Thursday, May 24, 2012

Olympiad Math


1 Geometry and Trigonometry
1.1 A Property of Equilateral Triangles
1.2 Cyclic Quadrilaterals
1.3 Power of  a Point
1.4 Dissections of Polygonal Surfaces
1.5 Regular Polygons
1.6 Geometric Constructions and Transformations
1.7 Problems with Physical Flavor
1.8 Tetrahedra Inscribed in Parallele pipeds
1.9 Telescopic Sums and Products in Trigonometry
1.10 Trigonometric Substitutions

2 Algebra and Analysis
2.1 NoSquare IsNegative
2.2 Look at the Endpoints
2.3 Telescopic Sums and Products in Algebra
2.4 On an Algebraic Identity
2.5 Systems of Equations
2.6 Periodicity
2.7 The Abel Summation Formula
2.8 x+1/x
2.9 Matrices
2.10 The Mean Value Theorem

3 Number Theory and Combinatorics
3.1 Arrange in Order
3.2 Squares and Cubes
3.3 Repunits
3.4 Digits ofNumbers
3.5 Residues
3.6 Diophantine Equations with the Unknowns as Exponents
3.7 Numerical Functions
3.8 Invariants
3.9 Pell Equations
3.10 Prime Numbers and Binomial Coefficients