Math 1312
Introduction to Mathematical Reasoning

Prerequisites: Credit for or placement out of Math 1310 or Math 1311.

Textbook: Elementary Geometry for College Students, Daniel C. Alexander and Geralyn M. Koeberlein, 4th edition, Houghton Mifflin Company, 2007, ISBN-10: 0-618-64525X

Course Description:  Credit 3 hours (3-0). Principles of logic and proof, set theory, formal and informal geometry.  May not apply toward a degree from the College of Natural Sciences and Mathematics.

Supplies: A small ruler and compass will be needed for some sections and a calculator will be needed for most sections.

Spring 08 Syllabus

Chapter 1 —Foundations of Geometry

1.1 Inductive and Deductive Reasoning
1.2 Points, Lines, and Planes
1.3 Segments, Rays, and Angles
1.4 Introduction to Deductive Proofs
1.5 Formalizing Geometric Proofs
1.6 Relationships:  Parallel and Perpendicular Lines
1.7 Formal Proofs of Theorems

Chapter 2 — Triangles

2.1 Classifying Triangles
2.2 Congruent Triangles
2.3 Proofs Involving Congruence
2.4 Isosceles Triangles, Medians, Altitudes, and Concurrent Lines
2.5 Proving Right Triangles Congruent
2.6 Constructions Involving Triangles

Chapter 3 —Parallel Lines and Polygons

3.1 Indirect Proof and the Parallel Postulate
3.2 Transversals and Angles
3.3 Polygons and Angles
3.5 Define and Use Triangle Inequality Theorems

Chapter 4 — Quadrilaterals

4.1 Parallelograms
4.2 Rhombus and Kite
4.3 Rectangles and Squares
4.4 Trapezoids

Chapter 5 — Similar Polygons and the Pythagorean Theorem

5.1 Ratio and Proportion
5.2 Similar Polygons
5.3 Properties of Right Triangles
5.4 Pythagorean Theorem
5.5 Inequalities Involving Triangles
5.6 Segments Divided Proportionally in Triangles

Chapter 6 — Circles

6.1 Circles and Related Segments and Angles
6.2 More Angle measures in a Circle
6.3 Line and Segment Relationships in the Circle
6.6 Concurrence of Lines

Chapter 7 — Area of Polygons and Circles

7.1 Area and Initial Postulates
7.2 Perimeter and Area of Polygons
7.3 Regular Polygons and Area

Chapter 8 — Solid Geometry

8.1 Planes and Polyhedrons
8.2 Prisms
8.3 Pyramids
8.4 Cylinders and Cones and Spheres