*This post is regarding the*

**"BEST BOOKS FOR INTERNATIONAL / HIGHER LEVEL MATH OLYMPIAD - (ALGEBRA PART)".**

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*1. 101 PROBLEMS IN ALGEBRA (from the training of the USA IMO Team):-*

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*☆ ABOUT THIS BOOK:-*

*This book contains one hundred highly rated problems used in the training and testing of the USA International Mathematical Olympiad (IMO) team. It is not a collection of one hundred very difficult, impenetrable*

*questions. Instead, the book gradually builds students' algebraic skills and techniques. This work aims to broaden students' view of mathematics and better prepare them for possible participation in various mathematical competitions. It provides in-depth enrichment in important areas*

*of algebra by reorganizing and enhancing students' problem-solving tactics and strategies. The book further stimulates students' interest for future study of mathematics.*

*In the United States of America, the selection process leading to participation in the International Mathematical Olympiad (IMO) consists of a series of national contests called the American Mathematics Contest 10 (AMC 10), the American Mathematics Contest 12 (AMC 12), the American Invitational Mathematics Examination(AIME), and the United States of America Mathematical Olympiad (USAMO). Participation in the AIME and the USAMO is by invitation only, based on performance in the preceding exams of the sequence. The Mathematical Olympiad Summer Program (MOSP) is a four-week, intense training of 24-30 very promising students who have risen to the top of the American Mathematics Competitions. The six students representing the United States of America in the IMO are selected on the basis of their USAMO scores and further IMO-type testing that takes place during MOSP. Throughout MOSP, full days of classes and extensive problem sets give students thorough preparation in several important areas of mathematics. These topics include combinatorial arguments and identities, generating functions, graph theory, recursive relations, telescoping*

*sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities.*

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*☆ MUST READ:- Universal self scorer physics for IITJEE*

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*☆ DOWNLOAD THIS BOOK FROM HERE:- Click here to download*

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2. CHALLENGING PROBLEMS IN ALGEBRA:-*

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☆ ABOUT THIS BOOK:- *

*Challenging Problems in Algebra is organized into three main parts:*

*"Problems," "Solutions," and "Answers." Unlike many contemporary problem-solving resources, this book is arranged not by problem-solving technique, but by topic. We feel that announcing the technique to be used stifles creativity and destroys a good part of the fun of problem solving.*

*The problems themselves are grouped into two sections.*

*Section 1 :-*

*covers eight topics that roughly parallel the sequence of a first year algebra course. Section 11 presents twelve topics that roughly parallel the second year algebra course. Within each topic, the problems are arranged in approximate order of*

*difficulty. For sorne problems, the basic difficulty may líe in making the distinction between relevant and irrelevant data or between known and unknown information. The sure ability to make these distinctions is part of the process of problem solving, and each devotee must develop this*

*power by him or herself. It will come with sustained effort.*

*In the "Solutions" part of the book, each problem is restated and then*

*its solution is given. From time to time we give altemate methods of solution, for there is rarely only one way to solve a problem. The solutions shown are far from exhaustive, and intentionally so, allowing you to try a variety of different approaches. Particularly enlightening is the strategy of using multiple methods, integrating algebra, geometry, and*

*trigonometry. lnstances of multiple methods or multiple interpretations appear in the solutions. Our continuing challenge to you, the reader, is to find a different method of solution for every problem.*

*The third part of the book, "Answers," has a double purpose. It contains the answers to ali problems and challenges, providing a quick check when you have arrived at a solution. Without giving away the*

*entice solution, these answers can also give you a hint about how to proceed when you are stuck. Appendices at the end of the book provide information about several specialized topics that are not usually covered in the regular currículum but are occasionally referred to in the solutions. This material should be of particular interest and merits special attention at the appropriate time.*

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☆ TOPICS COVERED:- *

*Section 1:-*

*The book begins with a chapter of general problems, simple to state and understand, that are generally appealing to students. These should serve as a pleasant introduction to problem solving early in the elementary algebra course.*

