Olympiad Algebra

By Rishabh Kumar

Olympiad Algebra

Advanced Techniques, Structures, and Problem Solving for Mathematical Olympiads

Master the Architecture of Algebra with Rishabh Kumar
IIT Guwahati & Indian Statistical Institute Alumnus Founder, Mathematics Elevate Academy

Olympiad Algebra is a rigorous and systematic guide designed for students preparing for National Mathematical Olympiads, the International Mathematical Olympiad (IMO) pathway, and advanced pre-university mathematics. This book goes far beyond routine calculation, developing algebra as a structural discipline. It emphasizes the symmetry, homogeneity, and synthesis methods that define high-level Olympiad problems.

What This Book Focuses On

Structural Mastery: Move beyond formula memorization to understand the deep architecture of algebraic expressions.

Systematic Reduction: Learn to simplify complex problems using symmetry, normalization, and homogenization.

Advanced Inequality Powerhouse: Comprehensive coverage of AM-GM, Cauchy-Schwarz, Titu's Lemma, H lder's Inequality, and the uvw and pqr methods.

Polynomial Sophistication: Master discriminant analysis, Vieta-based transformations, Newton's Sums, and cyclotomic polynomials.

Functional Equations & Inequalities: Proven Olympiad-style strategies for solving involutions, Cauchy-type equations, and bounding techniques.

Complex Numbers: Using complex multiplication and rotations as powerful algebraic and geometric tools.

The "Mentor-Style" Pedagogical Structure

Each chapter is built to foster long-term mathematical maturity:

Strategic Theory: Concepts presented with the "Olympiad Insight" necessary for competition.

Mentor Commentary: Fully worked examples featuring "thinking-out-loud" commentary to explain the motivation behind each step.

Graduated Exercise Sprints: A 150+ problem-per-chapter progression: Warm-up → Core → Olympiad → IMO.

Self-Tests: Timed sections designed to simulate real Olympiad conditions.

Equality & Extremal Analysis: A dedicated focus on the "boundary cases" that often hold the key to the solution.

Who This Book Is For

Aspirants: Students preparing for AMC 10/12, AIME, USAMO, INMO, and the IMO.

Advanced Learners: High school students seeking depth and rigor beyond the standard curriculum.

Mentors: Teachers and math circle leaders looking for a structured, best-in-class algebra syllabus.

About the Author

Rishabh Kumar is an alumnus of IIT Guwahati and the Indian Statistical Institute (ISI). As a dedicated educator, author, and the founder of Mathematics Elevate Academy, he has mentored countless students on their journey to mathematical excellence. His approach focuses on developing the "intuition of a competitor" combined with the "rigor of a mathematician."

Part of the Mathematics Elevate Series for Olympiads-a comprehensive collection dedicated to developing world-class thinking across Algebra, Number Theory, Combinatorics, and Geometry.

Visit: www.MathematicsElevateAcademy.com to preview the book and explore more.

This is not a shortcut book.
It is written for readers who choose understanding over memorization, structure over tricks, and depth over speed.

• Format: Paperback
• Language: English
• ISBN: B0GHKF9RK9
• ISBN13: 9798244448283
• Release Date: January 2026
• Publisher: Independently Published
• Length: 316 Pages
• Weight: 1.39 lbs.
• Dimensions: 0.7" x 8.0" x 10.0"