Algebra

Algebra

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Lecture notes on Algebra (for Math Olympiad — IOQM, RMO, INMO)

Click on the links below to download.

Algebra  
Warm up
\(a^3+b^3+c^3 - 3abc\)
Invariance principle
Polynomials
Quadratic polynomials
Cubic polynomials
Quartics
Viete’s relations
Differentiation and multiple roots
Finite differences
Telescoping
Growth of Polynomials
Binomial theorem
Arithmetic progressions
Rational and irrational numbers
Size of the roots
Roots of unity
[Complex numbers]  
Crossing the \(x\)-axis
Lagrange interpolation
Integer divisibility
Functional equations
System of equations
[Induction]  
Inequalities
  • Click here to download Combinatorics notes.
  • Click here to download Geometry notes.
  • Click here to download Number Theory notes.
  • Click here to download notes of INMO Training Camp 2025 for the Madhya Pradesh region.
  • Click here to download some problem set of IMO Training Camp 2025.

These notes

  • may be useful
    • to the students who would like to have a look at some of the past RMO problems, in order to have an idea of the notions/topics involved, and/or to have a glimpse before getting started, or just curious about it,
    • to the students, who would like to prepare and would like to have the relevant questions organized across the topics and sub-topics,
  • also aim

References/Resources

  • Olympiad Training Materials from IMOmath.
  • Mathematical Olympiad Treasures by Titu Andreescu, Bogdan Enescu
  • 101 Problems in Algebra by Titu Andreescu, Zuming Feng
  • Mathematical Olympiad Challenges by Titu Andreescu, Răzvan Gelca
  • Putnam and Beyond by Răzvan Gelca, Titu Andreescu
  • A video by Zlatko Salko Lagumdžija.