I am pleased to announce the release of Olympiad Algebra, a comprehensive and rigorous book dedicated to advanced algebraic problem solving for Mathematical Olympiads.

This book is the result of years of teaching, mentoring, and analyzing Olympiad-level algebra—across national contests, IMO-style problems, and advanced training programs. It is written for students who aim not merely to solve problems, but to understand algebra as a structured discipline.

Why Olympiad Algebra?

Algebra at the Olympiad level is not about routine manipulation or memorized tricks.
It is about:

• recognizing hidden symmetry,
• exploiting homogeneity,
• understanding equality cases,
• reducing problems to structural cores, and
• synthesizing multiple techniques into a single coherent solution.

Most students struggle not because the problems are impossible, but because they lack a systematic framework.
This book was written to build exactly that framework.

What This Book Covers

Olympiad Algebra develops algebra from the ground up to international level through carefully structured chapters, including:

• Symmetry and Homogeneity
• Advanced Inequalities (AM–GM, Cauchy–Schwarz, Titu’s Lemma, $uvw$, SOS)
• Polynomial Techniques and Discriminant Analysis
• Functional Equations and Functional Inequalities
• Complex Numbers as Algebraic and Geometric Tools
• Parameter Inequalities and Equality Analysis
• Mixed Algebraic Synthesis Problems
• Final Olympiad-Level Challenges

Each chapter is designed to train mathematical judgment, not just computation.

Pedagogical Philosophy

This book follows a strict educational structure:

• Conceptual theory with mentor-style insight
• Fully worked examples explaining why each step works
• Exercises organized as
  Warm-up → Core → Olympiad → IMO
• Self-tests designed for 90-minute Olympiad simulation
• Emphasis on equality cases, extremal principles, and normalization

There are no shortcuts, no gimmicks, and no pattern-hunting tricks.

Who Should Read This Book?

This book is ideal for:

• Students preparing for National Mathematical Olympiads
• Advanced learners on the IMO pathway
• Math circle participants and Olympiad training programs
• Teachers and mentors seeking structured Olympiad algebra material
• Serious students who value depth, rigor, and long-term mastery

A solid foundation in elementary algebra is expected. No advanced calculus is required.

Availability (Global)

The book is now available worldwide on Amazon:

• 🇺🇸 US: https://a.co/d/e8A7ohX
• 🇬🇧 UK: https://amzn.eu/d/2Mef8k0
• 🇦🇺 AU: https://amzn.asia/d/2CZZNG0
• 🇨🇦 CA: https://a.co/d/9PRSjPC
• 🇩🇪 DE: https://amzn.eu/d/7OioTjR
• 🇫🇷 FR: https://amzn.eu/d/gK2k8Vj
• 🇯🇵 JP: https://amzn.asia/d/8vIhIyg

Other countries: Check your local Amazon marketplace.

Preview the Book

A preview of the book (selected chapters and layout) is available here:

Preview:
https://drive.google.com/file/d/1xmkQVo2E5KtNsmoyBQOdTl5-LX9Qdm6x/view

Part of the Mathematics Elevate Series

Olympiad Algebra is part of the Mathematics Elevate Series, a long-term project aimed at building true Olympiad-level thinking across:

• Algebra
• Number Theory
• Geometry
• Combinatorics

Each volume is designed to be independent, yet conceptually aligned with the others.

Final Words

This book is not written for speed-reading or casual practice.

It is written for students who:

• choose understanding over memorization,
• structure over tricks,
• and mathematical maturity over short-term results.

I hope Olympiad Algebra becomes a reliable companion in your journey toward deeper mathematics.

— Rishabh Kumar