The number theory discussed in this book concerns counting the number of solutions to systems of equations of various kinds. For example, in Part I, we counted the number of solutions to a system of two polynomial equations. We discussed Bézout’s Theorem, which tells us how many solutions to expect when we count properly.

In other contexts, as we will see shortly, we indulge in an infinite sequence of counts. For example, a problem may depend on a parameter that takes on the values 0, 1, 2, …. The result of our counting is then an infinite sequence of counts.

EP - 180 PB - Princeton University Press PY - 2012 SN - 9780691151199 SP - 161 T2 - Elliptic Tales T3 - Curves, Counting, and Number Theory UR - http://www.jstor.org/stable/j.ctt7sx3k.16 Y2 - 2021/03/03/ ER -