Objective
To equip students with foundational and intermediate concepts in algebra, number theory, and inequalities essential for mathematical competitions and advanced studies.
Focus
Intensive problem-solving sessions covering abstract algebraic manipulation, number theory fundamentals, and inequality techniques through guided practice and competition-style problems.
Foundation Timeline
Fractional Equations
Solving rational equations, partial fractions, applications in competitive algebra
Irrational Equations
Radical equations, domain restrictions, squaring techniques
Indicial Functions
Exponential equations, properties of indices, growth and decay models
Logarithmic Function
Laws of logarithms, logarithmic equations, exponential-logarithmic systems
Introductory Inequalities
AM-GM, Cauchy-Schwarz, basic inequality techniques for competition problems
Sequences
Arithmetic and geometric progressions, summation formulas, telescoping sums
Polynomials
Vieta's formulas, polynomial division, factorisation techniques
Divisibility
Prime factorisation, GCD, LCM, Euclidean algorithm, applications in number theory
Congruence
Modular arithmetic, linear congruences
Intermediate Timeline
Intermediate Inequalities
Cauchy-Schwarz, Jensen's inequality, rearrangement techniques for competition-level problems
Recursive Relations I
First-order linear recurrences, characteristic equations, solving recurrence systems
Recursive Relations II
Higher-order recurrences, generating functions, applications in combinatorics
Polynomials
Fundamental theorem of algebra, irreducible polynomials, cyclotomic polynomials
Congruence
Modular arithmetic, linear congruences, Chinese Remainder Theorem
Quadratic Reciprocity
Legendre symbols, Gauss's law, applications in number theory
Diophantine Equation I
Linear Diophantine equations, Euclidean algorithm approach
Diophantine Equation II
Pythagorean triples, Pell's equation, method of infinite descent
Trigonometry
Compound angle formulas, inverse trigonometric functions, trigonometric equations
Foundation Classes
Mon, Wed, Fri
Intermediate Classes