Department of Mathematics

Syllabus

**Math 01.202 - Introduction to Geometry**

**CATALOG DESCRIPTION:**

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.

**OBJECTIVES:**

Students will be able to:

1. Discuss a variety of great geometric ideas in ways that transcend
mathematics.

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.

**CONTENT:**

1.** History of Geometry**

Theorems and proof

Pythagorean Theorem

Golden Rectangle

Axioms

2. Geometric Constructions

Congruence, similarity, and incidence

Parallelism and perpendicularity

Polyhedra

Duality

Extenstions to higher dimensions

3. Symmetry, Transformations and Equivalences

Reflections, rotations, translations

Isometries and symmetries

Topological equivalence

Projections

Self-similarity and fractal geometry

4. **Non-Euclidean Geometries**

Axiomatic systems

Finite geometries

Spherical geometry

Hyperbolic geometry

Comparing euclidean and non-euclidean geometries

Concepts of infinities

**TEXTBOOKS:
**

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
SOLVING
APPROACH WITH APPLICATIONS, PrenticeHall, Upper Saddle, NJ, 1994.