Conics and Cubics

1. Front Matter

   Pages i-x

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2. Intersections of Curves

   • Robert Bix

   Pages 1-68

3. Conics

   • Robert Bix

   Pages 69-125

4. Cubics

   • Robert Bix

   Pages 126-227

5. Intersection Properties

   • Robert Bix

   Pages 228-283

6. Back Matter

   Pages 285-292

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Algebraic curves are the graphs of polynomial equations in two vari­ 3 ables, such as y3 + 5xy2 = x + 2xy. By focusing on curves of degree at most 3-lines, conics, and cubics-this book aims to fill the gap between the familiar subject of analytic geometry and the general study of alge­ braic curves. This text is designed for a one-semester class that serves both as a a geometry course for mathematics majors in general and as a sequel to college geometry for teachers of secondary school mathe­ matics. The only prerequisite is first-year calculus. On the one hand, this book can serve as a text for an undergraduate geometry course for all mathematics majors. Algebraic geometry unites algebra, geometry, topology, and analysis, and it is one of the most exciting areas of modem mathematics. Unfortunately, the subject is not easily accessible, and most introductory courses require a prohibitive amount of mathematical machinery. We avoid this problem by focusing on curves of degree at most 3. This keeps the results tangible and the proofs natural. It lets us emphasize the power of two fundamental ideas, homogeneous coordinates and intersection multiplicities.

• Area
• Calc
• Grad
• Mathematica
• Microsoft Access
• Natural
• algebra
• algebraic curve
• algebraic geometry
• analytic geometry
• calculus
• class
• design
• proof
• topology

• Department of Mathematics, The University of Michigan-Flint, Flint, USA

  Robert Bix

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