*Chapter 2:- demonstrates the true value of*

*algebra in understanding arithmetic phenomena. With the use of algebraic methods, students are guided through fascinating investigations of arithmetic curiosities.*

*Familiar and unfamiliar relations are the bases for sorne cute problems in chapter 3.*

*A refreshing consideration of various base systems is offered in chapter 4. Uncommon problems dealing with the common topics of equations, inequalities, functions, and simultaneous equations and inequalities are presented along with stimulating*

*challenges in chapters 5, 6, and 7.*

*The last chapter of this section contains a collection of problems summarizing the tcchniques encountered earlier. These problems are best saved for the end of the elementary algebra course.*

*Section 11. The second section opens with a chapter on one of the oldest forms of algebra, Diophantine equations-indeterminate equations for which only integer solutions are sought. These problems often appear*

*formidable to the young algebra student, yet they can be solved easily after sorne experience with the type (which this section offers).*

*The next two chapters present sorne variations on familiar themes,*

*functions and inequalities, treated here in a more sophisticated manner than was employed in the first section.*

*The field of number theory includes sorne interesting topics for the secondary school student, but ali too often this area of study is avoided.*

*Chapter 12 presents sorne of these concepts through a collection of unusual problems. Naturally, an algebraic approach is used throughout. Aside from a brief exposure to maxium and mínimum points on a*

*parabola, very little is done with these concepts prior to a study of the calculus. Chapter 13 will demonstrate through problem solving sorne explorations of these concepts at a relatively elementary level.*

*Chapters 14, 15, 17, and 18 offer unconventional problems for sorne*

*standard topics: quadratic equations, simultaneous equations, series, and logarithms. The topic of logarithms is presented in this book as an end in itself rather than as a (computational) means toan end, which has been its usual role. Problems in these chapters should shed sorne new (and dare we say refreshing) light on these familiar tapies.*

*Chapter 16 attempts to bring sorne new life and meaning, via problem solving, to analytic geometry. Chapter 19 should serve as a motivator for further study of probability and a consideration of general*

*counting techniques. We conclude our treatment of problem solving in algebra with chapter 20, "An Algebraic Potpourri." Here we attempt to pull together sorne of the problems and solution techniques considered in earlier sections. These final problems are quite challenging as well as out of the*

*ordinary, even though the topics from which they are drawn are quite familiar.*

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*☆ ALSO WATCH:- MTG Arihant spectrum JEE edition books*

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*☆ DOWNLOAD THIS BOOK FROM HERE:- Click here to download*

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3. COMPLEX NUMBERS & GEOMETRY (Liang Shin Hahn):-*

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☆ CONTENT IN THIS BOOK:-*

*Chapter 1 (complex numbers):-*

*• introduction to imaginary numbers*

*• definition of complex numbers*

*• quadratic equations*

*• significance of the quadratic numbers*

*• order relation in the complex field*

*• the triangle inequality*

*• the complex plane*

*• polar representation of complex numbers*

*• the nth root*

*• exponential function*

Chapter 2 (applications to geometry):-

Chapter 2 (applications to geometry):-

*• triangles*

*• the ptolemy euler theorem*

*• the clifford theorems*

*• the nine point circle*

*• the simson circle*

*• generalization of the simson theorem*

*• the cantor theorem*

*• the feuerbach theorem*

*• the morley theorem*

Chapter 3 (the mobius transformations):-

Chapter 3 (the mobius transformations):-

*• stereographic projections*

*• mobius transformations*

*• cross ratios*

*• the principles of symmetry*

*• a pair of circle*

*• pencils of circle*

*• fixed point and classification of mobius transformations*

*• inversions*

*• the pointcare model of a non euclidean geometry*

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*☆ MUST PRACTICE:- Allen test series for JEE*

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*☆ DOWNLOAD THIS BOOK FROM HERE:- Click here to download*

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4. COMPLEX NUMBERS FROM A TO Z:-*

