Mathematics

W80 Elliptic Curves. The subject of elliptic curves is a beautiful example of the interconnectedness of the different braches of mathematics. This course will use geometry, calculus, number theory and group theory to study the subject. In addition to the purely mathematical aspects, some applications such as cryptography will be discussed. There will be a brief discussion of ho 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. This course meets the interim course requirement for mathematics majors. Prerequisite: Math 256, or a 300-level mathematics course in which proof is emphasized. J. Ferdinands . 2:00 p.m. to 5:00 p.m.

W81 Curricular Materials for K – 8 School Mathematics. This course examines and evaluates K–8 mathematics curricula in the context of the NCTM's Principles and Standards for School Mathematics. Although the emphasis is on grades 6–8, curricula at all grade levels is examined. Some of the curricula to be discussed are Everyday Mathematics, Investigations, Math TrailBlazers, Connected Mathematics, MathScape, MathThematics, and Mathematics in Context. Students are expected to complete assigned readings, to participate in and lead sample activities and lessons, and to contribute to discussions. 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 . Prerequisite: Mathematics 222. 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. J. Koop. 2:00 p.m. to 5:00 p.m.

W82 Exploring Advanced Euclidean Geometry . Almost all of the geometry that is studied in high school dates from the time of Euclid or even earlier, hundreds of years before Christ. But the development of Euclidean geometry did not end with Euclid. Over the past two millennia many fascinating and surprising results
have been discovered, with the nineteenth century being an especially
active period for such discovery.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.This course explores the results of higher (or advanced) Euclidean geometry. The geometric results are explored in two ways: using the ancient technique of Euclid (proof) and the modern tool of dynamic computer software ( Geometer's Sketchpad ). 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 GSP sketch. There are no tests or exams; evaluation of student work is based entirely on the quality of the notebook. This course satisfies an interim course requirement that is part of the math major. Prerequisite: At least one 300- level mathematics course in which proof is emphasized. G. Venema . 8:30 a.m. to noon.

MATH-160 Elementary Functions and Calculus (core). 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. G. Klassen.