Trang luyện tập môn Toán

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: 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

  • 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). Excellentbook 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 - 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).

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.
  • 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 ParvardiAVAILABLE 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.
  • 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

Number Theory

Geometry

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.
  • Problems 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 1A. M. Gleason, R. E. Greenwood, L. M. Kelly, Volume 2Gerald L. Alexanderson, Leonard F. Klosinski, Loren C. LarsonVolume 3Kiran 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, 3Charles T. Salkind, James M. EarlVolume 4Ralph 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.

GEOMETRY

150 nice geometry problem

FUNCTIONAL EQUATIONS

Bài 1

Bài 2

Bài 3

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