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☆ CONTENT OF THIS BOOK:-*

*1.1.1 Definition of complex numbers*

*1.1.2 Properties concerning addition*

*1.1.3 Properties concerning multiplication*

*1.1.4 Complex numbers in algebraic form*

*1.1.5 Powers of the number*

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1.1.6 Conjugate of a complex number

1.1.7 Modulus of a complex number

1.1.8 Solving quadratic equations

1.1.9 Problems

1.2 Geometric Interpretation of the Algebraic Operations

1.2.1 Geometric interpretation of a complex number

1.2.2 Geometric interpretation of the modulus

1.2.3 Geometric interpretation of the algebraic operations

1.2.4 Problems

2. Complex Numbers in Trigonometric Form:-

2.1 Polar Representation of Complex Numbers

2.1.1 Polar coordinates in the plane

2.1.2 Polar representation of a complex number

2.1.3 Operations with complex numbers in polar representation

2.1.4 Geometric interpretation of multiplication

2.1.5 Problems

2.2 The nth Roots of Unity

2.2.1 Defining the nth roots of a complex number

2.2.2 The nth roots of unity

2.2.3 Binomial equations

2.2.4 Problems

3. Complex Numbers and Geometry:-

3.1 Some Simple Geometric Notions and Properties

3.1.1 The distance between two points

3.1.2 Segments, rays and lines

3.1.3 Dividing a segment into a given ratio

3.1.4 Measure of an angle

3.1.5 Angle between two lines

3.1.6 Rotation of a point

3.2 Conditions for Collinearity, Orthogonality and Concyclicity

3.3 Similar Triangles

3.4 Equilateral Triangles

3.5 Some Analytic Geometry in the Complex Plane

3.5.1 Equation of a line

3.5.2 Equation of a line determined by two points

3.5.3 Area

3.5.4 Equation of a line determined by a point and a direction

3.5.5 The foot of a perpendicular from a point to a line

3.5.6 Distance from a point to a line

3.6 The Circle

3.6.1 Equation of a circle

3.6.2 The power of a point with respect to a circle

3.6.3 Angle between two circles

4. More on Complex Numbers and Geometry:-

4.1 The Real Product of Two Complex Numbers

4.2 The Complex Product of Two Complex Numbers

4.3 The Area of a Convex Polygon

4.4 Intersecting Cevians and Some Important Points in a Triangle

4.5 The Nine-Point Circle of Euler

4.6 Some Important Distances in a Triangle

4.6.1 Fundamental invariants of a triangle

4.6.2 The distance OI

4.6.3 The distance ON

4.6.4 The distance OH

4.7 Distance between Two Points in the Plane of a Triangle

4.7.1 Barycentric coordinates

4.7.2 Distance between two points in barycentric coordinates

4.8 The Area of a Triangle in Barycentric Coordinates

4.9 Orthopolar Triangles

4.9.1 The Simson–Wallance line and the pedal triangle

4.9.2 Necessary and sufficient conditions for orthopolarity

4.10 Area of the Antipedal Triangle

4.11 Lagrange’s Theorem and Applications

4.12 Euler’s Center of an Inscribed Polygon

4.13 Some Geometric Transformations of the Complex numbers

4.13.1 Translation

4.13.2 Reflection in the real axis

4.13.3 Reflection in a point

4.13.4 Rotation

4.13.5 Isometric transformation of the complex plane

4.13.6 Morley’s theorem

4.13.7 Homothecy

4.13.8 Problems

5. Olympiad-Caliber Problems:-

5.1 Problems Involving Moduli and Conjugate

5.2 Algebraic Equations and Polynomials

5.3 From Algebraic Identities to Geometric Properties

5.4 Solving Geometric Problems

5.5 Solving Trigonometric Problems

5.6 More on the nth Roots of Unity

5.7 Problems Involving polygons

5.8 Complex Numbers and Combinatorics

5.9 Miscellaneous Problems

### ☆ MUST PRACTICE:- Play with graphs by Amit M. agarwal pdf

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#### 5. POLYNOMIAL BY E.J BARBAEU:-

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