Books and Compilations

Primarily targeted at the Olympiad

The following books treat, quite comprehensively, the topics that are broadly covered in the Mathematical Olympiads, and provide a rich source of problems -- highly recommended.

  • Excursion

    An Excursion in Mathematics

    Editors: M.R. Modak, S.A. Katre and V.V. Acharya (Bhaskaracharya Pratishthana, Pune, 2015)
  • PreCollege

    Challenge and Thrill of Pre-College Mathematics

    V. Krishnamurthy, C.R. Pranesachar, K.N. Ranganathan and B.J. Venkatachala (New Age International Publishers, New Delhi, 2007)
  • Problem Primer

    Problem Primer for the Olympiads

    C.R. Pranesachar, B.J. Venkatachala and C.S. Yogananda (Prism Books Pvt. Ltd., Bangalore, 2008)
  • Arthur Engel

    Problem Solving Strategies

    Arthur Engel (Springer-Verlag, Germany, 1999)
  • Mathematical Circles

    Mathematical Circles: Russian Experience

    Dmitri Fomin, Sergey Genkin and Ilia Itenberg (University Press, Hyderabad, 2008)
  • Olympiad Challenges

    Mathematical Olympiad Challenges

    Titu Andreescu and Razvan Gelca (Springer India, 2014)
  • Functional Equations

    Functional Equations

    B.J. Venkatachala (Prism Books Pvt. Ltd., Bangalore, 2008)

Most of these books are available at the College Street area of Kolkata, or online, through Flipkart or Amazon. You may also contact Saraswati Pustakalaya, 138/1 Gopal Lal Thakur Road, Kolkata 700 108.

Sample Problems

Previous Olympiad Papers

The students must try to solve the problems from the old exams of RMO and INMO. All these problems can be solved without using Calculus or calculators. However, these problems are not routine text book problems. They are considerably harder, calling for ingenuity on the part of the solver. Therefore, it is highly advisable that a student solves as many new problems as possible, with no or with minimum help. Note that if you are unable to solve at least one problem from each old RMO exam without any help, RMO is not for you.


RMO -- Problems (1990 to 1999)
RMO 1990   |   RMO 1991   |   RMO 1992   |   RMO 1993   |   RMO 1994   |   RMO 1995   |   RMO 1996   |   RMO 1997   |   RMO 1998   |   RMO 1999   |  

RMO -- Problems and Solutions (2000 to 2010)
RMO 2000   |   RMO 2001   |   RMO 2002   |   RMO 2003   |   RMO 2004   |   RMO 2005   |   RMO 2006   |   RMO 2007   |   RMO 2008   |   RMO 2009   |   RMO 2010   |  

RMO -- Problems and Solutions (2011 onwards)
RMO 2011   :   CRMO 1   -- renamed to CRMO (4 different papers in general)
RMO 2012   :   CRMO 1   |   CRMO 2   |   CRMO 3   |   CRMO 4   |   RMO Mumbai
RMO 2013   :   CRMO 1   |   CRMO 2   |   CRMO 3   |   CRMO 4   |   RMO Mumbai
RMO 2014   :   CRMO 1   |   CRMO 2   |   CRMO 3   |   CRMO 4   |   RMO Mumbai
RMO 2015   :   CRMO 1   |   CRMO 2   |   CRMO 3   |   CRMO 4   |   RMO Mumbai
RMO 2016   :   CRMO 1   |   CRMO 2   |   CRMO 3   |   CRMO 4


INMO -- Problems (1989 to 1999)
INMO 1989   |   INMO 1990   |   INMO 1991   |   INMO 1992   |   INMO 1993   |   INMO 1994   |   INMO 1995   |   INMO 1996   |   INMO 1997   |   INMO 1998   |   INMO 1999

INMO -- Problems and Solutions (2000 onwards)
INMO 2000   |   INMO 2001   |   INMO 2002   |   INMO 2003   |   INMO 2004   |   INMO 2005   |   INMO 2006   |   INMO 2007   |   INMO 2008   |   INMO 2009   |   INMO 2010   |   INMO 2011   |   INMO 2012   |   INMO 2013   |   INMO 2014   |   INMO 2015   |   INMO 2016   |   INMO 2017


  Previous Question Papers and their Solutions on the HBCSE Olympiad Website.

