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Class XII Math Course Descriptions

FUNDAMENTALS OF CALCULUS: concepts, techniques and applications of differential and integral calculus paced to allow both depth and exploration.

CALCULUS: differential and integral calculus of functions of one variable with applications. Students wishing to take the College Board AP AB calculus exam will find that this course provides suitable preparation.

LINEAR ALGEBRA: vectors, linear transformations, general vector spaces and the algebra of matrices.

ADVANCED CALCULUS: differential and integral calculus of functions of one variable with applications; power series. Students wishing to take the College Board AP BC calculus exam will find this course provides suitable preparation. After the AP exam students study combinatorics and probability.

STATISTICS AND STATISTICAL MODELING: introduction to the practice of statistics. Topics include organization of data, probability and random variables and drawing inferences from data. Computers and calculators are used extensively.

CHAOS THEORY AND FRACTALS: chaos theory, a cutting-edge field of math that took off with the advent of modern computing, has applications in everything from meteorology to the stock market and beyond. This course studies fundamental ideas in chaos theory and the mathematical discipline of dynamical systems, an area of math focused on systems that change over time. Starting with the idea of iteration, students will explore how small changes in initial conditions can produce big differences in outcomes and come to understand a hallmark of chaos theory and dynamics: Even the most simple and deterministic systems can produce unpredictable behavior and even the most complex systems can reveal some kind of order. Finally, students will see how these ideas apply to the beautiful world of fractals, including the Julia sets and the Mandelbrot set. This course is offered through the Interschool consortium.

COLLABORATIVE PROBLEM-SOLVING: collaborative exploration of problem-solving skills and strategies including topics from combinatorics, number theory, advanced algebra, geometry, probability and graph theory. Problems studied include examples from past AIME and US Math Olympiad competitions. This course is offered through the Interschool consortium.

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