Problem Solving Skills

Here’s an archive of my posts sorted according to different topics.

General:

  1. How to solve an Olympiad problem

Algebra:

Polynomials:

  1. Symmetric Polynomials (1, 2)
  2. Monotonic functions
  3. Elementary substitution strategies
  4. Lagrange’s interpolation formula
  5. Completing the square
  6. Factorisation
  7. Factorisation using Sophie Germain’s Identity and Complex Numbers
  8. Miscellaneous techniques in algebra
  9. System of equations
  10. Polynomial functions

Inequalities:

  1. Tips for solving inequalities
  2. Strengthening the proposition
  3. A property of convex functions
  4. Inequalities with constraint abc=1
  5. Inequalities concerning sides of a triangle
  6. Power-mean inequality
  7. Trigonometric substitution
  8. Geometric construction
  9. Hölder’s inequality

Functional equations:

  1. Common replacements in solving functional equations
  2. Mathematical induction and Cauchy’s functional equations
  3. Importance of bijection in solving functional equations

Recurrence relations:

  1. Method of fixed points
  2. Characteristic equation

Geometry:

Planar Geometry:

  1. Stewart’s Theorem
  2. Geometric inequalites
  3. Relating areas and angles using Ceva’s and Menalaus’ Theorem
  4. Proving perpendicularity (1, 2, 3)
  5. Constructing auxiliary circles
  6. Proving Collinearity

Trigonometry:

  1. Expansion formulas and Chebyshev polynomials

Analytical Geometry:

Number Theory:

  1. How to approach a number theory problem
  2. Last digits
  3. Factorisation using Sophie Germain’s Identity and Complex Numbers
  4. Techniques in solving Diophantine equations (1, 2)
  5. Number bases

Combinatorics:

  1. Types of combinatorial problems
  2. Combinatorics: The Next Step
  3. Distribution problems
  4. Catalan numbers
  5. Incidence Matrix
  6. Combinatorial Geometry

Still under construction…

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