Contents
Foreword: MASS and REU at Penn State University xi
Preface xiii
Chapter 1. Various Ways of Representing Surfaces and
Basic Examples 1
Lecture 1 1
a. First examples 1
b. Equations vs. other methods 4
c. Planar models 8
d. Projective plane and flat torus as factor spaces 9
Lecture 2 11
a. Equations for surfaces and local coordinates 11
b. Other ways of introducing local coordinates 14
c. Parametric representations 16
d. Metrics on surfaces 17
Lecture 3 18
a. More about the M¨ obius strip and projective plane 18
b. A first glance at geodesics 20
c. Parametric representations of curves 22
d. Difficulties with representation by embedding 24
e. Regularity conditions for parametrically defined
surfaces 27
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