01:640:435 Geometry Fall 2021 Syllabus

All numbers refer to sections of Stillwell's Four Pillars of Geometry (This syllabus may be revised during the semester. This verison revised 8/30/21)

Week 1
- Wednesday, September 1
  - Euclidean Constructions with straightedge and Compass
  - 1.1 Construction Axioms
  - 1.2 Construction of equilateral triangle and hexagon
  - 1.3 Construction of bisectors,
- Wednesday, September 8 (Monday schedule at Rutgers due to holiday
  - 1.4 Multiplication and division
  - 1.5 Similar triangles
Week 2
- Monday, September 13 Homework 1 Due
  - 2.1 Neutral geometry, Euclid's Axioms, parallel lines
  - 2.2 Congruence of triangles
  - 2.3 Areas
  - 2.4 Area of parallelograms
- Wednesday, September 15
  - 2.5 The Pythagorean theorem
  - 2.6 Thales Theorem via areas
  - 2.7 Angles in a circle
  - 2.8 Squaring the rectangle
Week 3
- Monday, September 20 Homework 2 Due
  - 2.9 Review of Euclidean Geometry from axioms
  - 3.1 Number line and number plane
  - 3.2 Lines, slopes and equations
  - 3.3 Distance
  - 3.4 Intersections of lines and circles, constructible points
- Wednesday, September 22
  - 3.5 Slopes and angles
  - 3.6 Isometries
  - 3.7 Reflections
Week 4
- Monday, September 27
  - 3.8 Review of isometries of the plane
  - 4.1 Vectors
  - 4.2 Linear Independence
- Wednesday, September 29
  - 4.3 Midpoints
  - 4.4 Inner products
Week 5
- Monday , October 4 Homework 3 Due
  - 4.5 Law of cosines
  - 4.6 Triangle inequality
  - 4.7 Rotations and orthogonal transformations
- Wednesday, October 6
  - 5.1 Perspective drawing
  - 5.2 More perspectives
  - Exam 1 will be on 10/13/21 ( Review questions for Exam )
Week 6
- Monday, October 11 Homework 4 Due
  - 5.3 Projective planes and models
  - 5.4 Homogeneous coordinates
- Wednesday, October 13
  - Exam 1 (covering topics on syllabus through 5.2 of the text)
Week 7
- Monday, October 18 Homework 5 Due
  - 5.5 Projections
  - 5.6 Linear fractional maps of the projective line
  - 5.7 The cross ratio of 4 points on the projective line
- Wednesday, October 20
  - 5.8 Cross ratio as the basic invariant of 4 points on the projective line
  - Spherical Geometry and Elliptic geometry
Week 8
- Monday, October 25 Homework 6 Due
  - 5.8 More on cross ratios, Pappus theorem
- Wednesday, October 27
  - 6.1 Projective planes, Desarques theorem
  - Conic sections and projective geometry ( supplementary notes on plane conics)
Week 9
- Monday, November 1 Homework 7 Due
  - 7.1 Transformations of the Euclidean plane
  - 7.2 Transformations of the Cartesian plane
  - 7.3 Transformations of the Real Projective plane
- Wednesday, November 3
  - The Fundamental Theorem of Real Projective geometry
  - 7.4 Spherical and Elliptic geometry
Week 10
- Monday, November 8 Homework 8 Due
  - 7.4 Spherical triangles
- Wednesday, November 11
  - 7.5 Rotations of the sphere
Week 11
- Monday, November 15 Homework 9 Due
  - 7.6 Quaternions and rotations
- Wednesday, November 18
  - 7.7 Rotations of the tetrahedron
  - 7.8 Geometry of rotations
  - 7.9 Discussion
Week 12
- Monday, November 22 Homework 10 due
  - More Spherical Geometry
- Monday, November 29 (Wednesday schedule at Rutgers due to holiday)
  - Exam 2 will be on 11/29/21, covering sections on syllabus through 7.5 ( Review questions for Exam 2 )
Week 13
- Wednesday, December 1
  - 8.1 The complex upper half plane
  - 8.2 Conjugation
- Monday, December 6 Homework 11 Due
  - 8.3 Reflections and Mobius transformations
  - 8.4 NonEuclidean Lines
Week 14
- Wednesday, December 8
  - 8.5 Angles
  - 8.6 Non-Euclidean distance
- Monday, December 13 Homework 12 Due
  - 8.7 Non-Euclidean translations and rotations
  - 8.8 Non-Euclidean reflections
  - 8.9 Discussion
  - Review for final exam ( Review questions for Final Exam )