Ebooks and magazines

101 PROBLEMS IN ALGEBRA

• FROM THE TRAINING OF THE USA IM0 TEAM
• Chairman: GRAHAM H POLLARD, Canberra AUSTRALIA
• Editor: PETER J TAYLOR, Canberra AUSTRALIA
• WARREN J ATKINS, Canberra AUSTRALIA
• ED J BARBEAU, Toronto CANADA
• GEORGE BERZSENYI, Terra Haute USA
• RON DUNKLEY, Waterloo CANADA
• WALTER E MIENTKA, Lincoln USA
• NIKOLAY KONSTANT1NOV, Moscow RUSSIA
• ANDY Liu, Edmonton CANADA
• JORDAN
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The secrets of TRIANGLES

ALFRED S. PDSAMENTIER and INBMAR LEHMANN

CONTENTS

Acknowledgments
Preface
1. Introduction to the Triangle
2. Concurrencies of a Triangle
3. Noteworthy Points in a Triangle
4. Concurrent Circles of a Triangle
5. Special Lines of a Triangle
6. Useful Triangle Theorems
7. Areas of and within Triangles
8. Triangle Constructions
9. Inequalities in a Triangle
10. Triangles and Fractals
Appendix ... Voir plus

SSC Mathematics Guide

Illustrations & examples
25 Chapters with explanations
2 levels of Exercise
5 Practices Sets

CONTENTS

1. Fundamentals 1-34
2. Number System 35-56
3. Averages 57-68
4. Alligations 69-78
5. Percentages 79-96
6. Profit, Loss and Discount 97-118
7. Interest 119-134
8. Ratio, Proportion and Variation 135-156
9. Time and Work 157-176
10. Time, Speed and Distance 177-202 ... Voir plus

Equations and Inequalities

Elementary Problems and Theorems in Algebra and Number Theory
Translated by Karl Dilcher

CONTENTS

I. Algebraic Identities and Equations
1- Formulas for Powers
2- Finite Sums
3- Polynomials
4- Symmetric Polynomials
5- Systems of Equations
6- Irrational Equations
7- Some Applications of Complex Numbers

II. Algebraic Inequalities
1- Definitions and
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Euclidean Geometry in Mathematical Olympiads

With 248 Illustrations

Contents

Preface xi
Preliminaries xiii
0.1 The Structure of This Book. .xiii
0.2 Centers of a Triangle . .xiv
0.3 Other Notations and Conventions . .xv

I Fundamentals . .1

1 Angle Chasing 3
1.1 Triangles and Circles . .3
1.2 Cyclic Quadrilaterals . .6
1.3 The Orthic Triangle. .7
1.4 The Incenter/Excenter Lemma . .9
1.5
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HANDBOOK OF MATHEMATICS

CONTENTS

1 Arithmetics 1
1.1 Elementary Rules for Calculations . 1
1.1.1 Numbers . 1
1.1.2 Methods for Proof . 4
1.1.3 Sums and Products . 6
1.1.4 Powers, Roots, and Logarithms . 7
1.1.5 Algebraic Expressions . 10
1.1.6 Integral Rational Expressions . 11
1.1.7 Rational Expressions . 14
1.1.8 Irrational Expressions . 17

1.2 Finite Series . 18
1.2.1 Definition of a
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Inequalities A Mathematical Olympiad Approach

Radmila Bulajich Manfrino
José Antonio Gémez Ortega
Rogelio Valdez Delgado

lnequalities
A Mathematical Olympiad Approach

Contents

Introduction vii
1 Numerical Inequalities 1
1.1 Order in the real numbers . . . . . . . . . . . . 1
1.2 The quadratic function ax2 + 2bx + c . . . 4
1.3 A fundamental inequality,
arithmetic mean-geometric mean . . . . .
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