https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Hamster1800&feedformat=atomAoPS Wiki - User contributions [en]2021-01-17T10:28:27ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:AoPS_Community_Awards&diff=34269AoPS Wiki:AoPS Community Awards2010-04-08T05:27:17Z<p>Hamster1800: </p>
<hr />
<div>This '''AoPS Community Awards''' page is a celebration of the accomplishments of members of the [[AoPS]] community.<br />
<br />
<br />
== IMO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Mathematical Olympiad]].<br />
<br />
=== Participants ===<br />
* Alex Zhai (2008) <br />
* Krishanu Roy Sankar (2008)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Marco Avila (2006)<br />
* John Berman (2009)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Wenyu Cao (2009)<br />
* Sherry Gong (2002, 2003, 2004, 2005, 2007)<br />
* Elyot Grant (2005)<br />
* Darij Grinberg (2006)<br />
* Mahbubul Hasan (2005)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Brian Lawrence (2005, 2007) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Richard Peng (2005, 2006)<br />
* Eric Price (2005)<br />
* David Rhee (2004, 2005, 2006)<br />
* Peng Shi (2004, 2005, 2006)<br />
* Arne Smeets (2003, 2004)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* Yi Sun (2006)<br />
* [[Valentin Vornicu]] (AoPS/MathLinks webmaster)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2005, 2006, 2007, 2008)<br />
* Yufei Zhao (2004, 2005, 2006)<br />
* Tigran Sloyan(2003,2004,2005,2006,2007)<br />
* Marco Avila (2006)<br />
* Vipul Naik (2003,2004)<br />
* Bhargav Narayanan (2007)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
<br />
===Perfect Scorers===<br />
*Brian Lawrence (2005)<br />
*Alex Zhai (2008)<br />
<br />
=== Gold medalists ===<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Darij Grinberg (2006)<br />
* Kiran Kedlaya (1990, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Arnav Tripathy (2006)<br />
* Eric Price (2005)<br />
* Yufei Zhao (2005)<br />
* Alex Zhai (2007, 2008)<br />
*Sherry Gong (2007)<br />
*Krishanu Sankar (2008)<br />
* John Berman (2009)<br />
<br />
=== Silver medalists ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Sherry Gong (2004, 2005)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Richard Peng (2005)<br />
* David Rhee (2006)<br />
* Naoki Sato (AoPS instructor)<br />
* Peng Shi (2006)<br />
* Arne Smeets (2004)<br />
* Yi Sun (2006)<br />
* [[Sam Vandervelde]] (1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2006)<br />
* Yufei Zhao (2006)<br />
* Tigran Sloyan(2006,2007)<br />
* Vipul Naik (2003,2004)<br />
* Delong Meng (2009)<br />
* Qinxuan Pan (2009)<br />
* Wenyu Cao (2009)<br />
<br />
=== Bronze medalists ===<br />
* Sherry Gong (2003)<br />
* Elyot Grant (2005)<br />
* Richard Peng (2006)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* [[Valentin Vornicu]] (AoPS/[[MathLinks]] webmaster)<br />
* Yufei Zhao (2004)<br />
* Tigran Sloyan(2004;2005)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
<br />
== IPhO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Physics Olympiad]].<br />
=== Participants ===<br />
* Sherry Gong (2006)<br />
* Yi Sun (2004)<br />
* Arnav Tripathy (2006)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
<br />
=== Gold Medalists ===<br />
* Yi Sun (2004)<br />
* Rahul Singh (2007)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
<br />
=== Silver Medalists ===<br />
* Sherry Gong (2006)<br />
<br />
== IOI Medalists ==<br />
This list is of AoPSers who have won medals at the [[International Olympiad in Informatics]].<br />
<br />
===Gold Medalists ===<br />
* David Benjamin (2008)<br />
* Neal Wu (2008, 2009)<br />
* Brian Hamrick (2009)<br />
<br />
===Silver Medalists ===<br />
* Brian Hamrick (2008)<br />
* Jacob Steinhardt (2008)<br />
* Wenyu Cao (2009)<br />
* Travis Hance (2009)<br />
<br />
===Bronze Medalists ===<br />
* David Benjamin (2007)<br />
<br />
<br />
