# Olympiad books

Here is a list of **Olympiad Books** that have Olympiad-level problems used to train students for future mathematics competitions.

You can discuss here about these books or request new books. Let's categorize books into **Theory** books, **Problem** books, and **Both** books.

## Contents

## Algebra

### Inequalities

- Advanced Olympiad Inequalities: Algebraic & Geometric Olympiad Inequalities by
**Alijadallah Belabess**. *Inequalities An Approach Through Problems -***B. J. Venkatachala***Secrets In Inequalities volume 1 - Basic Inequalities*-**Pham Kim Hung**.*Secrets In Inequalities volume 2 - Advanced Inequalities*-**Pham Kim Hung**.*Algebraic Inequalities - Old And New Methods*-**Vasile Cirtoaje**.*Old And New inequalities volume 1*-**Titu Andreescu, Vasile Cirtoaje, Gabriel Dospinescu, Mircea Lascu**.*Old And New Inequalities volume 2*-**Vo Quoc Ba Can, Cosmin Pohoata**.*The Cauchy-Schwarz Master Class*-**J. Michael Steele**.*Inequalities: A Mathematical Olympiad Approach*-**Radmila Bulajich Manfrino, Jose Antonio Ortega, Rogelio Valdez Delgado**.*An Introduction to Inequalities*-**Bellman, Beckenbach**.*Analytic Inequalities*-**Mitrinovic**.*Inequalities Theorems and Formulas*forum.*Useful Inequalities*topic.

### Polynomials

*Polynomials and Polynomial Inequalities (Graduate Texts in Mathematics)*- (Springer) -**Peter Borwein - Tamas Erdely**.

*Geometry of Polynomials*- (American Mathematical Society) -**Morris Marden**.

*Polynomials*- (Springer) -**E.J. Barbeau**.- Solving Polynomial Equations: Foundations, Algorithms, and Applications - (Springer) -
**Alicia Dickenstein - Ioannis Z. Emiris**.

### Functional Equations

*Functional Equations in Mathematical Olympiads (2017 - 2018): Problems and Solutions (Vol. I)*- (Amazon) -**Amir Hossein Parvardi**.*Functional Equations and Inequalities in Several Variables*- (World Scientific Publication) -**Stefan Czerwik**.*Lectures on Functional Equations*- (Academic Press) -**J. Aczel**.*Functional Equations: A Problem Solving Approach*- (Prism Books) -**B.J. Venkatchala**.*Functional Equations and How to Solve Them*- (Springer) -**Christopher G. Small**.

## Number Theory

*Number Theory Structures, Examples, and Problems*-**Titu Andreescu, Dorin Andrica**-**Both**Book (olympiad examples followed by problems).**Excellent**book for number theory.*An Introduction to Diophantine Equations*-**Titu Andreescu, Dorin Andrica, Ion Cucurezeanu**-**Both**Book (olympiad examples followed by problems).**Excellent**book for Diophantine equations.*104 Number Theory Problems*-**Titu Andreescu, Dorin Andrica, Zuming Feng**-**Both**Book.*250 problems in number theory*-**W. Sierpinski**-**Problem**Book.

*A Selection of Problems in Theory of Numbers*-**W. Sierpinski**-**Problem**Book.**Great**book.*The Theory of Numbers - a Text and Source Book of Problems*-**Andrew Adler, John E. Coury**-**Both**Book (olympiad examples followed by problems).**Excellent**book.*Number Theory*-**Naoki Sato (nsato)**-**Theory**Book.*Solved and Unsolved Problems in Number Theory*-**Daniel Shanks**-**Problem**Book.*Elementary Number Theory (Revised Printing)*-**David M. Burton**-**It is a nice book for theory building and is low-impact in its approach.***An Introduction to the Theory of Numbers*-**Ivan Niven, Herbert S. Zuckerman**-**Theory**Book.*Elementary Number Theory*-**W. Edwin Clark**[free online -**download here**] -**Theory**Book.*Numbers and Curves*-**Franz Lemmermeyer**[free online -**download here**] -**Theory**Book.*Algorithmic Number Theory*-**S. Arun-Kumar**[free online -**download here**] -**Theory**Book.*Elementary Number Theory*-**William Stein**- [free online -**download here**] -**Both**Book (lots of theorems with problems at the end of each section).*Number Theory, An Introduction via the Distribution of Primes*-**Benjamin Fine, Gerhard Rosenberger**-**Theory**Book.*Number Theory for Computing*-**Song Y. Yan**-**Theory**Book (this book contains computational examples/theorems for number theory).*Pell's Equation*-**Edward J. Barbeau**[level is a little above olympiad] -**Both**Book (olympiad examples followed by problems).- "Topics in Number Theory" - ''
*Masum Bilal and Amir Hossein Parvardi"*- "Both" Book

