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This book was written as a friendly introduction to plane algebraic curves.
IT'S FOR …
Mathematicians who never took a course on algebraic curves, or took one years ago and have forgotten most of it.
Students who are curious about algebraic curves and would like an easy-to-read account of what it is and what its major highlights are.
Anyone taking an elementary course on algebraic curves. This book can serve as a useful companion, supplying perspective and concrete examples to flesh out abstract concepts.
Outsiders who have heard that algebraic geometry is useful in attacking an increasingly wide range of applied problems and want an entry point that doesn't require an extensive mathematical background.
WHAT THIS BOOK IS, AND WHAT IT ISN'T.
What it is. This book emphasizes geometry and intuition, and the presentation is kept concrete. Learning about plane algebraic curves provides a foundation for going on to higher dimensional algebraic geometry. We work mainly over the complex numbers, where results are beautifully unified and consistent. You'll find an abundance of pictures and examples to help develop your intuition, so basic to understanding and asking fruitful questions. The book covers the highlights of the elementary theory which for some could be an end in itself, and for others an invitation to investigate further, including algebraic geometry and more general methods.
What it isn't. This is not a “Theorem, Proof, Corollary” book. Proofs, when given, are mostly sketched, some in more detail, but typically with less. We often include references to texts that provide further discussion.
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