Difference between revisions of "Olympiad books"

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==Algebra==
 
==Algebra==
 
===Inequalities===
 
===Inequalities===
 +
* [https://www.amazon.co.uk/Advanced-Olympiad-Inequalities-Algebraic-Geometric/dp/1794193928/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=1556093238&sr=1-1-catcorr 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 1 - Basic Inequalities'' - '''Pham Kim Hung'''.
 
*''Secrets In Inequalities volume 2 - Advanced Inequalities'' - '''Pham Kim Hung'''.
 
*''Secrets In Inequalities volume 2 - Advanced Inequalities'' - '''Pham Kim Hung'''.
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===Functional Equations===
 
===Functional Equations===
*''Functional Equations and Inequalities in Several Variables'' - (World Scientific Publication) -  '''Stefan Czerwik'''.
+
*[https://parvardi.com/FE2018 ''Functional Equations in Mathematical Olympiads (2017 - 2018): Problems and Solutions (Vol. I)''] - (Amazon) -  '''Amir Hossein Parvardi'''.
*''Lectures on Functional Equations'' - (Academic Press) -  '''J. Aczel'''.
+
*[https://www.worldscientific.com/worldscibooks/10.1142/4875 ''Functional Equations and Inequalities in Several Variables''] - (World Scientific Publication) -  '''Stefan Czerwik'''.
 +
*[https://www.elsevier.com/books/lectures-on-functional-equations-and-their-applications/aczel/978-0-12-043750-4 ''Lectures on Functional Equations''] - (Academic Press) -  '''J. Aczel'''.
 +
*[https://www.amazon.in/Functional-Equations-Revised-Updated-2nd/dp/8172867816 ''Functional Equations: A Problem Solving Approach''] - (Prism Books) -  '''B.J. Venkatchala'''.
 +
*[https://www.springer.com/gp/book/9780387345345 ''Functional Equations and How to Solve Them''] - (Springer) - '''Christopher G. Small'''.
 +
 
 
==Number Theory==
 
==Number Theory==
  
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*''Number Theory Structures, Examples, and Problems'' - '''Titu Andreescu, Dorin Andrica''' - '''Both''' Book (olympiad examples followed by problems). '''Excellent''' book for 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.
 
*''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.
+
*''104 Number Theory Problems'' - '''Titu Andreescu, Dorin Andrica, Zuming Feng''' - '''Both''' Book.
 
*''250 problems in number theory'' - '''W. Sierpinski''' - '''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.
 
*''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.
 
*''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.
*''[http://www.artofproblemsolving.com/Resources/Papers/SatoNT.pdf Number Theory]'' - '''Naoki Sato (nsato)''' - '''Theory''' Book.
+
*''[http://parvardi.com/download/number-theory-naoki-sato/ Number Theory]'' - '''Naoki Sato (nsato)''' - '''Theory''' Book.
 
*''Solved and Unsolved Problems in Number Theory'' - '''Daniel Shanks''' - '''Problem''' 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.
 
*''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.
 
*''An Introduction to the Theory of Numbers'' - '''Ivan Niven, Herbert S. Zuckerman''' - '''Theory''' Book.
*''Elementary Number Theory'' - '''W. Edwin Clark''' [free online - [http://www.artofproblemsolving.com/Forum/download/file.php?id=32932 '''download here''']] - '''Theory''' Book.
+
*''Elementary Number Theory'' - '''W. Edwin Clark''' [free online - [http://parvardi.com/download/elementary-number-theory-w-edwin-clark/ '''download here''']] - '''Theory''' Book.
*''Numbers and Curves'' - '''Franz Lemmermeyer''' [free online - [http://www.artofproblemsolving.com/Forum/download/file.php?id=32931 '''download here''']] - '''Theory''' Book.
+
*''Numbers and Curves'' - '''Franz Lemmermeyer''' [free online - [http://parvardi.com/download/numbers-and-curves-franz-lemmermeyer/ '''download here''']] - '''Theory''' Book.
*''Algorithmic Number Theory'' - '''S. Arun-Kumar''' [free online - [http://www.artofproblemsolving.com/Forum/download/file.php?id=32930 '''download here''']] - '''Theory''' Book.
+
*''Algorithmic Number Theory'' - '''S. Arun-Kumar''' [free online - [http://parvardi.com/download/algorithmic-number-theory-s-arun-kumar/ '''download here''']] - '''Theory''' Book.
*''Elementary Number Theory'' - '''William Stein''' - [free online - [http://www.artofproblemsolving.com/Forum/download/file.php?id=32929 '''download here''']] - '''Both''' Book (lots of theorems with problems at the end of each section).
+
*''Elementary Number Theory'' - '''William Stein''' - [free online - [http://parvardi.com/download/elementary-number-theory-william-stein/ '''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, 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).
 
