curriculum (3 This course examines the ways in which high school students acquire mathematical knowledge, considers the particular mathematical knowledge they should have at each grade level (as articulated by the Principles and Standards of School Mathematics), and applies this understanding to the design of secondary mathematics curricula. MED 603 Assessment in Secondary Mathematics (3 This course is a practical guide to designing a variety of assessment tools. Students will learn how to design projects, group activities, writing activities, ptfolios and tests that together can be used to assess what students know and can do. The role of assessment is twofold: to assess what students have learned, and to modify our teaching strategies to enhance student learning. Students will be concerned with the curriculum of the secondary mathematics program, grades MED 604 Advanced Perspectives on Secondary Mathematics (3 This course is an in depth study of the mathematics typically learned in middle and high school mathematics classes. We will identify ce mathematical ideas and then also the common errs that students make, the misunderstandings they frequently have, and the questions they ask. We will develop strategies f addressing misconceptions and compose answers to questions that might arise in the classroom and in so doing

6 further our own understanding of mathematics. We will situate the ideas within a broader mathematical context to be sure that we are generating responses that further students mathematical development. We will use this infmation to create examples, problems and projects that would enrich students understanding. MED 605 Interdisciplinary Mathematics and Science Teaching (3 This course exples ways to integrate math and science teaching at the secondary level. We review the mathematics and science secondary curricula and identify places where connections can be made and determine approaches to teach math and science so that concepts learned in one discipline can be used to reinfce concepts learned in the other. We consider existing projects that combine mathematics and science and use what is learned to develop new projects. MED 611 Geometry f Teachers: from Problem Solving to Proof (3 This course discusses specific topics from geometry, their impact on the changing geometry curriculum, their application through technology and their connection to other areas within and outside mathematics. Students will examine recent research trends and practical methods f teaching geometry at the secondary level and exple several methods of geometry curriculum design and instruction. Students will learn what role the processes of visualization, construction and reasoning play in learning and teaching geometry. Classroom materials, activities and techniques are discussed and developed and concepts explained and expled through a variety of modes including manipulatives, interactive computer software and graphing calculats. Prerequisite: MED 554 permission of the MED vary depending on interests and backgrounds of students. Prerequisites: MED 559 permission of the MED MED 783 Research in Mathematics I (3 MED 784 Research in Mathematics II (3 Students will design and carry out a research project in mathematics as an independent study, wking closely with a faculty ment. Permission and approval by the ment and MED direct are required. MED 793 Research in Mathematics Education I (3 MED 794 Research in Mathematics Education II (3 Students will design and carry out a research project in mathematics education as an independent study, wking closely with a faculty ment. Permission and approval by the ment and MED direct are required. MED 770 Topics in Mathematics Education (3 Topics and issues in secondary mathematics teaching, from theetical underpinnings to practical applications. Topics will vary depending on interests and backgrounds of students. Permission of the MED direct required. MED 771 Topics in Mathematics (3 Topics in mathematics such as advanced abstract algebra, real analysis, combinatics, graph they, topology, logic, and dynamical systems. Topics will

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