Nov 18, 2010

23 Jun		arXiv:1006.4257 Impact of network structure on competitive evolutionary processes. V. Nicosia, F. Bagnoli, V. Latora. physics.soc-ph (nlin.PS physics.stat-mech).

22 Jun		arXiv:1006.3923 Complex Networks and Symmetry: a Review with Applications to the Evolution of World Trade. Franco Ruzzenenti, Diego Garlaschelli, Riccardo Basosi. physics.soc-ph (nlin.AO physics.stat-mech).

22 Jun		arXiv:1006.3863 Normalization of research evaluation results across academic disciplines. Ralph Kenna, Bertrand Berche. physics.soc-ph (cs.DL).

Cross-listings

23 Jun		arXiv:1006.4294 NetzCope: A Tool for Displaying and Analyzing Complex Networks. Michael J. Barber, Ludwig Streit, Oleg Strogan. physics.data-an (physics.soc-ph).

23 Jun		arXiv:0902.0878 Backbone of complex networks of corporations: The flow of control. J. B. Glattfelder, S. Battiston. Phys. Rev. E 80, 036104 (2009). q-fin.GN (physics.soc-ph).

21 Jun		arXiv:1006.3708 Econophysics studies in Estonia. M. Patriarca, E. Heinsalu, R. Kitt, J. Kalda. q-fin.GN (physics.soc-ph).

Revisions

22 Jun		arXiv:1003.0088 A Condition for Cooperation in a Game on Complex Networks. Tomohiko Konno. physics.soc-ph.

22 Jun		arXiv:1002.3282 Cooperation in the snowdrift game on directed small-world networks under self-questioning and noisy conditions. Tian Qiu, Tarik Hadzibeganovic, Guang Chen, Li-Xin Zhong, Xiao-Run Wu. physics.soc-ph (cs.GT physics.comp-ph q-bio.PE).

Revised crosses

23 Jun		arXiv:0911.4729 Hearing the clusters in a graph: A distributed algorithm. Tuhin Sahai, Alberto Speranzon, Andrzej Banaszuk. math.CO (cs.DC physics.comp-ph physics.soc-ph).

23 Jun		arXiv:0809.1040 Patterns in high-frequency FX data: Discovery of 12 empirical scaling laws. J. B. Glattfelder, A. Dupuis, R. B. Olsen. q-fin.ST (physics.soc-ph).

22 Jun		arXiv:0909.3257 The Shield that Never Was: Societies with Single-Peaked Preferences are More Open to Manipulation and Control. P. Faliszewski, E. Hemaspaandra, L. A. Hemaspaandra, J. Rothe. URCS TR-2009-950. cs.GT (cs.CC cs.MA physics.soc-ph).

22 Jun		arXiv:0908.1879 Multinetwork of international trade: A commodity-specific analysis. Matteo Barigozzi, Giorgio Fagiolo, Diego Garlaschelli. Physical Review E 81, 046104 (2010). q-fin.GN (physics.soc-ph physics.stat-mech).

Jul 27, 2010

New Zealand Maths Olympiad Committee online

http://www.nzamt.org.nz/nzimo/category/notes/algebra/

Limits, continuity and completeness

Wednesday, April 8, 2009 22:09

Posted in category Algebra

1 Comment

Occasionally, in contest problems, it helps to have a careful understanding of real numbers and real-valued functions. But what, exactly, is a real number? These Auckland squad training lecture notes by Heather Macbeth outline some basics.

(Update, 19/4/09: several errors fixed.)

Polynomials, pure mathematics, Princeton Companion

Thursday, April 2, 2009 13:23

Posted in category Algebra, Links

2 Comments

Round about sixth form one learns that every polynomial can be factorized, as a product of linear factors. Why? Well, here’s a polynomial, see. It’s probably a cubic with integer coefficients — after all, most nontrivial polynomials that one encounters are. You play with it until you discover a root, likely by looking at integer factors of the highest and lowest coefficients. Then you polynomial-divide through by the linear factor which that root gives you, and get a quadratic, whose roots there’s a formula for finding. Tada!

