Lecture Section Topic
1 1.1, 1.2 Introduction to Geometry
2 1.4, 1.5 Axiomatic Method, Properties of Axiomatic Systems
3
4
1.6 Euclid’s Axiomatic Geometry
2.1 Angles, Lines and Parallels
5
6
7
2.2 Congruent Triangles and Pasch’s Axiom
2.4, 2.5
Measurement and Area in Euclidean Geometry, Similar
Triangles
2.6 Circle Geometry
8 3.1, 3.2 Cartesian Coordinate System, Vector Geometry
13
14
15
16
9 3.4, 3.5 Angles in Coordinate Geometry, The Complex Plane
10 3.6 Birkhos Axiomatic System for Analytic Geometry
11
12
--- Review
--- Midterm # 1
4.1 Euclidean Constructions
4.3 Constructibility
7.1 Background and History of Non-Euclidean Geometry
7.2 Models of Hyperbolic Geometry
17
18
7.3 Basic Results in Hyperbolic Geometry
7.3 cont.
19 7.4, 7.5 Saccheri Quadrilateral, Lambert Quadrilateral and triangles
20 7.6 Area in Hyperbolic Geometry
21
22
7.8 Models and Isomorphism
--- Review
23 --- Midterm # 2
24 9.1, 9.2 Introduction to Fractal Geometry, Self-Similarity
25
26
27
9.3 Similarity Dimension
9.5 Contraction Mappings and the Space of Fractals
9.6 Fractal Dimension
28 9.8 Algorithmic Geometry
29 --- Review
* Note: Instructors may choose to replace the Fractals topic with either the Symmetry or Transformational
Geometry chapters. In addition, if time permits 2-3 lectures about Knot Theory may be added to the course
(from instructor notes).