Download 161_syllabus

Math 161 Suggested Syllabus
Text: Geometry with Geometry Explorer, M. Hvidsten, UCI Custom Reprint.
Lecture
1
2
3
4
5
Section
1.1, 1.2
1.4, 1.5
1.6
2.1
2.2
6
2.4, 2.5
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
2.6
3.1, 3.2
3.4, 3.5
3.6
----4.1
4.3
7.1
7.2
7.3
7.3
7.4, 7.5
7.6
7.8
----9.1, 9.2
9.3
9.5
9.6
9.8
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Topic
Introduction to Geometry
Axiomatic Method, Properties of Axiomatic Systems
Euclid’s Axiomatic Geometry
Angles, Lines and Parallels
Congruent Triangles and Pasch’s Axiom
Measurement and Area in Euclidean Geometry, Similar
Triangles
Circle Geometry
Cartesian Coordinate System, Vector Geometry
Angles in Coordinate Geometry, The Complex Plane
Birkhos Axiomatic System for Analytic Geometry
Review
Midterm # 1
Euclidean Constructions
Constructibility
Background and History of Non-Euclidean Geometry
Models of Hyperbolic Geometry
Basic Results in Hyperbolic Geometry
cont.
Saccheri Quadrilateral, Lambert Quadrilateral and triangles
Area in Hyperbolic Geometry
Models and Isomorphism
Review
Midterm # 2
Introduction to Fractal Geometry, Self-Similarity
Similarity Dimension
Contraction Mappings and the Space of Fractals
Fractal Dimension
Algorithmic Geometry
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).