*''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).
 
*''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==
 
==Geometry==
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*''Famous Problems of Geometry and How to Solve Them'' - '''Benjamin Bold''' - '''Both''' book (solved examples and approaches + problems).
 
*''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.
 
*''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.
 
*''Elements of Projective Geometry'' - '''Luigi Ceremona''' - '''Both''' book, again.
 
*''Japanese Temple Geometry Problems'' - '''San Gaku''' - '''Problem''' book (it contains lots of theorems about circles).
 
*''Japanese Temple Geometry Problems'' - '''San Gaku''' - '''Problem''' book (it contains lots of theorems about circles).
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*''Complex Numbers in Geometry'' - '''I. M. Yaglom''' - '''Theory''' 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''.
 
*''Forum Geometricorum (A Journal on Classical Euclidean Geometry and Related Areas)'' - '''Authors''' - Uploaded by '''Amir Hossein Parvardi'''. ''AVAILABLE for DOWNLOAD''.
**[http://www.4shared.com/file/9Ay946kL/Forum_Geometricorum_-_All_volu.html '''''All Volumes''''']
+
** [http://www.mediafire.com/download/v2rzcic8irni53r/Forum_Geometricorum_-_All_volumes.rar '''''All Volumes (direct link to the RAR file)'''''] - Alternative link: [http://s3.picofile.com/file/8211244900/Forum_Geometricorum_All_volumes.rar.html '''''All Volumes''''']
**[http://www.4shared.com/document/Nm86Tfiv/Volume_1_-_FORUM_GEOMETRICORUM.html '''First Volume''']
+
 
**[http://www.4shared.com/document/-Kg5kOx8/Volume_2_-_FORUM_GEOMETRICORUM.html '''Second Volume''']
+
 
**[http://www.4shared.com/document/dcCAx9Vp/Volume_3_-_FORUM_GEOMETRICORUM.html '''Third Volume''']
 
**[http://www.4shared.com/document/tNqXyU1F/Volume_4_-_FORUM_GEOMETRICORUM.html '''Fourth Volume''']
 
**[http://www.4shared.com/document/NFT7Irys/Volume_5_-_FORUM_GEOMETRICORUM.html '''Fifth Volume''']
 
**[http://www.4shared.com/document/NqofMPAt/Volume_6_-_FORUM_GEOMETRICORUM.html '''Sixth Volume''']
 
**[http://www.4shared.com/document/LllTHOec/Volume_7_-_FORUM_GEOMETRICORUM.html '''Seventh Volume''']
 
**[http://www.4shared.com/document/yIx2G_2X/Volume_8_-_FORUM_GEOMETRICORUM.html '''Eighth Volume''']
 
**[http://www.4shared.com/document/3u061hi3/Volume_9_-_FORUM_GEOMETRICORUM.html '''Ninth Volume''']
 
  
*[http://www.cip.ifi.lmu.de/%7Egrinberg/faq.html#books ''This''] note by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=432 '''Darij Grinberg''']
 
  
 
*[http://sites.google.com/site/darijgrinberg/website '''''Darij Grinberg's''' whole site download''] - his [http://www.cip.ifi.lmu.de/~grinberg/ ''website''] has a great number of articles/solved problems that you may use in your Olympiad studying - '''Great'''.
 
*[http://sites.google.com/site/darijgrinberg/website '''''Darij Grinberg's''' whole site download''] - his [http://www.cip.ifi.lmu.de/~grinberg/ ''website''] has a great number of articles/solved problems that you may use in your Olympiad studying - '''Great'''.
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*''Introduction to Geometry'' - '''Coxeter''' - '''Theory''' 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.
 
*''Modern Geometry with Applications'' - '''Jennings''' - '''Both''' book.
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*''Proofs that Really Count (The Art of Combinatorial Proof)''' - '''Benjamin and Quinn'''.
 
*''Proofs that Really Count (The Art of Combinatorial Proof)''' - '''Benjamin and Quinn'''.
 
*''A Course in Combinatorics'' - '''Lint and Wilson'''.
 
*''A Course in Combinatorics'' - '''Lint and Wilson'''.
 +
*[https://drive.google.com/file/d/1sQtirXxkEfWYuGSKDZ-d7VGYkR_idebY/view ''Olympiad Combinatorics''] - '''Pranav A. Sriram'''.
  
