I.1. The Algebra of Sets

I.2. Intervals and Linear Inequalities

I.3. Functions and their Basic Properties

I.4. Functions Given by Simple Formulas

I.5. Manipulating Functions

I.6. Piecewise Functions

I.7. Functions on Subsets of the Plane

I.8. Linear Systems and Feasible Sets

II.1. Vectors and Translation

II.2. Scaling Vectors and Subsets of the Plane

II.3. Scaling Quantities

II.4. Movement along Lines

II.5. Orthogonality and Reflection

II.6. Inverse Functions

II.7. Describing Rotation in Cartesian Coordinates

II.8. Polar Coordinates and Rotation

II.9. Involution

III.1. Lines and Planes

III.2. Polynomial Functions

III.3. Rational Functions

III.4. Solving Piecewise Rational Inequalities

III.5. Orders of Intersection

III.6. Rigidity of Tangential Intersections 

IV.1. Introduction to Symmetry

IV.2. Translational Symmetry

IV.3. Symmetric Change

IV.4. Symmetry of Tangential Intersections