 Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk. |
(Click here for the complete list of courses)
From students
"This is the most wonderful math course I have ever had. I could not have progressed so fast without this class."
"This was a great course; it taught me many things that I probably couldn't have learned otherwise."
"Great Job Art of Problem Solving! This is by far the best mathematical experience I have ever met!"
This course covers the introduction and evaluation of trigonometric functions, trigonometric identities, complex numbers, exponential form of complex numbers, De Moivre's Theorem, geometric representation of complex numbers, roots of unity, applications of complex numbers to geometry, two-dimensional and three-dimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry. (Note: This course used to be called "Intermediate Trigonometry/Complex Numbers." This course contains seven weeks of material covering two- and three-dimensional vector spaces that the old course did not include.)
Week 1: Basic Trigonometry
Week 2: Graphs of Trig Functions and Inverse Trig Functions
Week 3: Trigonometric Identities I
Week 4: Trigonometric Identities II
Week 5: Laws of Sines and Cosines
Week 6: Geometry with Trigonometry
Week 7: Introduction to Complex Numbers and the Complex Plane
Week 8: Trigonometry and Complex Numbers
Week 9: Exponential Form and Roots of Unity
Week 10: Applications of Complex Numbers to Geometry I
Week 11: Applications of Complex Numbers to Geometry II
Week 12: Vectors and Matrices in Two Dimensions I
Week 13: Vectors and Matrices in Two Dimensions II
Week 14: Vectors and Matrices in Three Dimensions I
Week 15: Vectors and Matrices in Three Dimensions II
Week 16: Beyond Three Dimensions
Week 17: Applications of Vectors to Geometry
Week 18: Challenging Problems and Extensions
Students should have completed algebra II or an equivalent course before taking this class. Students who have already taken a standard trigonometry or pre-calculus class should not simply assume this class is too easy for them. Instead, they should take the diagnostic test below to determine if this class is appropriate for them. Similarly, a student who has completed an algebra II course should consider taking our Algebra 3 class prior to taking our Precalculus class. Our Algebra 3 class includes the non-trigonometric topics of a typical precalculus class, plus a great many interesting topics left out of most standard curricula.
We recommend trying the following tests to determine whether the class is appropriate for you:
Are You Ready?
Do You Need This?
This course requires the Art of Problem Solving textbook Precalculus, which will be released in fall, 2009. The price of the book is included in the fee for the course.
|
|