## Geometry

*103 Trigonometry Problems*-**Titu Andreescu, Zuming Feng**-**Both**book (solved examples and approaches + problems).*Triangles, Concurrency and Quadrilaterals*- [free online -**download here**].*Geometry Unbound*-**Kedlaya**-**Theory**book - this book is available online for download. See**here**l -**Great**book.*Famous Problems of Geometry and How to Solve Them*-**Benjamin Bold**-**Both**book (solved examples and approaches + problems).*Challenging Problems in Geometry*-**Alfred S. Posamenter, Charles T. Salkind**-**Both**book -**Great**book.*Euclidean Geometry in Mathematical Olympiads*-**Evan Chen**-**Both**book -**good**book. By far the greatest geometry book to prepare for olympiads. if you had to choose one book, its definitely this one*Elements of Projective Geometry*-**Luigi Ceremona**-**Both**book, again.*Japanese Temple Geometry Problems*-**San Gaku**-**Problem**book (it contains lots of theorems about circles).*Geometric Problems on Maxima and Minima*-**Titu Andreescu, Oleg Mushkarov, Luchezar Stoyanov**-**Problem**book -**Great**book.*Complex Numbers in Geometry*-**I. M. Yaglom**-**Theory**book.*Forum Geometricorum (A Journal on Classical Euclidean Geometry and Related Areas)*-**Authors**- Uploaded by**Amir Hossein Parvardi**.*AVAILABLE for DOWNLOAD*.- Alternative link:**All Volumes (direct link to the RAR file)****All Volumes**

- his**Darij Grinberg's**whole site download*website*has a great number of articles/solved problems that you may use in your Olympiad studying -**Great**.

*Geometry revisited*-**Coxeter and Greitzer**-**Both**book.

*Problems in Geometry*-**Kutepov, Rubanov**-**Problem**book.

*Investigations in Geometry (Math Motivators!)*-**Posamentier, Sheridan**-**Both**book.

*Introduction to Geometry*-**Coxeter**-**Theory**book.

*Modern Geometry with Applications*-**Jennings**-**Both**book.

*Geometric Transformations (4 volumes)*-**Yaglom**-**Theory**book.

## Combinatorics

*A Path to Combinatorics for Undergraduates*-**Andreescu, Feng**.*Proofs that Really Count (The Art of Combinatorial Proof)'*-**Benjamin and Quinn**.*A Course in Combinatorics*-**Lint and Wilson**.*Olympiad Combinatorics*-**Pranav A. Sriram**.

## Improve Your Skills With Problem Solving

### Algebra

*100 Inequality Problems Proposed by Vasc and arqady*-**Amir Hossein Parvardi**.*115 Algebra Problems*-**Mohammad Jafari**.*100 Nice Polynomial Problems (With Solutions)*-**Amir Hossein Parvardi**.*100 Functional Equations Problems (With Solutions)*-**Amir Hossein Parvardi**.*Trigonometry Problems Collection*-**Amir Hossein Parvardi**.*567 Nice And Hard Inequalities*-**Nguyễn Duy Tùng**.*Inequalities From 2007 and 2008 Competitions Around The World*-**Manh Dung Nguyen**.*Technical Analysis of Three Variable Inequalities*-**Nguyen Duy Tung, Zhou Yuan Zhe**.

### Number Theory

*1220 Number Theory Problems (With Sources)*-**Amir Hossein Parvardi**.*Lifting the Exponent Lemma (LTE)*-**Amir Hossein Parvardi**.*Solving Diophantine Equations*-**lamphong**.*Several Things About Sum of Squares*-**lamphong**.*Some Own Problems In Number Theory*-**mathmdmb**.*Primitive Roots, Order, and Quadratic Residues*-**mathmdmb**.*Number Theory Marathon Problems*-**M4RI0**.

### Geometry

*150 Nice Geometry Problems (With Solutions)*-**Amir Hossein Parvardi**.- his**Darij Grinberg's**whole site download*website*has a great number of articles/solved problems that you may use in your Olympiad studying.

Euclidean Geometry in Mathematical Olympiads [1]

### Combinatorics

*100 Combinatorics Problems (With Sources)*-**Amir Hossein Parvardi**.*102 Combinatorial Problems*-**Andreescu, Feng**.*Problems in Combinatorics and Graph Theory*-**Ioan Tomescu**.