Of course, there’s a problem with this algorithm: it depends on figuring out how to break down your polynomial into only linear and quadratic factors.

Recurrence relations

Tuesday, January 27, 2009 17:06

Posted in category Algebra, Combinatorics

1 Comment

Some notes and problems on finding and solving recurrence relations. Read these if you’ve ever wondered how to find a formula for the Fibonacci sequence!

Symmetric polynomials

Monday, January 26, 2009 15:56

Posted in category Algebra

No Comments

These notes by Arkadii Slinko explain how to extract information from symmetric polynomials of a set of variables, and how to break any symmetric polynomial down into a few simple ones. The final section gives some applications to triangle geometry.

Functional equations

Sunday, January 25, 2009 1:36

Posted in category Algebra

No Comments

These notes by Arkadii Slinko cover techniques — some standard, some exotic — for solving functional equations: groups of substitutions, commutativity, the Cauchy functional equation.

Solutions to some of the problems are available, and can be obtained by writing to nzmathsolymp@gmail.com.

Convex functions

Wednesday, January 14, 2009 21:08

Posted in category Algebra

No Comments

Notes from Heather Macbeth’s algebra lecture at the January 2009 camp.

(Update, 24/1/2009: some typos fixed.)

Jul 26, 2010

More Math Videos!

Below are several math-related videos produced by others. We'll add more periodically. Please let us know of others we should add to our collection.

Beautiful Math

International Mathematics Olympiad

http://olympiads.win.tue.nl/imo/#international

PDATED (March 2007) Recommended literature, such as Paul Zeitz' The Art and Craft of Problem Solving
Amazon Kindle 2, Amazon's new e-reader for digital books
More about IMO: HARD PROBLEMS: The Road to the World's Toughest Math Contest

The International Mathematics Olympiad (IMO, also known as the International Mathematical Olympiad) is an annual mathematics competition for high school students [IMO Article in Wikipedia]. It is one - in fact, the oldest - of the International Science Olympiads. The first IMO was held in Romania in 1959. The problems come from various areas of mathematics, such as are included in math curricula at secondary schools. Finding the solutions of these problems, however, requires exceptional mathematical ability and excellent mathematical knowledge on the part of the contestants.

Topics covered (see Unwritten Syllabus and Tutorials at Arkadii Slinko's Math Olympiad Website, currently being transferred):

Number Theory, including
- Fundamental Theorems on Arithmetic
- Linear and quadratic Diophantine equations, including Pell's equation
- Arithmetic of residues modulo n, Fermat's and Euler's theorems
Algebra, including
- Fundamental Theorems on Algebra, e.g. inequalities, factorization of a polynomial into a product of irreducible polynomials
- Symmetric polynomials of several variables, Vieta's theorem
Combinatorics, including
- Graph theory
Geometry, including
- Properties of the orthocentre, Euler's line, nine-point-circle, Simson line, Ptolemy's inequality, Ceva and Menelaus etc.

Excluded topics:

Calculus (!)
Complex numbers (though present in the past)
Inversion in geometry
Solid geometry (though present in the past; may return)

The usual size of an official delegation to an IMO is (a maximum of) six student competitors and (a maximum of) two leaders. There is no official ``team''. The student competitors write two papers, on consecutive days, each paper consisting of three questions. Each question is worth seven marks. (The preceding information is taken from an Overview of the IMO provided by the IMO'95 host country, Canada; also see below.) A total score of 42 points is possible. Awards are determined as follows:

GOLD MEDAL: the top 1/12 of scores receive gold medals
SILVER MEDAL: the next 2/12 of scores receive silver medals
BRONZE MEDAL: the next 3/12 of scores receive bronze medals
HONORABLE MENTION: any competitor who receives a perfect score of 7 on any one question, but who does not receive a medal, is awarded an honorable mention

My report on IMO 2002 provides further details of how the IMO is run.

A list of recommended mathematics literature for self-study is slowly evolving.

General Information
International Mathematics Competitions
Regional Mathematics Competitions
National Mathematics Competitions
Archives and Link Collections
Schools
Mathematics on WWW
Miscellaneous Links

Without doubt, these lists of web addreses are far from complete. If you send relevant web addresses that are not listed here, then they will be included.

