Textbook: None. But I do recommend John Stillwell's Numbers and Geometry.
Here is the course syllabus.
Here is the daily agenda from the course.

In Class Work 
Homework 
The Pythagorean Theorem 
 What is the Pythagorean Theorem?
 Why is it true?
 Is it true?
 Definition of Triangle on a Sphere
 Area of a Triangle on a Sphere
 Record of What We Did

 Find a proof of the Pythagorean Theorem.
 Present it to the class.
 Write it up and hand it in.
 Investigate Pythagoras of Samos.
 Investigate Euclid of Alexandria.

Surface Area of a Sphere 
 What is Area? What is Volume?
 Dimensions X 1/2 = Volume X 1/8
 Volume of a Tetrahedron
 Volume of a Cone
 Volume of a Sphere
 Surface Area of a Sphere
 Record of What We Did

 Find a proof of 4\pi r^2 using Calculus.
 Present it to the class.
 Investigate Archimedes of Syracuse.
 Investigate "hyperspheres".
 Resubmit your proof of Pythagorean Theorem.

Cartesian Coordinates 
 What is Space?
 Cartesian Coordinates
 Equation of a Circle
 Equation of a Line
 Intersection of Lines and Circles
 Record of What We Did

 Investigate René Descartes.
 Investigate Pierre de Fermat.
 Investigate equations of planes/lines in R^3.
 Choose your favorite mathematician. Write a one page summary.

Vectors 
 Distance betwenn points in R^3
 Equation of a Sphere in R^3
 Equation of a Plane/Line in R^3?
 What is a Vector?
 Equivalence of Vectors
 Addition/Subtraction of Vectors
 The Dot Product!
 Record of What We Did

 Read this history of vectors.
 Choose a topic for Independent Study 1.
 Go to the library and get a book for IS1.
 Submit a list of sources for IS1.
 Set up a meeting with me to discuss IS1.
 Resubmit PT and sketch of mathematician.

The Dot Product 
 Definition of the Dot Product
 When are two vectors perpendicular?
 The Law of Cosines
 Angles Between Vectors
 Methane Molecules
 Equation of a Plane in R^3
 Parametrized Lines in R^3
 Record of What We Did

 Find a proof of the Law of Cosines and be prepared to share it with us.
 Hand in a 1 or 2 page outline of your Independent Study 1, including bibliography.
 Hand in your Independent Study 1.

Independent Study 1, due October 14 (Suggested Topics) 
Pythagorean Triples 
 Pythagorean Triples
 Euclid's Trick
 Diophantus' Trick
 Rational Points on Circles
 Fermat's Christmas Theorem

 Look up "Plimpton 322".
 Look up Diophantus of Alexandria.
 Write up your favorite proof of the Law of Cosines and hand it in.
 Look up Hypatia of Alexandria.
 Look up Fermat's Christmas Theorem.

Funny Numbers 
 The DiophantusBrahmaguptaFibonacci Identity
 A Funny Multiplication on R^2
 The Square Root of 1
 De Moivre's Formula
 Rotations of the Plane

 Look up Brahmagupta.
 Look up Fibonacci.
 Look up De Moivre and his formula.
 Look up Hypatia of Alexandria.
 Look up Fermat's Christmas Theorem.
 Look up Carl Friedrich Gauss and the Fundamental Theorem of Algebra.

Independent Study 2, due December 9 (Suggested Topics) 