Part I Problems
1 Algebra
1．1 An Algebraic Identity
1．2 Cauchy-Schwarz Revisited
1．3 Easy Ways Through Absolute Values
1．4 Parameters
1．5 Take the Conjugate！
1．6 Inequalities with Convex Functions
1．7 Induction at Work
1．8 Roots and Coefficients
1．9 The Rearrangements Inequality
2 Geometry and Trigonometry
2．1 Geometric Inequalities
2．2 An Interesting Locus
2．3 Cyclic Quads
2．4 Equiangular Polygons
2．5 More on Equilateral Triangles
2．6 The "Carpets" Theorem
2．7 Quadrilaterals with an Inscribed Circle
2．8 Dr．Trig Learns Complex Numbers
3 Number Theory and Combinatorics
3．1 Arrays of Numbers
3．2 Functions Defined on Sets of Points
3．3 Count Twice！
3．4 Sequences of Integers
3．5 Equations with Infinitely Many Solutions
3．6 Equations with No Solutions
3．7 Powers of 2
3．8 Progressions
3．9 The Marriage Lemma

Part II Solutions
4 Algebra
4．1 An Algebraic Identity
4．2 Cauchy-Schwarz Revisited
4．3 Easy Ways Through Absolute Values
4．4 Parameters
4．5 Take the Conjugate！
4．6 Inequalities with Convex Functions
4．7 Induction at Work
4．8 Roots and Coefficients
4．9 The Rearrangements Inequality
5 Geometry and Trigonometry
5．1 Geometric Inequalities
5．2 An Interesting Locus
5．3 Cyclic Quads
5．4 Equiangular Polygons
5．5 More on Equilateral Triangles
5．6 The "Carpets" Theorem
5．7 Quadrilaterals with an Inscribed Circle
5．8 Dr．Trig Learns Complex Numbers
6 Number Theory and Combinatorics
6．1 Arrays of Numbers
6．2 Functions Defined on Sets of Points
6．3 Count Twice！
6．4 Sequences of Integers
6．5 Equations with Infinitely Many Solutions
6．6 Equations with No Solutions
6．7 Powers of 2
6．8 Progressions
6．9 The Marriage Lemma

Glossary
Index of Notations
Index to the Problems