General Information

Official IMO web site < < < < < N E W

A new website about the IMO, including a problem and results archive.

Logos

An overview of all available logos

Regulations

Regulations Pertaining to the IMO

These Regulations define the IMO as of ?. New aspects are the IMO Advisory Board and the IMO Trust Fund.

General (but not official) IMO site

Future IMOs

IMO 2009

The 50th IMO will be hosted by Germany in Bremen on 10-22 July, 2009.

IMO 2010

The 51st IMO will be hosted by Kazakhstan in ? on ?-? ?, 2010.

IMO 2011

The 52nd IMO will be hosted by the Netherlands in ? on ?-? ?, 2011.

Past IMOs

IMO 2008 [ local files ]

The 49th IMO was hosted by Spain in Madrid on 10-22 July, 2008. (arrival day for contestants is 14 July).

IMO 2007 [ local files: logo | problems day 1, day 2 ]

The 48th IMO was hosted by Vietnam in Hanoi on 19-31 July, 2007 (arrival day for contestants is 23 July).

IMO 2006 [ local files: about | logo | problems day 1, day 2 | solutions | results ]

The 47th IMO was hosted by Slovenia in Ljubljana on 6-18 July, 2006.

The 46th IMO was hosted by Mexico in Mérida, Yucatán, on 8-19 July, 2005.

IMO 2004 [ logo | rules | problems day 1, day 2 | all data | UK report incl. problems ]

The 45th IMO was hosted by Greece in Athens on 6-18 July, 2004.

The 44th IMO was hosted by Japan in Tokyo on 7-19 July, 2003. Submission deadline for problems was 15 Feb. 2003.

The 43rd IMO was hosted by the United Kingdom in Glasgow on 19-30 July, 2002.

The 42nd IMO was hosted by the United States of America in Washington DC on 1-14 July, 2001.

The 41st IMO was hosted by South Korea in Taejon on 13-25 July, 2000.

IMO 1999 [ logo | problems day 1 | problems day 2 | results | mailing list ]

The 40th IMO was hosted by Romania in Bucharest on 10-22 July, 1999.

IMO 1998 [ logo | problems | results ]

The 39th IMO was hosted by Taiwan in Taipei on 10-21 July, 1998.

IMO 1997 [ logo | problems day 1 | problems day 2 | results ]

The 38th IMO was hosted by Argentina in Mar del Plata on July 18-31, 1997. There is an IMO97 mailing list.

IMO 1996 [ logo | the problems ]

The 37th IMO was hosted by India in Mumbai (Bombay) on July 5-17, 1996.
Contact information:
Professor A.M. Vaidya
IMO-Cell, School of Mathematics,
Tata Institute of Fundamental Research
Homi Bhabha Road, Mumbai (Bombay) -400005
India

Telephone:91(022) 2152971, 2152311, 2188654
Telefax: 91 (022) 2152110/2152181
Email: imo@tifrvax.tifr.res.in or imo@math.tifr.res.in

IMO 1995 [ logo | regulations | the problems ]

The 36th IMO was hosted by Canada in Toronto on July 10-28, 1995.

IMO 1994 [ logo | the problems and results ]

The 35th IMO was hosted by Hong Kong on July 12-19, 1994.

IMO 1993 [ logo | problems day 1 | problems day 2 ]

The 34th IMO was hosted by Turkey in Istanbul on July 12-19, 1993.

Journals and other info

IMOnet

The network for the participants to the IMO. Has information on three mailing lists (for IMO'99, IMO2000, and IMO problems).

IMO News at MAA

The Mathematical Association of America (MAA) carries some information on the IMO and publishes books with IMO problems.

IMO Scores

This site has some statistics about scores at IMO 1993 an on (except 1994). Maintained by Joseph Myers.

KöMaL - Mathematical and Physical Journal for Secondary Schools

More than one hundred years ago, Dániel Arany, a high school teacher from the city of Gyõr, decided to found a mathematical journal for high school students. His goal was "to give a wealth of examples to students and teachers". The journal's first edition appeared on January 1, 1894.

