Course
syllabusThis course is required for all mathematics and mathematics education majors. We will devote a good deal of time (particularly in the fall semester) to many of the underpinnings of high school mathematics, including a solid understanding of number systems and polynomials, as well as constructibility issues. In the spring semester, we will study group theory, symmetries, and some projective geometry. One of the highlights of the course will be Abel and Galois's earthshattering result that there can be no analogue of the quadratic formula (or cubic formula) for polynomials of degree 5 and higher; it turns out that this is a consequence of understanding the symmetries of the regular dodecahedron.
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