MATH W80 Advanced Euclidean Geometry. The development of Euclidean geometry did not end with Euclid. Over the past two millennia many fascinating and surprising results have been discovered. This course explores the results of higher (or advanced) Euclidean geometry. Topics include the theorems of Ceva, Menelaus, Desargues, Brionchon, Napoleon, Miquel, Feuerbach, and Morley as well as Pascal’s Mystic Hexagram, Euler and Simson lines, Fermat and Gergonne points, and the nine-point circle. We will examine these results in two ways: using modern software (GeoGebra) to explore geometry in a dynamic context, and using the ancient technique of Euclid (proof) to establish the results. Students learn to be comfortable with both. The two goals of the course are to explore the mathematics itself and to learn an appropriate balance between proof and computer exploration. Students in the course produce a notebook that contains statements and proofs of all the major theorems studied. Each theorem and proof is illustrated
with an appropriate GeoGebra sketch. There are no tests or exams; evaluation of student work is based entirely on the quality of the notebook. This course satisfies the interim course requirement for the mathematics major. Prerequisite: Math 256, or a 300-level mathematics course that emphasizes proof. Math 301 is helpful but not required. C. Moseley. 2:00 p.m. to 5:00 p.m.
MATH W81 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, Bridges, Connected Mathematics, MathScape, MathThematics, Mathematics in Context, and Singapore Math. 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, written quizzes, and several written projects. Optional K-8 classroom observations can be arranged for the morning hours. Students should arrange their schedules so that they can spend additional hours in the Curriculum Center. This course is required for the Mathematics Elementary major, and replaces Math 110 for Mathematics Elementary minors (with permission of their mathematics advisor). Prerequisite: MATH 222. J. Koop. 2:00 p.m. to 5:00 p.m.
MATH 170 Elementary Functions and Calculus. This course is a continuation of Mathematics 159. Topics include applications of derivatives, integrals, the fundamental theorem of calculus, and applications of integrals. Grades are based on problem sets, tests, and a final exam. Prerequisite: Mathematics 159. M. Bolt. 8:30 a.m. to noon and 2:00 p.m. to 5:00 p.m.