Courses course description course schedule tuition
IDEA MATH provides in-depth enrichment in important mathematical areas, particularly in those fields from which contests problems are drawn: algebra, combinatorics, geometry, and number theory. The program provides five major series for students with different mathematical backgrounds. Each series consists of several 6-weeks courses. All classes meet on Saturdays during the school year. We have tried our best to avoid SAT test dates, major competition (MATHCOUNTS, HMMT, etc.) dates and school vacations. [See courses schedule]
Math Roots Series back to list check schedule
Math Roots is best for students just beginning their problem-solving careers, perhaps at the level of the MATHCOUNTS School and Chapter rounds. We help them to gain a solid grasp of the fundamental algebra and geometry skills that will guide them throughout the rest of middle school and high school. To start, students will master algebraic manipulation: how to setup variables and equations for word problems; how to solve linear equations (with one or more variables); how to solve quadratic and selected higher-degree equation; how to solve equations with radicals and absolute values; the basics of polynomial multiplication and division, and how to graph lines and other functions and understanding the meaning of the graphs. We will also visit the essential ideas with measurements, shapes, special figures, congruence, and geometric computations with areas, lengths, and angles. We also develop students' number sense including divisibility rules, bases, simple Diophantine equations and their applications, as well as their understanding of logic and counting and probability, specifically in terms a case analysis and the Addition and Multiplication principles. We will guide students to improve their abilities to communicate ideas and reasoning both orally and in written presentations. We highly recommend this course to all budding math whizzes - without good study habits and a solid grasp of these concepts, they may make progress for a year or two, but eventually, they will hit a wall through which one cannot break without an appreciation for the fundamentals.
Beyond MATHCOUNTS Series back to list check schedule
Beyond MATHCOUNTS is for serious students at the MATHCOUNTS level who wish to prepare for the State and National rounds while solidifying and deepening their command of algebra and geometry. We explore basic analytic geometry, 2D and 3D vector operations and linear parametric equations; then we walk them through the core of Euclidean geometry. Topics of study include: shapes of polygons; circles; intercepted arcs; congruence and similarity; the basics of angle chasing; the Power of a Point Theorem; the Pythagorean Theorem and its 3D analogues, calculating lengths and areas, and applying trigonometry in right triangles. We introduce students to divisibility, bases, prime and relatively prime integers and other number theoretic concepts as well as a powerful tool for application - modular arithmetic and congruence. Counting skills become critical: the Addition and Multiplication principles, permutations and combinations, and binomial coefficients and Pascal's Triangle. To help students develop their problem-solving skills and strengthen their conceptual understanding instead of memorizing formulas, we incorporate problems that apply their knowledge creatively and apply seemingly detached ideas.
Math Circles Series back to list check schedule
Math Circles will help experienced math students extend their grasp of algebraic and geometric tools and apply them to combinatorial and number theoretic problems. We start with the fundamental elements of Euclidean geometry: triangle centers, cyclic quadrilaterals, the Power of a Point Theorem, the Euler Line, Ceva's Theorem; barycentric coordinates, polar coordinates, and other non-Cartesian coordinate systems; the law of sines, the law of cosines and its vector form, relations between trigonometric functions; vector operations, analytic transformations, and non-calculus approaches to limit situations as well as optimization. We discuss unit circle trigonometry; circular parametric equations; the surprising ubiquity of trigonometry and its applications; polygons, circles, parabolas, cones, prisms, pyramids, and related 3D polyhedra. We also provide an overview of basic properties of functions and their applications with a focus on exponential and logarithmic relations and recursive sequences. From there, we review the fundamentals of counting, from Pascal’s Triangle, basic combinatorial identities and Inclusion-Exclusion, and then unite what we know to discuss intensive techniques such as double-counting, bijection, and – a profound application of algebra – generating functions.
Math Challenge Series back to list check schedule
Mathematical Proofs Series (MP1, MP2, MP3, MP4) back to list check schedule
The math proofs series constitutes an introduction to formal proof-based mathematics with a focus on preparing students for the next step in mathematical problem-solving and introducing them to the mathematical studies they will see in college. Through helping students to construct their own proofs and assess the validity of others’, we will teach students to understand and master increasingly demanding levels of rigor and to deal with more sophisticated mathematical notation. The following topics are explored: axiomatic structures; the principle of mathematical induction; proofs by contradiction; the Pigeonhole principle, well-ordering and other existence arguments; mathematical logic; elementary set theory; countable and uncountable sets; injections, surjections and bijections between sets; elementary combinatorics and properties of binomial coefficients; fundamental theorems in Euclidean geometry, and concepts of abstract structure and isomorphism. The plethora of topics will assist the students in answering the fundamental question of this course: What is a mathematical proof, and what is not? This is also the first course in which we delve into college-level number theory through an exploration of unconventional number theory and algebra problems, many of them presented in an original fashion. Students will encounter: properties of divisibility; congruence; Fermat’s Little Theorem, Euler’s Totient Function, and Wilson’s Theorem as well as fundamental algebraic inequalities and their proofs and applications -- Cauchy-Schwarz, Schur’s Inequality, and the Power Mean Inequality Chain. As the problems grow more and more difficult, we assign fewer and fewer – and we don’t expect students to solve all of them – but they will find each one beautiful and instructive, as they are hand-picked from college textbooks and high-school mathematical contests from around the world.
Small Group and Private Lessons back to list more ...
Lessons for all levels of math competitions and standard tests can be arranged to suit small group or individual needs. Please call (603)772-2336 to inquire.