MathPro Press

MathPro Press specializes in the publication of compendiums and indexes of mathematics problems.

WFNMC

The World Federation of National Mathematics Competitions (WFNMC) publishes a journal entitled Mathematics Competitions. Also see Australia below.

M&IQ

The Mathematics and Informatics Quarterly is an international journal which:

Publishes articles, notes, problems and solutions in school mathematics and informatics.
Is devoted to teachers and students, who are interested in mathematics and informatics clubs, olympiads and competitions.

In the World of Mathematics

This new quarterly journal is aimed at pupils, students, and teachers interested in mathematical problems and puzzles as well as in the history of mathematics and its new trends.

SIPROMA Bulletin (in Spanish)

SIPROMA is the ``Sociedad Iberoamericana para la Promoción de la Matemática''.

International Mathematics Competitions

Kangourou Sans Frontières / Kangaroo without Frontiers: International Mathematics Competition (French site)

Kangourou Sans Frontières (KSF) is an international mathematics competition for various levels of students. History and Rules (old)

France: Le Kangourou de Mathématiques
Germany: Känguru der Mathematik
Italy: Kangourou Italia
Netherlands: Wiskunde Kangoeroe
Poland: Kangur Matematyczyny
Russia: Kenguru
United States of America: Math Kangaroo

Mathematical Olympiads for Elementary and Middle Schools

Created in 1977 by Dr. George Lenchner, an internationally known math educator, the Math Olympiads went public in 1979. In the year 2000, over 120,000 students from 5,000 teams worldwide participated in the Olympiads, representing 26 countries.

International Living Maths Mathletics Olympiad <<<<< N E W

Living Maths (South Africa) organizes the International Living Maths Mathletics Olympiad for ages 6 to 13 (K-7). Look under: Events, Olympiad.

Mental Calculation World Cup

Regional Mathematics Competitions

Asian Pacific Mathematics Olympiad: Problems in English and French.
Balkan Math Olympiad: No link yet.
Bay Area Mathematical Olympiad: The Bay Area Mathematical Olympiad (BAMO) is a contest for high school students sponsored jointly by the Mathematical Sciences Research Institute (MSRI), the American Institute of Mathematics (AIM), the University of California at Berkeley (UCB), and the University of San Francisco (USF).
Colorado Mathematical Olympiad: The Colorado Mathematical Olympiad (CMO) is the largest essay-type mathematical competition in the United States, with 600 to 1,000 participants competing annually for fine prizes.
Ibero-American Mathematics Olympiad: Home page (in Spanish) of the Olimpíadas Iberoamericanas de Matemática (OIM).
The Math League (USA & Canada): The Math League is dedicated to bringing challenging mathematics materials to students, and specializes in math contests (for high schools in the USA and Canada), books, and computer software.

National Mathematics Competitions

Argentina

The Olimpíada Matemática Argentina (OMA) is the Argentinian Mathematics Olympiad. Currently, information is only available in Spanish.

Australia

The Australian Mathematics Trust (AMT) is a national non-profit organization which conducts mathematics competitions in Australia. Includes information on theWFNMC.

Belgium

Information about the Mathematics Olympiads in Belgium:

The Flanders Mathematics Olympiad (Vlaamse Wiskunde Olympiade = VWO), maintained by Paul G. Igodt (Paul.Igodt@kulak.ac.be).
The Olympiade Mathématique Belge (OMB).

Brazil [ also see here ]

Information about the Brazilian Mathematics Olympiad (OBM=Olimpíada Brasileira de Matemática). All material in Portuguese only.

Bulgaria

Information about the National Mathematical Olympiad in Bulgaria as part of the Bulgarian Competitions in Mathematics and Informatics.

Canada

Information about the Canadian Mathematics Competition (CMC) maintained by Ruth Malinowski (cmc@math.uwaterloo.ca).

The Canadian Mathematical Society also has an Olympiads Home Page.

