Math 01.202 - Introduction to Geometry
Math 01.202 Introduction to Geometry 3 s.h.
Prerequisites: Basic Algebra II
This course develops the fundamental concepts of Euclidean geometry
from a modern point of view.
Its topics include sets, points, lines, space, betweeness, incidence, congruence, parallelism, similarity, transformations, volumes, and areas. Non-Euclidean geometries are introduced. Not open to mathematics majors. Use of calculators is required. Students are expected to have completed an equivalent of Intermediate Algebra.
Students will be able to:
1. Discuss a variety of great geometric ideas in ways that transcend
2. Use synthetic, analytic, and transformational techniques.
3. Discuss the similarities and differences between Euclidean and non-Euclidean geometries.
4. Apply the concepts of incidence, dimension, parallelism, congruency, similarity, self-similarity, perpendicularity, cardinality, and transformal geometry.
5. Use a variety of tools, physical models, and appropriate technology to develop and describe geometric concepts and relationships and their uses.
6. Demonstrate the kinds of proofs found in geometry.
7. Present written and oral arguments to justify conjectures and generalizations based on explorations.
1. History of Geometry
Theorems and proof
2. Geometric Constructions
Congruence, similarity, and incidence
Parallelism and perpendicularity
Extenstions to higher dimensions
3. Symmetry, Transformations and Equivalences
Reflections, rotations, translations
Isometries and symmetries
Self-similarity and fractal geometry
4. Non-Euclidean Geometries
Comparing euclidean and non-euclidean geometries
Concepts of infinities
Edward B. Burger and Michael Starbird: THE HEART OF MATHEMATICS, 2/E, Wiley, 2005.
L. Christine Kinsey and Teresa E. Moore: SYMMETRY, SHAPE, AND SPACE,
Key Collegle, 2002.
Gary L. Musser and Lynn E. Trimpe: COLLEGE GEOMETRY: A PROBLEM
APPROACH WITH APPLICATIONS, PrenticeHall, Upper Saddle, NJ, 1994.