Math 362: Survey of Geometry - Revision history

Ls5: /* Offered */

2016-02-05T20:43:53Z

‎Offered

Ls5: moved Math 362 to Math 362: Survey of Geometry

2013-04-03T22:06:41Z

moved Math 362 to Math 362: Survey of Geometry

Cpg: /* Desired Learning Outcomes */

2010-07-28T16:12:30Z

‎Desired Learning Outcomes

Show changes

Cpg: /* Desired Learning Outcomes */

2010-07-28T16:03:59Z

‎Desired Learning Outcomes

Cpg: /* 9. Van Hiele Levels */

2010-07-28T16:02:37Z

‎9. Van Hiele Levels

Dgw4 at 21:42, 20 May 2010

2010-05-20T21:42:03Z

Dgw4: This is a major edit.

2010-05-20T21:35:53Z

This is a major edit.

Cpg: /* Prerequisite */

2009-06-04T18:57:51Z

‎Prerequisite

Cpg at 17:23, 9 May 2008

2008-05-09T17:23:27Z

Cpg at 15:31, 9 May 2008

2008-05-09T15:31:54Z

@@ Line 8: / Line 8: @@
 === Offered ===
-F, W, Su
+F, W, Sp
 === Prerequisite ===

@@ Line 23: / Line 23: @@
 === Minimal learning outcomes ===
-<div style="-moz-column-count:2; column-count:2;">
+Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts, and prove many of the theorems.
 </div>
-a.	Understand the historical importance of Euclid’s Elements.
+====1.	====
 b.	Understand and interpret Euclid’s definitions, axioms, and common notions.

@@ Line 138: / Line 138: @@
 ====9.	Van Hiele Levels====
 a.	Be familiar with the van Hiele Model of the development of geometric thought.
 === Additional topics ===

@@ Line 29: / Line 29: @@
 Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts, and prove many of the theorems.
-.	Euclid’s Elements
+====1.	Euclid’s Elements====
 a.	Understand the historical importance of Euclid’s Elements.
@@ Line 37: / Line 37: @@
 c.	Identify the logical gaps in Euclid’s proofs.
-.	Axiomatic Systems and Incidence Geometry
+====2.	Axiomatic Systems and Incidence Geometry====
 a.	Give examples of axiomatic systems and understand the axioms for Incidence Geometry.
@@ Line 47: / Line 47: @@
 d.	Write direct and indirect proofs of theorems of Incidence Geometry.
-.	Set Theory and Real Numbers
+====3.	Set Theory and Real Numbers====
 a.	Understand basic facts from set theory including sets, elements, intersections, unions, and distinguish between “element of” and “subset of.”
@@ Line 55: / Line 55: @@
 c.	Understand the properties of the real numbers including trichotomy, density of rational numbers, the Archimedean property, and the least upper bound property.
-.	Axioms for Plane Geometry
+====4.	Axioms for Plane Geometry====
 a.	Identify undefined terms for neutral geometry.
@@ Line 75: / Line 75: @@
 i.	Understand the Euclidean, elliptic, and hyperbolic parallel postulates and examples of geometries that satisfy each of the parallel postulates.
-.	Theorems in Neutral Geometry
+====5.	Theorems in Neutral Geometry====
 a.	Prove theorems about isosceles triangles and perpendicular lines.
@@ Line 93: / Line 93: @@
 h.	Be able list and prove that statements are equivalent to the parallel postulate.
-.	Basic Theorems of Euclidean Geometry
+====6.	Basic Theorems of Euclidean Geometry====
 a.	Prove and understand the Euclidean theorems about parallel lines cut by a transversal.
@@ Line 109: / Line 109: @@
 g.	Work with triangles including altitudes, medians, angle bisectors and perpendicular bisectors.  Prove and understand the concurrency theorems and the Euler Line Theorem.
-.	Hyperbolic Geometry
+====7.	Hyperbolic Geometry====
 a.	Prove and understand the angle sum theorem for triangles and define the angle defect of a triangle.
@@ Line 123: / Line 123: @@
 f.	Model the hyperbolic plane with the Poincaré disk or the upper half plane.
-.	Transformations
+====8.	Transformations====
 a.	Contrast the transformational perspective with the Euclidean perspective of Euclid.
@@ Line 136: / Line 136: @@
-.	Van Hiele Levels
+====9.	Van Hiele Levels====
 a.	Be familiar with the van Hiele Model of the development of geometric thought.

@@ Line 14: / Line 14: @@
 === Description ===
-Logical and historical development of Euclidean and non-Euclidean geometry, transformations and symmetry; relationships among axiomatic systems; use of software and other geometric models; proofs and Van Hiele levels.
+This course studies the foundations of geometry going back more than two thousand years to Euclid and the ancient Greeks.  This course is especially aimed at understanding the importance of Euclid’s parallel postulate and the alternative non-Euclidean geometries that arise from alternative axioms.  This course places an emphasis on logical thinking and clear mathematical writing.  Geometry software such as Geometer’s Sketchpad should be used throughout the course when appropriate.
 == Desired Learning Outcomes ==
+Students should gain familiarity with axioms of geometry, both Euclidean and non-Euclidean.  Students should be able to prove the major theorems of geometry based on the axioms.
 === Prerequisites ===
 === Minimal learning outcomes ===
@@ Line 25: / Line 26: @@
 </div>
 === Additional topics ===
 === Courses for which this course is prerequisite ===
 [[Category:Courses|362]]

← Older revision	Revision as of 22:06, 3 April 2013
(No difference)

@@ Line 11: / Line 11: @@
 === Prerequisite ===
-[[Math 112]], [[Math 190|190]].
+[[Math 290]].
 === Description ===

← Older revision		Revision as of 15:31, 9 May 2008
Line 1:		Line 1:
		+	== Catalog Information ==
		+
		+	=== Title ===
		+
		+	=== (Credit Hours:Lecture Hours:Lab Hours) ===
		+
		+	=== Offered ===
		+
		+	=== Prerequisite ===
		+
		+	=== Description ===
		+
		+	=== Note ===
		+
	== Desired Learning Outcomes ==		== Desired Learning Outcomes ==