User:Marty/UCSC Math 110 Fall 2008/Week 4

This week, we are covering the basic properties of topographs of binary quadratic forms. These topics belong to the binary quadratic forms cluster.


 * The Covers::Def/Range topograph of a Covers::Def/Binary quadratic form. The Covers::State/Arithmetic progression rule for binary quadratic forms, and using it to extend the range topograph from three adjacent values.  The fact that Covers::State/Binary quadratic forms are uniquely determined by their values at a superbasis, and how to recover a binary quadratic form from its range topograph.
 * Rivers and lakes in the range topograph. Analyzing the topography with the Covers::Def/Discriminant of a binary quadratic form.  The behavior near lakes.  The geometry of rivers.  Double-lakes.
 * Covers::State/Climbing in topographs, Covers::State/The domain topograph has no loops.