Math 5335      Fall 2005   (Section 2)
Text supplements

Last update: Tuesday, December 6, 2005

The following materials are posted here:

• A few writeups that explain how different parts of the text relate to one another.
• Explanations about some difficult points in the subject matter, and alternative ways of looking at certain proofs.
   

The following materials are currently available:

• General introduction   (Same as the Online course description)
   
• Chapter 1 supplements   These relate to the Fall 2004 version of the text, corresponding to Chapters 1 and 2 of the Fall 2005 version
  Topics include:
  1. Chapter introduction  
  2. §1.1: A few properties of the inner product
  3. §1.4: Simple curves and their lengths
  4. §§1.4 and 1.5 About the integral used in the definition of angular measure
  5. §1.5: A concrete interpretation of angular measure
  6. [optional]   Angular measure: our definition compared with protractor measure
      
• Chapter 2 supplements   This relates to the Fall 2004 version of the text, corresponding to Chapter 3 of the Fall 2005 version
  Topics include:
  1. §2.2: angles with a given angular measure
  2. Preview of Chapter 3: another viewpoint about angular measure
  3. §2.4: the outward angles of a triangle
      
• Chapter 4 and 5 supplements   This has been updated, to correspond to the current (Fall 2005) version of the text.
  Topics include:
  1. Heron's formula (Theorem 8 in Section 4.5)
  2. §4.4: Another proof of Theorem 7
  3. §4.4: A proof of Theorem 8
  4. §4.7: The barycentric coordinates of the incenter
  5. Chapter 5: The inner product and the cosine
  6. Chapter 5: The cosine function, the inner product, and right angle trigonometry
  7. §5.4: About the law of cosines
      
• Hyperbolic area and angular measure in Poincaré triangles
  This material pertains to Theorem 18 in §10.5.

Comments and questions to:  roberts@math.umn.edu

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