Colombia

The WWW Home Page for the Colombian Olympiads (in Spanish), covering Mathematics, Phyisics, and Informatics, maintained by Fernando Vega Salamanca (fvega@zulima.uanarino.edu.co).
E-mail: olimpia@federman.uanarino.edu.co

Czech Republic

Denmark

Estonia

Information about the Estonian Matemaatika Olümpiaadid (also in the Estonian language), maintained by Uve Nummert (uve@math.ut.ee). Includes IMO information (in English).

France

Information about mathematics competitions in France, includes French translations of IMO problem sets and recommended French mathematics literature for IMO preparation.

Germany

The Verein Mathematik-Olympiaden e.V. coordinates the German Mathematics Olympiads (DeMO). There is also information available about the German Mathematics Olympiad 1995.

Ireland

Information on Irish participation in the International Mathematical Olympiads and (eventually) copies of Irish Maths Olympiad questions and photographs. Contact: Gordon Lessells (gordon.lessells@ul.ie).

Israel

Italy

Information on the Italian (?) Mathematics Olympiad (in Italian). E-mail contact: mvillani@cibs.sns.it

Japan

Information about the IMO in general (starting from 34th) and the Mathematical Olympiad Foundation of Japan. Maintained by Naomasa Maruyama (maruyama@ism.ac.jp).

Luxembourg

Mexico

Information (in Spanish) on the Mexican Mathematics Olympiad (OMM) and problem sets (mostly in Spanish) of various (regional) mathematics contests. E-mail:omm@hp.fciencias.unam.mx. Maintained by Felipe Lemaitre Carabias (iker@hardy.fciencias.unam.mx).

There is also an unofficial page for the Mexican Mathematical Olympiad (in Spanish), maintained by Pedro Sánchez.

Pierre Fermat Math Competition (in Spanish: Concurso de Matemáticas Pierre Fermat).

The Netherlands

Information about the Dutch Mathematics Olympiad (now also in English), maintained by Tom Verhoeff (Tom.Verhoeff@acm.org).

New Zealand

Information about the New Zealand Math Olympiads

Norway

The Niels Henrik Abels Mathematics Competition selects students for partiticipation in the IMO. This site also contains problem sets of the Norwegian Mathematical Olympiad and the IMO, including some solutions and results. Maintained by Einar Andreas Rødland (einara@math.uio.no).

Panama

Peru

Information about Peru's math olympiad and the Cono Sur olympiads, maintained by Enrique Valeriano (evaleri@pucp.edu.pe).

Poland

Information (including problem sets) on the math olympiads in which Polish high school students participate (in particular: the Polish Mathematical Olympiad, the Austrian-Polish Mathematics Competition, and the Baltic Team Contest). Maintained by Krzysztof Chelminski (chel@mathematik.th-darmstadt.de) and Waldemar Pompe (waldipo@mimuw.edu.pl).

Mirror: http://www.mathematik.tu-darmstadt.de/~chelminski/Olimp/olympiads.html

Portugal

Olimpíadas Portuguesas de Matemática.

Singapore

Information about the IMO and Singapore's participation.

Slovakia

Mathematical olympiad in Slovakia.

Slovenia

Mathematical competitions in Slovenia are supervised by DMFA.

South Africa

South African Mathematics Olympiad.

Spain

Information and problem sets (in Spanish) for the math olympiads in which Spanish high school students participate, including the Spanish Mathematics Olympiad (Olimpiada Matemática Española = OME). Maintained by Cristobal Sánchez Rubio (csanchez@platea.pntic.mec.es).

Unoficcial Spanish Math Olympiad page maintained by Ramon Esteban Romero (Ramon.Esteban@uv.es).

Switzerland

Information about the Swiss participation in the IMO in English, French, German, Italian.

United Kingdom

Information about the British Mathematical Olympiad (BMO). The UK IMO Register offers a lot of historic information about the UK's participation in the IMO. Do browse the Leaders's Reports.
Related: United Kingdom Mathematics Trust (UKMT), a registered charity which conducts a number of mathematical enrichment activities via schools.

Uruguay

USA

Information on the USA Math Olympiad and the IMO.

USA: AMC

The American Mathematics Competitions (AMC).

