 # Algebra

This class will build on concepts learned in the Pre-Calculus and Introduction to Calculus courses. Students will learn advanced concepts that include polynomials, inequality, radicals, and functions. This class is designed to expand on the Algebra and Pre-Calculus curriculum to introduce students to the problem solving strategies required for success on the AMC and AIME competitions. ##### Who is this course for
This course is for students who have completed our Introduction to Algebra course.
This course typically takes 3-6 months to complete. This depends on the student's experience and how fast they can master the concepts and the knowledge. Our instructors move at the pace of the student, it may take extra time for some students to reinforce what they have learned.
##### Curriculum
###### Chapter 1: Basic Techniques for Solving Equations Solving system of equations by substitution and elimination
###### Chapter 2: Functions Review Definition of functions, graph of functions, composition, and inverse functions
###### Chapter 3: Complex Numbers Arithmetics of complex numbers, complex plane Factoring, Vieta’s formulae, discriminant, quadratic inequalities
###### Chapter 5: Conics Parabolas, Circles, Ellipses, Hyperbolas
###### Chapter 6: Polynomial Division Division, synthetic division, remainder theorem
###### Chapter 7: Polynomial Roots I Factor Theorem, Fundamental Theorem of Algebra
###### Chapter 8: Polynomial Roots II Irrational and complex roots, Vieta’s Formula
###### Chapter 9: Factoring Multivariable Polynomials Grouping, sums and differences of powers
###### Chapter 10: Sequences and series Arithmetic series and sequences, geometric series and sequences, summation and product notation
###### Chapter 11: Identities, Manipulations, and Induction Brute Force, Induction, Binomial Theorem
###### Chapter 12: Inequalities Trivial and AM-GM inequality, Cauchy Schwarz inequality
###### Chapter 13: Exponents and Logarithms Exponential Functions, Properties of Logarithm Working with expressions with radicals, conjugates
###### Chapter 15: Special Classes of Functions Rational Function, even and odd functions, monotonic functions
###### Chapter 16: Piecewise Defined Functions Piecewise functions, absolute value, floor and ceiling
###### Chapter 17: More Sequences and series Recursive Sequences, Telescoping series
###### Chapter 18: More Inequalities Rearrangement Inequality
###### Chapter 19: Functional Equations Solving functional equations with substitution, separation
###### Chapter 20: Some advanced strategies Solving problems by exploiting the symmetry in the problem, substitution, using undetermined coefficients

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