# MAT 347 Modern Geometry

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### Course Description

MAT 347 covers topics in synthetic and analytic geometry; transformations, similarity, congruence, distance, angles, constructions; introduction to projective and/or non-Euclidean geometry.

MAT 347 meets for three hours of lecture per week.

### Prerequisites

Students must have earned a grede or "C" or better in courses equivalent to MAT 211 and MAT 271 to be eligible to enroll in MAT 347.

### Objectives

After completing MAT 347 the student should be able to

• understand Euclidean geometry as a deductive system
• use the basic assumptions, techniques, and constructions of Euclidean geometry: parallel postulate, construction of triangles, congruence, similarity, angles, transformations, the Pythagorean theorem, circles, trigonometric ratios, to prove theorems and solve applied problems in two and three dimensions
• demonstrate an understanding of the basic synthetic and analytic theory of conic sections and its uses
• understand the consequences of the Euclidean parallel postulate and be familiar with at least one example of a non-Euclidean geometry e.g. spherical geometry, hyperbolic geometry, the geometry of curved surfaces
• demonstrate familiarity with the use of other non-classical geometries: e.g. projective geometry, Minkowski geometry
• use the theory of conic sections, and non-Euclidean and non-classical geometries to solve applied problems
• write coherent and readable deductive arguments and proofs.

### Expected outcomes

Students should be able to demonstrate through written assignments, tests, and/or oral presentations, that they have achieved the objectives of MAT 347.

### Method of Evaluating Outcomes

Evaluations are based on homework, class participation, short tests and scheduled examinations covering students' understanding of Euclidean and non-Euclidean geometry, deductive reasoning, applications of geometry to applied problems, and related topics that are covered in MAT 347.

### Text

Modern Geometry with Applications, by George Jennings. Springer-Verlag, 1994.

• 1. Euclidean Geometry
• 2. Spherical Geometry
• 3. Conics
• 4. Projective Geometry
• 5. Special Relativity

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in MAT 347. The instructor determines the relative weights of these factors.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates and Make-Up Work

Due dates and policy regarding make-up work are set by the instructor.

### Schedule of Examinations

The instructor sets all test dates except the date of the final exam. The final exam is given at the date and time announced in the Schedule of Classes.