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".
- Re-submit 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.
- Re-submit 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 Diophantus-Brahmagupta-Fibonacci 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) |