 
==Improve Your Skills With Problem Solving==
 
==Improve Your Skills With Problem Solving==
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*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=386343 ''567 Nice And Hard Inequalities''] - '''Nguyễn Duy Tùng'''.
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=386343 ''567 Nice And Hard Inequalities''] - '''Nguyễn Duy Tùng'''.
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=398739 ''Inequalities From 2007 and 2008 Competitions Around The World''] - '''Manh Dung Nguyen'''.
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=398739 ''Inequalities From 2007 and 2008 Competitions Around The World''] - '''Manh Dung Nguyen'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=398915 ''A Collection of Limits''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=61082 '''Pain rinnegan'''].
 
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=407914 ''Technical Analysis of Three Variable Inequalities''] - '''Nguyen Duy Tung, Zhou Yuan Zhe'''.
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=407914 ''Technical Analysis of Three Variable Inequalities''] - '''Nguyen Duy Tung, Zhou Yuan Zhe'''.
  
 
=== Number Theory ===
 
=== Number Theory ===
  
 
+
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=492767 ''1220 Number Theory Problems (With Sources)''] - '''Amir Hossein Parvardi'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=412253 ''100 Number Theory Problems (With Sources)''] - '''Amir Hossein Parvardi'''.
 
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=401494 ''Lifting the Exponent Lemma (LTE)''] - '''Amir Hossein Parvardi'''.
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=401494 ''Lifting the Exponent Lemma (LTE)''] - '''Amir Hossein Parvardi'''.
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=410293 ''Solving Diophantine Equations''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=94338 '''lamphong'''].
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=410293 ''Solving Diophantine Equations''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=94338 '''lamphong'''].
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*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=399036 ''Primitive Roots, Order, and Quadratic Residues''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=85314 '''mathmdmb'''].
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=399036 ''Primitive Roots, Order, and Quadratic Residues''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=85314 '''mathmdmb'''].
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=396930 ''Number Theory Marathon Problems''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=16383 '''M4RI0'''].
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=396930 ''Number Theory Marathon Problems''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=16383 '''M4RI0'''].
 
  
 
=== Geometry ===
 
=== Geometry ===
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*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=385682 ''150 Nice Geometry Problems (With Solutions)''] - '''Amir Hossein Parvardi'''.
 
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=385682 ''150 Nice Geometry Problems (With Solutions)''] - '''Amir Hossein Parvardi'''.
 
*[http://sites.google.com/site/darijgrinberg/website '''''Darij Grinberg's''' whole site download''] - his [http://www.cip.ifi.lmu.de/~grinberg/ ''website''] has a great number of articles/solved problems that you may use in your Olympiad studying.
 
*[http://sites.google.com/site/darijgrinberg/website '''''Darij Grinberg's''' whole site download''] - his [http://www.cip.ifi.lmu.de/~grinberg/ ''website''] has a great number of articles/solved problems that you may use in your Olympiad studying.
 +
*
 +
Euclidean Geometry in Mathematical Olympiads [http://web.evanchen.cc/geombook.html]
  
 
=== Combinatorics ===
 
=== Combinatorics ===
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*''USA Mathematical Olympiads 1972-1986 ''(Problems and Solutions)'' - '''Murray S. Klamkin'''.
 
*''USA Mathematical Olympiads 1972-1986 ''(Problems and Solutions)'' - '''Murray S. Klamkin'''.
 
*''USSR Mathematical Olympiads 1989-1992'' - '''Arkadii M. Slinko'''.
 
*''USSR Mathematical Olympiads 1989-1992'' - '''Arkadii M. Slinko'''.
*''Problems From THE BOOK'' - '''Martin Aigner, Günter M. Ziegler'''.
+
*''Proofs From THE BOOK'' - '''Martin Aigner, Günter M. Ziegler'''.
 
*''Techniques of Problem Solving'' - '''Steven G. Krantz'''.
 
*''Techniques of Problem Solving'' - '''Steven G. Krantz'''.
 
*''Junior Balkan Mathematical Olympiads'' - '''Dan Branzei, loan Serdean, Vasile Serdean'''.
 
*''Junior Balkan Mathematical Olympiads'' - '''Dan Branzei, loan Serdean, Vasile Serdean'''.

Revision as of 15:15, 11 August 2020

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

  • 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

Functional Equations

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 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.
  • 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.



  • 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

Number Theory

Geometry

Euclidean Geometry in Mathematical Olympiads [1]

Combinatorics

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.