Topics to be covered include Kolmogorov's axiomatic setup for probability, events, independence, and conditioning. Students develop the technique of probability trees, and do a detailed study of the binomial, hypergeometric, negative binomial and uniform distributions. Students establish and apply combinatorial techniques to solving probability problems, and if time permits, study finite-state markov chains. In this course, the student's knowledge of systems of linear equations is extended. Students solve systems with two, three and four unknowns and learn to use matrices.
Study includes inverse, identity and augmented matrices.
Students use determinants to solve equations and learn Cramer's rule. In addition to pure computation, the students also learn to use graphing calculators to solve matrix equations. Students are introduced to theories of Linear Algebra and solutions for MxN matrices. Full Year Math Research prepares students for participation in the U.S. Mathematics Olympiads and the Westinghouse Science competitions by conducting research in advanced topics in pre-calculus mathematics. Permission of math faculty.