Introduction to Algebraic Geometry

<p>In algebraic geometry you will study those curves, surfaces, and higher-dimensional generalizations which can be described with polynomial equations. The polynomial coefficients will usually be complex numbers, but could also lie in any field. In the beginning of the course you will study second- and third-degree curves using elementary mathematics, and quite a lot can be done with such methods. But we will also see the need for new algebraic tools, which we introduce when the need arises. The course ends with a study of the fascinating geometry of cubic surfaces.</p>