Math 325

Summer 2017

Spring 2014

sphere

We will approach this study of geometry from four different directions:

  1. The classical (Greek) approach.
  2. The analytic approach using vector geometry and linear algebra.
  3. The projective approach.
  4. The geometric transformations approach.

Required Text: The four pillars of geometry, by John Stillwell.

Projects

Homework

  1. Page 6 # 1.2.1, 1.2.2, and Page 9 # 1.3.3, 1.3.5, 1.3.6 Solution
  2. Homework set 1 Solutions to Homework set 1
  3. Homework set 2 solutions homework set 2
  4. Homework set 3 Homework set 3 solutions
  5. Homework set 4 Homework set 4 solutions
  6. Homework set 5 #4.3.2, 4.3.3, 4.3.4, 5.1.1, 5.3.1, 5.3.3 Solutions to Homework set 5
  7. Homework set 6 Homework set 6 solutions
  8. Homework set 7 Solution Homework set 7
  9. Homework set 8 with solutions

Quizzes and Exams

  1. Quiz 1
  2. Quiz 2 Quiz 2 Solutions

Fall 2013

We will begin with a fairly classical approach to Euclidean geometry, discussing fundamental theorems of geometry, constructions with straightedge and compass, and so on. Some of the material might ring a bell from a high school geometry class, although our emphasis will be on the foundations of geometry  and the proofs of these results, we will include some computational aspect of geometry as well. Toward the end of the course, we will see a contrast to Euclidean geometry through a study of hyperbolic geometry and if we have time spherical geometry as well. Text:  A Survey of Classical and Modern Geometries, by Arthur Baragar, published by Prentice Hall.

Week 1

Week 2

Week 3

Week 4

Week of October 23rd (Section 1.7 and 1.8)

Week of November 4th

Week of November 19th

Week of November 25th

Spring 2013

We will begin with a fairly classical approach to Euclidean geometry, discussing fundamental theorems of geometry, constructions with straightedge and compass, and so on. Some of the material might ring a bell from a high school geometry class, although our emphasis will be on the foundations of geometry  and the proofs of these results, we will include some computational aspect of geometry as well. Toward the end of the course, we will see a contrast to Euclidean geometry through a study of hyperbolic geometry and if we have time spherical geometry as well. Text:  A Survey of Classical and Modern Geometries, by Arthur Baragar, published by Prentice Hall.

Schedule for 325 Handouts

Projects

Worksheets

 

—————————

Fall 2012

We will begin with a fairly classical approach to Euclidean geometry, discussing fundamental theorems of geometry, constructions with straightedge and compass, and so on. Some of the material might ring a bell from a high school geometry class, although our emphasis will be on the foundations of geometry  and the proofs of these results, we will include some computational aspect of geometry as well. Toward the end of the course, we will see a contrast to Euclidean geometry through a study of hyperbolic geometry and if we have time spherical geometry as well. Text:  A Survey of Classical and Modern Geometries, by Arthur Baragar, published by Prentice Hall. My notes for the course are here Syllabus

Worksheet

  1. worksheet 1
  2. Coordinates of center of mass
  3. Worksheet on construction

Lecture notes

  1. Mathematical Proofs
  2. Lecture notes Part I contains sections 0.2 , o.3, sections 1.1 and 1.3
  3. Lecture notes Part II contains sections 1.4, 1.5, 1.6, 1.7
  4. Vectors and Inner Products
  5. Lecture notes Section 1.8
  6. Lecture notes Section 1.10
  7. Incenter excicles, incircles
  8. Sections 3.1 3.2 3.3
  9. Section 3.4
  10. Chapter 6 and Chapter 7
  11. Geometrical Transformations

Mathematica Codes

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s