HIGH SCHOOL 2011–2012
Algebra II
This course is a rigorous examination of the theory of polynomial algebra. Topics will include: conic sections, rational roots, root finding algorithms, and graphing techniques. The course will be taught from the point of view of the general theory of functions. Applications will be taken from the physical sciences and will be chosen according to the preparedness of the class. Texts (for 2011 – 2012): Rusczyk, The Art of Problem Solving: Introduction to Algebra ; Rusczyk and Crawford, The Art of Problem Solving: Intermediate Algebra
Trigonometry and Analysis
Largely a continuation of Algebra II, this course will include a number of topics preparatory to beginning the Calculus and Physics sequence. In particular, the course will cover trigonometric functions, exponents and logarithms, probability and counting, recursive methods, and numerical techniques. Students will implement some general problem solving methods in Mathematica and, in general, will pursue a rigorous computational approach to the theory and applications of functions. Texts (for 2011 – 2012): Gelfand and Saul, Trigonometry; Rusczyk and Crawford, The Art of Problem Solving: Intermediate Algebra.
Calculus AB
This single year course in the Calculus of real variables will introduce the concepts of limit, derivative, and integral along with all the fundamental techniques and applications. This course will complete the syllabus attached to the AB Advanced Placement examination. In addition, the course will explore some applications of calculus to mechanics, biology, and chemistry. Text (for 2011 – 2012): Stewart, Calculus
Calculus BC (I and II)
A two year course in the Calculus of real variables, it largely focuses on the differentiation and integration of functions of a single variable. The material will also include infinite series and numerical methods. This course will complete all the material required by the BC Advanced Placement examination. In addition, the course will explore physical applications, some differential equations, and computational methods.Texts (for 2011 – 2012): Marsden and Weinstein, Calculus II and III.
Statistics
This course offers an introduction to probability, data analysis, and statistical inference. In addition to learning the mathematics of statistics, students will look critically at experiments in the sciences and social sciences with a focus on methods of experimental intervention and sampling. Students will collect and analyze their own data in survey projects to cement the topics covered.Texts (for 2011 – 2012): Moore and McCabe, Introduction to the Practice of Statistics; Gonick and Smith, Cartoon Guide to Statistics
PREVIOUS OFFERINGS
Advanced Topics in Calculus (2010 – 2011)
This course will begin with a discussion of Differential Equations and Dynamical Systems, with an emphasis on those topics arising in the Biological Sciences. Standard theoretical techniques will be covered, but the course will largely center on numerical methods and associated modeling issues. Specific topics will include Population Statistics, Predator/Prey equations, and Evolutionary Dynamics. Where feasible, we will use computer simulations to investigate the behavior of the systems we are studying.Texts (for 2010 – 2011): Robert Devaney, Morris W. Hirsch, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd Edition; Martin A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life)
|
|