### General Problem Solving

*Challenging Mathematical Problems With Elementary Solutions (Volume I, Combinatorial Analysis and Probability Theory)*-**A. M. Yaglom, I. M. Yaglom**.*Challenging Mathematical Problems With Elementary Solutions (Volume II, Problem From Various Branches of Mathematics)*-**A. M. Yaglom, I. M. Yaglom**.-**AoPS Resources Page Problems (IMO and ShortLists Added)****Amir Hossein Parvardi**.*Mathematics as Problem Solving*-**Alexander Soifer**.*A Primer For Mathematics Competitions*-**Alexander Zawaira, Gavin Hitchcock**.*Problem Solving Strategies For Efficient And Elegant Solutions (A Resource For The Mathematics Teacher)*-**Alfred S. Posamentier, Stephen Kruli**.*Problems for the Mathematical Olympiads (From the First Team Selection Test to the IMO)*-**Andrei Negut**.*Problem Primer for the Olympiad*-**C. R. Pranesachar, B. J. Venkatachala, C. S. Yogananda**.*Chinese Mathematics Competitions and Olympiads (two volumes)*-**Andy Liu**.*Hungarian Problem Book'**(three volumes)*-**Andy Liu**.*Canadian Mathematical Olympiad 1969-1993 (Problems and Solutions)*-**Michael Doob**.*The Art and Craft of Problem Solving*-**Paul Zeitz**.*APMO 1989-2009*(Problems & Solutions)*-***Dong Suugaku**-**download here**.*International Mathematical Olympiads 1978-1985 and Forty Supplementary Problems*-**Murray S. Klamkin**.*USA Mathematical Olympiads 1972-1986*(Problems and Solutions)*-***Murray S. Klamkin**.*USSR Mathematical Olympiads 1989-1992*-**Arkadii M. Slinko**.*Proofs From THE BOOK*-**Martin Aigner, Günter M. Ziegler**.*Techniques of Problem Solving*-**Steven G. Krantz**.*Junior Balkan Mathematical Olympiads*-**Dan Branzei, loan Serdean, Vasile Serdean**.*The IMO Compendium (A Collection of Problems Suggested for the Mathematical Olympiads, 1959-2004)*-**Dusan Djukic, Vladimir Jankovic, Ivan Matic, Nikola Petrovic**.*Five Hundred Mathematical Challenges*-**Edward J. Barbeau, Murray S. Klamkin, William O. J. Moser**.*The USSR Olympiad Problem Book (Selected Problems and Theorems of Elementary Mathematics)*-**D. O. Shklarsky, N. N. Chentzov, I. M. Yaglom**.*The William Lowell Putnam Mathematical Competition (Problems and Solutions 1965-1984) (three volumes)*-**Volume 1**:**A. M. Gleason, R. E**. Greenwood, L. M. Kelly,**Volume 2**:**Gerald L. Alexanderson, Leonard F. Klosinski, Loren C. Larson**,**Volume 3**:**Kiran S. Kedlaya, Bjorn Poonen, Ravi Vakil**.*International Mathematics TOURNAMENT OF THE TOWNS (Questions & Solutions)*- (five volumes) -**Peter J. Taylor**.*Mathematical Problems and Proofs (Combinatorics, Number Theory and Geometry)*-**Branislav Kisacanin**.*360 Problems for Mathematical Contests*-**Titu Andreescu, Dorin Andrica**.*PROBLEMS FROM AROUND THE WORLD*- (six volumes) -**Titu Andreescu, Kiran S. Kedlaya, Paul Zeitz**.*Mathematical Olympiad Treasures*-**Titu Andreescu, Bogdan Enescu**.*Mathematical Olympiad Challenges*-**Titu Andreescu, Razvan Gelca**.*Lecture Notes on Mathematical Olympiad Courses*-**Xu Jiagu**.*Putnam and Beyond*-**Titu Andreescu, Razvan Gelca**.*Hungary-Israeli Mathematics Competition*-**Shay Gueron**.*MAA - The Contest Problem Book (Annual High School Contests)*- (four volumes) -**Volumes 1, 2, 3**:**Charles T. Salkind, James M. Earl**,**Volume 4**:**Ralph A. Artino, Anthony M. Gaglione, Niel Shell**.*Mathematical Olympiad in China (2007-2008) (Problems and Solutions)*-**Xiong Bin, Lee Peng Yee**.*What to Solve (Problems and Suggestions For Young Mathematicians)*-**Judita Cofman**.