## Interim 2010

#### Mathematics

**W80 Curricular Materials for K-8 Mathematics.** This course examines and evaluates K-8 mathematics curricula in the context of the NCTM Principles and Standards for School Mathematics. Although the emphasis this year will be on grades K-5, curricula at all grade levels will be examined. Some of the curricula to be discussed are Everyday Mathematics, Investigations, Math TrailBlazers, Connected Mathematics, MathScape, MathThematics and Mathematics in Context. Familiarity with a variety of K-8 mathematics curricula, with state and national mathematics grade level standards, and with state and national K-8 mathematics testing instruments is important for prospective teachers. Practice in designing exemplary mathematics lessons, making mathematics/literature connections, and solving mathematics problems are valuable skills for classroom mathematics teachers. Students are expected to complete assigned readings, to participate in and lead sample activities and lessons, and to contribute to small-group and whole-class discussions of the materials under consideration. Evaluation is based on in-class participation, presentation of grade-level lessons, several written quizzes, and written projects. Optional K-8 classroom observations can be arranged for the morning hours. Students should arrange their schedules so that they can spend some additional hours in the Curriculum Center. This course may replace Mathematics 110 in the elementary education mathematics minor for students who have completed four years of high school mathematics and who have received permission from their mathematics advisor. Prerequisite: MATH 222. *J. Koop*. 2:00 p.m. to 5:00 p.m.

**W81 Elliptic Curves**. The subject of elliptic curves is a beautiful example of the interconnectedness of the different branches of mathematics. The student will use geometry, calculus, number theory and group theory to understand the basics of the subject. In addition to the purely mathematical aspects, some applications such as cryptography will be discussed. There will be a brief discussion of how Fermat’s Last Theorem, a 300 year old unsolved problem, was proved using ideas from elliptic curves. There will be daily assignments and a final project. The course meets the Interim course requirement for mathematics majors. Prerequisites: Math 256, or a 300-level mathematics course in which proof is emphasized. *J. Ferdinands*. 2:00 p.m. to 5:00 p.m.

**W82 Geometry and Gravitation**. This course is an introduction to the mathematics of Einstein’s theory of gravity, also known as the General Theory of Relativity. Topics will include the geometry of special relativity (flat spacetime), Lorentz transformations, the equivalence principle, the geometry of curved spacetime, the geodesic equation, gravitational redshift, and Schwarzschild spacetime near black holes. Student evaluation will be based on homework and student presentations. This course may fulfill an elective in the Mathematics major. Prerequisites: MATH 261, or 231 and 232. *C. Mosele*y. 2:00 p.m. to 5:00 p.m.

**170 Elementary Functions and Calculus II **. This course is a continuation of Mathematics 169. Topics include derivatives, applications of derivatives, and integrals. Historical and philosophical aspects of calculus are integrated with the development of the mathematical ideas, providing a sense of the context in which calculus was developed. Prerequisite: Mathematics 169. *C. Hampton *. 8:30 a.m. to noon and 2:00 p.m. to 5:00 p.m.