arthur engel problem solving strategies pdf free download

• © 1998

Problem-Solving Strategies

• Arthur Engel 0

Institut für Didaktik der Mathematik, Johann Wolfgang Goethe-Universität Frankfurt am Main, Frankfurt am Main 11, Germany

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• The most complete training book on the market
• A must-have for instructors wishing to enrich their teaching with interesting non-routine problems
• Provides individuals with a wide array of interesting, challenging problems
• Each chapter starts with typical examples illustrating the central concepts, followed by carefully selected problems and their solutions
• Very few problems have no solutions

Part of the book series: Problem Books in Mathematics (PBM)

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Table of contents (14 chapters)

Front matter, the invariance principle, coloring proofs, the extremal principle, the box principle, enumerative combinatorics, number theory, inequalities, the induction principle, polynomials, functional equations, further strategies, back matter.

Problem-Solving Strategies is a unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. The discussion of problem solving strategies is extensive. It is written for trainers and participants of contests of all levels up to the highest level: IMO, Tournament of the Towns, and the noncalculus parts of the Putnam Competition. It will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", "problem of the month", and "research problem of the year" to their students, thus bringing a creative atmosphere into their classrooms with continuous discussions of mathematical problems. This volume is a must-have for instructors wishing to enrich their teaching with some interesting non -routine problems and for individuals who are just interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. Very few problems have no solutions. Readers interested in increasing the effectiveness of the book can do so by working on the examples in addition to the problems thereby increasing the number of problems to over 1300. In addition to being a valuable resource of mathematical problems and solution strategies, this volume is the most complete training book on the market.

• Problem-solving
• mathematics

Arthur Engel

Book Title : Problem-Solving Strategies

Authors : Arthur Engel

Series Title : Problem Books in Mathematics

DOI : https://doi.org/10.1007/b97682

Publisher : Springer New York, NY

eBook Packages : Springer Book Archive

Copyright Information : Springer-Verlag New York 1998

Softcover ISBN : 978-0-387-98219-9 Published: 12 December 1997

eBook ISBN : 978-0-387-22641-5 Published: 19 January 2008

Series ISSN : 0941-3502

Series E-ISSN : 2197-8506

Edition Number : 1

Number of Pages : X, 403

Topics : Mathematics, general

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Includes bibliographical references (p. [397]-398) and index.

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Related Papers

Matheus Felipe

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Resources for mathematically gifted students Tutorials in Algebra, Number Theory, Combinatorics and Geometry The aim of this section is, in the series of tutorials, to cover the material of the unwritten syllabus of the IMO, more precisely that part of it which is not in the school curriculum of most participating countries.

Regional Mathematical Olympiad

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.

An Excursion in Mathematics

Challenge and Thrill of Pre-College Mathematics

Problem Primer for the Olympiads

Problem Solving Strategies

Mathematical Circles: Russian Experience

Mathematical Olympiad Challenges

Functional Equations

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.