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:
- Chapter introduction
- §1.1: A few properties of the inner product
- §1.4: Simple curves and their lengths
- §§1.4 and 1.5 About the integral used in the
definition of angular measure
- §1.5: A concrete interpretation of angular measure
- [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:
- §2.2: angles with a given angular measure
- Preview of Chapter 3: another viewpoint about angular measure
- §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:
- Heron's formula (Theorem 8 in Section 4.5)
- §4.4: Another proof of Theorem 7
- §4.4: A proof of Theorem 8
- §4.7: The barycentric coordinates of the incenter
- Chapter 5: The inner product and the cosine
- Chapter 5: The cosine function, the inner product,
and right angle trigonometry
- §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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