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.

Algebra

Inequalities

• 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 - Hardy, Littlewood, Polya.
• 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 and Inequalities in Several Variables - (World Scientific Publication) - Stefan Czerwik.
• Lectures on Functional Equations - (Academic Press) - J. Aczel.

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 - Problem 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 - Both Book (olympiad examples followed by problems).
• 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).

Geometry

• 103 Trigonometry Problem - 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 herel - 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.
• 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.
  • All Volumes
  • First Volume
  • Second Volume
  • Third Volume
  • Fourth Volume
  • Fifth Volume
  • Sixth Volume
  • Seventh Volume
  • Eighth Volume
  • Ninth Volume

• This note by Darij Grinberg

• Darij Grinberg's whole site download - his 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.

• 103 Trigonometry Problems - Andreescu, Feng - Problem book - this is a very good 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.

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.
• A Collection of Limits - Pain rinnegan.

==Number Theory==

• 100 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.