Algebra
Algebra
Handouts
- 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]
- [Crossing the \(x\)-axis]
- [Lagrange interpolation]
- Functional equations
- [System of equations]
- [Induction]
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.
These notes may be useful
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to the students who would like to have a look at some of the past RMO problem before getting started, or just curious about it.
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as a reference, to anyone who would like to provide guidance to students, and is eager to do so as soon as having the relevant questions across the topics and sub-topics available in an organized form.