USA: USAMTS

The USA Mathematical Talent Search (USAMTS) is a free mathematics competition open to any US middle or high school student. It is a great contest for students aspiring to Olympiad problem solving, since many of the problems require proof-based solutions.

Archives and Link Collections

The IMO Collection =====NEW=====

Here you will find a large collection of olympiad problems from all over the world. You will also find all the information regarding The IMO Compendium, the most complete collection of problems proposed to the International Mathematical Olympiads.

The Art of Problem Solving

The Art of Problem Solving contains a variety of resources for avid students of mathematics in middle and high school. There are many free resources (in addition to a Forum) such as articles, a LaTeX tutorial, and online Math Jam sessions. Olympiad problem solvers from all over the world participate in problem discussions. The site also sells a set of problem solving textbooks and has an online school.

Includes IMO Problems and Solutions, with authors.

Mathematical Problem Solving Advice by Prof. Shapiro

This website covers some general techniques for solving mathematical problems. It intends to grow into an interactive website. Maintained by Harold Shapiro.

MathLinks.ro

Math problem collections, a frequent (hard!) math contest, and a large problem solving community with many on-line formus for discussions. Maintained byValentin Vornicu.

A Large Collection of Math Contest Material

Includes Problems in Elementary Number theory (PEN), Topics in INequalities (TIN), and Problem-Solving Web-Directory (PSD). Archive maintained by Hojoo Lee(a.k.a. "ideahitme") in Republic of Korea.

PEN: Problems in Elementary Number Theory

A forum around the number-theory problem collection of Hojoo Lee (see above).

A Collection of Math-Olympiad-Problems

Archive maintained by Hans Vernaeve (Hans.Vernaeve@rug.ac.be) in Belgium.

Arkadii Slinko Mathematics Olympiad Site (gradually being transferred)

Provides: a collection of problems, tutorials, training material, articles, a Monthly Internet Mathematics Olympiad, and information on the New Zealand Math Olympiads.

Math Competitions Archive

Kiran Kedlaya (MIT, USA, kray@post.com) has a Math Competitions Archive with some of the recent (back to 1991) IMO problem sets in various formats, and information about the USA Mathematical Olympiad (USAMO). He now has a separate Math Problem Directory.

Math Competition on the Web

Archive and links maintained by Naoki Sato (ensato@hotmail.com) in Toronto, Canada.

OMAP: Online Math Problems

Database of problems that appeared on various national and international math competitions around the world, including detailed info about the Putnam Math Competition. Maintained by meeroh@mit.edu.

Soviet Union 1961-1986

The problems of the All-Soviet-Union national mathematical competitions (final part), 1961-1986 were translated into English and put on the Web by Vladimir Pertsel (voldemar@sagantec.co.il). There is also a plain ASCII version, and a compressed archive with everything: HTML, ASCII, and GIF pictures. [The original page and original archive are still available.]

Olympiad Math Madness

A collection of mathematical brain-busters, specially for those who are tired of not-very-hard problems. Maintained by jefflock@geocities.com.

Mathematics Olympiad Lecture Notes

By Greg Gamble (gregg@maths.uwa.edu.au).

20,000 Problems Under the Sea: Mathematical Treasures on the Web

Online reference to mathematical problems.

Kalva Homepage

Problem collections maintained by John Scholes.

Le Thai Hoang's Math Olympiad

Le Thai Hoang's Math Olympiad Page contains many math problem sets, including shortlists for IMO from 1983 to 1998.

Nick's Mathematical Puzzles

A collection of puzzles ranging over geometry, probability, number theory, algebra, calculus, and logic. Hints are provided, along with answers, fully worked solutions, and links to related mathematical topics. Many of the puzzles are elementary in their statement, yet challenging. New puzzles are added on a regular basis.

A key feature of the site is the detailed exposition, from first principles, of the puzzle solutions. Some of the puzzles are used to showcase particular mathematical concepts. See, for example, puzzle 56, which introduces a partition identity, and puzzle 63, where Ptolemy's Theorem permits a surprisingly simple solution. Further references are provided with many of the solutions.