Weekly Assignments     Assignment 1     Assignment 2     Assignment 3     Assignment 4     Assignment 5     Assignment 6     Assignment 7     Assignment 8     Assignment 9     Assignment 10     Assignment 11

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.

Michael Henle
Office Hours: Tuesday and Thursday 2:30-4:30 in King 202, Friday 5:00-6:00
Phone: X8383 or 775-7676

Modern Geometries (Second Edition) by Michael Henle (errata sheet)

Homework:

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         Multi-dimensional Projective Geometry

November 19         Universal Geometry

November 26         Hilbert's Axioms

December 3           Further axioms of Hilbert

December 10         Bachmann's Axioms

Weekly Assignments:

Assignment 1.

Chapter Two/ 1, 2, 3(c), 5, 9, 10, 11, 12, 14(g, h), 17, 18(g, i), 19(d, f)
Chapter Three/ 2, 3, 4, 6, 7, 8, 10, 11, 12, 15(c, d)

                Chapter Four/ 2-4, 7, 9, 12, 13, 16
                Chapter Five/ 2(last part), 3(b), 4, 6(last part), 11, 12, 14, 15, 17

Assignment 3.

                 Chapter Five/ 19, 20, 22, 24, 25
                 Chapter Six/ 2, 3(b, c), 4, 6, 8, 9, 11, 12, 14, 15, 16

Assignment 4.

                Chapter Seven/ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,12
                Chapter Eight/ 1, 2, 3

Assignment 5.

                Chapter Eight/ 6, 8, 9, 10, 11, 12
                Chapter Nine/ 1, 4, 5, 7, 8, 9, 10, 11, 12, 15, 16

Assignment 6.

                Chapter Nine/ 18, 20, 21, 22
                Chapter Ten/ 3, 4, 5, 6, 7, 8, 11, 12, 13

Assignment 7

                Chapter Eleven/ 5, 6, 11, 12, 15
                Chapter Twelve/ 6, 8, 9, 10, 12, 14, 16, 18, 19
                Chapter Thirteen/ 1, 2, 3, 6

Assignment 8

                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

Assignment 9

                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

Assignment 10

                Chapter Fifteen/  16, 17, 18, 21, 24
                Chapter Twenty/  24, 25

Assignment 11

                Chapter Twenty-One/  1, 2, 3, 5, 7, 9, 10, 14, 17
                Chapter Twenty-Four/  4, 8, 9, 10, 21, 24, 26
                Chapter Twenty-Five/  1, 2, 3, 6, 8, 9, 10, 11, 15, 18