
Inversion of a checkerboard (displayed by Mathematica)
Introduction:
Modern geometry is not a single subject. Projective geometry, elliptic geometry, finite geometries and particularly hyperbolic geometry all expand the scope and application of geometry far beyond its Greek foundation in Euclidean geometry. All these geometries were developed, if not discovered, in the past 150 years. This course will study them all, as well as a modern axiomatic treatment of Euclidean geometry. In the process the course uses several branches of algebra (group theory and linear algebra) and reviews complex numbers and parts of multivariable calculus.Instructor:
Michael HenleText:
Office Hours: Tuesday and Thursday 2:304:30 in King 202, Friday 5:006:00
Phone: X8383 or 7757676
Modern Geometries (Second Edition) by Michael Henle (errata sheet)Evaluations:
Homework:Outline of the Semester:Approximately 10 weekly assignments: due on Wednesdays.Exams:Two midterm exams (October 19 and November 30)
Final exam (2:00 PM on Thursday 20 December).
Week of Topics
September 4 Complex Numbers
September 10 The Erlangen Programm
September 17 Moebius Geometry
September 24 Hyperbolic Geometry
October 1 Cycles
October 8 Hyperbolic Length
October 15 Hyperbolic Area
Fall Break
October 29 Elliptic and Absolute Geometry
November 5 Projective Geometry
November 12 Multidimensional Projective Geometry
November 19 Universal Geometry
November 26 Hilbert's Axioms
December 3 Further axioms of Hilbert
December 10 Bachmann's Axioms
Weekly Assignments:
Chapter Two/ 1, 2, 3(c), 5, 9, 10, 11, 12, 14(g, h), 17, 18(g, i), 19(d, f)Assignment 2.
Chapter Three/ 2, 3, 4, 6, 7, 8, 10, 11, 12, 15(c, d)
Chapter Four/ 24, 7, 9, 12, 13, 16
Chapter Five/ 2(last part), 3(b), 4, 6(last part), 11, 12, 14, 15, 17
Chapter Five/ 19, 20, 22, 24, 25
Chapter Six/ 2, 3(b, c), 4, 6, 8, 9, 11, 12, 14, 15, 16
Chapter Seven/ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,12
Chapter Eight/ 1, 2, 3
Chapter Eight/ 6, 8, 9, 10, 11, 12
Chapter Nine/ 1, 4, 5, 7, 8, 9, 10, 11, 12, 15, 16
Chapter Nine/ 18, 20, 21, 22
Chapter Ten/ 3, 4, 5, 6, 7, 8, 11, 12, 13
Chapter Eleven/ 5, 6, 11, 12, 15
Chapter Twelve/ 6, 8, 9, 10, 12, 14, 16, 18, 19
Chapter Thirteen/ 1, 2, 3, 6
Chapter Thirteen/ 7, 8, 11(a, c, f), Extra Which parts of
figure 13.10 are configurations?
Chapter Fourteen/ 3(d, e, f), 6, 8, 9, 10, 15, 16, 17, 18
Chapter Fifteen/ 3, 4, 5, 8(b, c), 9(b, c), 12, 13, 14(c, d), 15
Chapter Twenty/ 1, 5, 12, 15, 17, 18, 19
Chapter Fifteen/ 16, 17, 18, 21, 24
Chapter Twenty/ 24, 25
Chapter TwentyOne/ 1, 2, 3, 5, 7, 9, 10, 14, 17
Chapter TwentyFour/ 4, 8, 9, 10, 21, 24, 26
Chapter TwentyFive/ 1, 2, 3, 6, 8, 9, 10, 11, 15, 18