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Full Description
Math Leads for Mathletes Book 2 is part of the Math Leads for Mathletes series, providing more challenging units for young math problem solvers and many others! The book draws on the authors' experience working with young mathletes and on the collective wisdom of mathematics educators around the world to help parents and mentors challenge and teach their aspiring math problem solvers. The topics contained in this book are best suited for middle schoolers, although students who discovered competitive mathematics in later grades will also benefit from the material. This book will help students advance in several directions important in competitive mathematics: algebra, combinatorics, geometry, and number theory. It presents a variety of problem solving strategies and challenges readers to explain their solutions, write proofs, and explore connections with other problems.
Contents
Part 1 Concepts, Exercises, and Problems
The Spotlight is on: Impossible Ancient Greek Problems
1.1 Counting I
1.2 Pascal's Triangle and Binomial Coefficients
1.3 Probability I
1.4 Mathematical Induction
1.5 Problem Set 1
The Spotlight is on: Pascal's Sharing Problem
1.6 Counting II
1.7 Probability II
1.8 Fibonacci Numbers
1.9 Pigeonhole Principle
1.10 Problem Set 2
The Spotlight is on: Buffon's Needle and ?
1.11 Quadratic Equations
1.12 Algebraic Expressions
1.13 Systems of Linear Equations
1.14 Inequalities
1.15 Problem Set 3
The Spotlight is on: Solution of Equations in Radicals
1.16 Angle Chasing I
1.17 Angle Chasing II
1.18 Geometry of Triangles I
1.19 Geometry of Triangles II
1.20 Problem Set 4
The Spotlight is on: Euclid's Pons Asinorum
1.21 Dissection Time
1.22 Dissections Again
1.23 Equilateral vs Equiangular
1.24 Combinatorial Geometry
1.25 Problem Set 5
The Spotlight is on: Bertrand's Paradox
1.26 Around the Division Algorithm
1.27 Least Common Multiple
1.28 Nice Numbers
1.29 Problems Involving 2016
1.30 Problem Set 6
The Spotlight is on: Perfect Numbers
Part 2 Solutions to Problems
2.1 Counting I
2.2 Pascal's Triangle and Binomial Coefficients
2.3 Probability I
2.4 Mathematical Induction
2.5 Problem Set 1
2.6 Counting II
2.7 Probability II
2.8 Fibonacci Numbers
2.9 Pigeonhole Principle
2.10 Problem Set 2
2.11 Quadratic Equations
2.12 Algebraic Expressions
2.13 Systems of Linear Equations
2.14 Inequalities
2.15 Problem Set 3
2.16 Angle Chasing I
2.17 Angle Chasing II
2.18 Geometry of Triangles I
2.19 Geometry of Triangles II
2.20 Problem Set 4
2.21 Dissection Time
2.22 Dissections Again
2.23 Equilateral vs Equiangular
2.24 Combinatorial Geometry
2.25 Problem Set 5
2.26 Around the Division Algorithm
2.27 Least Common Multiple
2.28 Nice Numbers
2.29 Problems Involving 2016
2.30 Problem Set 6