Reference Books

Recommended reading

The following books form the recommended reading for various mathematical competitions at the pre-college level. Some of these are elementary, and some quite advanced.

  • S. Barnard and J.M. Child, Higher Algebra
    Macmillan & Co., London, 1939; reprinted Surjeet Publishers, Delhi, 1990
  • H.S. Hall and S.R Knight, Higher Algebra
    Macmillan & Co., London; Metric Edition, New Delhi, 1983
  • W. S Burnside and A.W. Panton, The Theory of Equations
    S. Chand & Co., New Delhi, 1990
  • P.P. Korovkin, Inequalities
    MIR Publishers, Moscow, 1975
  • R.A. Brualdi, Introductory Combinatorics
    Elsevier, North-Holland, New York, 1977
  • A.W. Tucker, Applied Combinatorics
    John Wiley & Sons, New York, 1984
  • D.M. Burton, Elementary Number Theory
    Universal Book Stall, New Delhi, 1991
  • I. Niven, H.S. Zuckerman and H.L. Montgomery, An Introduction to the Theory of Numbers, Wiley Eastern, New Delhi, 2000
  • G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers
    Oxford University Publishers, UK, 2008
  • C.V. Durell, Modern Geometry
    Macmillan & Co., London, 1961
  • H.S.M. Coxeter and S.L. Greitzer, Geometry Revisited
    The Mathematical Association of America, New York, 1967
  • N.D. Kazarinoff, Geometric Inequalities
    Random House and The L.W. Singer Co., New York, 1961
  • S.L. Loney, Plane Trigonometry
    Macmillan & Co., London.
  • G.N. Yakovlev, High School Mathematics
    MIR Publishers, Moscow, 1984
  • R. Honsberger, Mathematical Gems
    The Mathematical Association of America, New York
  • D. O. Shklyarshky, N. N. Chensov and I. M. Yaglom, The USSR Olympiad Problem Book
    Dover Publications Inc., 1993
  • W. Sierpenski, 250 Problems in Elementary Number Theory
    Elsevier Science Ltd., 1971
  • I.R. Sharygin, Problems in Plane Geometry
    Mir Publishers, 1988

This list of references is always a work-in-progress. Please feel free to suggest more such useful resources for the Mathematical Olympiads, in case we have missed out on any. Your input will be highly appreciated.

Lecture Notes, Handouts and Links

Miscellaneous online resources for the Olympiad

Just like the IMO Training Camp organized by HBCSE, various countries organize their own training camps for the IMO. The lecture notes and handouts from these training camps provide a rich source of preparatory material and problems for the Mathematical Olympiad. Several noted mathematicians and previous champions of the Olympiads contribute to these materials regularly. The students are encouraged to consult the following resources.

  Lecture Notes from the Canada IMO Training Camps (since 1998)
  Olympiad Training Handouts from Yufei Zhao (since 2007)
  Olympiad Training Handouts from Alexander Remorov (since 2010)
  Lecture Notes from the Indian IMO Training Camps (since 2013)

  Lecture Notes on Inequalities by Kiran Kedlaya (1999)
  Lecture Notes on Inequalities by Thomas J. Mildorf (2005)
  Lecture Notes on Number Theory by Thomas J. Mildorf (2010)
  Lecture Notes on Number Theory by Naoki Sato

Art of Problem Solving (AoPS) offers an amazing online community of likeminded students and educators who enjoy discussing interesting mathematical problems. You may find AoPS community and their resources extremely useful while preparing for the Olympiads. Please note that AoPS may hold quick answers to many mathematical problems -- but the goal for you should be to arrive at the solution by yourself -- even if it is really painstaking. So, have fun discussing problems, but please avoid any shortcut to problem-solving.


This list of references is always a work-in-progress. Please feel free to suggest more such useful resources for the Mathematical Olympiads, in case we have missed out on any. Your input will be highly appreciated.