== USAMO ==<br />
The following AoPSers have won the [[United States of America Mathematical Olympiad]] (USAMO). (Note that the definition of "winner" has changed over the years -- currently it is the top 12 scores on the USAMO, but in the past it has been the top 6 or top 8 scores.)<br />
=== Perfect Scorers ===<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2006) ([[WOOT]] instructor)<br />
<br />
=== Winners ===<br />
* Yakov Berchenko-Kogan (2006)<br />
* Wenyu Cao (2009)<br />
* Sherry Gong (2006, 2007)<br />
* Yi Han (2006)<br />
* Adam Hesterberg (2007)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005, 2006, 2007) ([[WOOT]] instructor)<br />
* Tedrick Leung (2006, 2007)<br />
* Haitao Mao (2007)<br />
* Richard Mccutchen (2006)<br />
* Albert Ni (2005)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
* David Rolnick (2008) (AoPS assistant instructor)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* Krishanu Sankar (2007,2008)<br />
* Peng Shi (2006)<br />
* Jacob Steinhardt (2007)<br />
* Yi Sun (2006)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Sam Vandervelde]] (1987, 1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* David Yang (2009)<br />
* Alex Zhai (2006, 2007,2008)<br />
* Yufei Zhao (2006)<br />
* David Bay Rush (2009)<br />
<br />
== Putnam Fellows ==<br />
The top 5 students (including ties) on the collegiate [[Putnam Exam|William Lowell Putnam Competition]] are named Putnam Fellows.<br />
* David Ash (1981, 1982, 1983)<br />
* Daniel Kane (2003, 2004, 2005) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1994, 1995, 1996) ([[AoPS Foundation]] board member)<br />
* Matthew Ince (2005) (AoPS assistant instructor)<br />
* Alexander Schwartz (2000, 2002)<br />
* Jan Siwanowicz (2001) <br />
* Melanie Wood (2002) ([[WOOT]] instructor)<br />
*Arnav Tripathy (2008)<br />
*Brian Lawrence (2008)<br />
<br />
== Siemens Competition Winners ==<br />
The annual [[Siemens Competition]] (formerly Siemens-Westinghouse) is a scientific research competition.<br />
* Michael Viscardi (1st Individual,2005)<br />
* Lucia Mocz (2nd Team, 2006)<br />
<br />
==Intel STS Finalists==<br />
The annual [[Intel Science Talent Search]] is a science competition seeking to find and reward the most scientifically accomplished seniors.<br />
<br />
* Philip Mocz (2008)<br />
* Yihe Dong (2008)<br />
* Qiaochu Yuan (2008)<br />
* Greg Brockman (2007)<br />
<br />
== Clay Junior Fellows ==<br />
Each year since 2003, the [[Clay Mathematics Institute]] has selected 12 Junior Fellows.<br />
* Thomas Belulovich (2005) (AoPS assistant instructor)<br />
* Atoshi Chowdhury (2003) (AoPS assistant instructor)<br />
* Robert Cordwell (2005)<br />
* Eve Drucker (2003) (AoPS assistant instructor)<br />
* Matthew Ince (2004) (AoPS assistant instructor)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Raju Krishnamoorthy (2005)<br />
* Alison Miller (2003) (AoPS assistant instructor)<br />
* Brian Rice (2003) (AoPS assistant instructor)<br />
* Dmitry Taubinski (2005) (AoPS assistant instructor)<br />
* Ameya Velingker (2005)<br />
<br />
<br />
== Perfect AIME Scores ==<br />
Very few students have ever achieved a perfect score on the [[American Invitational Mathematics Examination]] (AIME)<br />
<br />
* David Benjamin (2006)<br />
* [[Mathew Crawford]] (1992) (AoPS instructor)<br />
* Sam Elder (2008)<br />
* [[Sandor Lehoczky]] (1990) (AoPS author)<br />
* Tedrick Leung (2006)<br />
* Tony Liu (2006)<br />
* Haitao Mao (2008)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* [[Sam Vandervelde]] (1988) ([[WOOT]] instructor)<br />
<br />
== Perfect AMC Scores ==<br />
=== Perfect AMC 12 Scores ===<br />
The [[AMC 12]] is a challenging examination for students in grades 12 and below administered by the [[American Mathematics Competitions]].<br />
* Zachary Abel (2005) (AoPS assistant instructor)<br />
* David Benjamin (2006)<br />
* Wenyu Cao (2009)<br />
* Sam Elder (2008)<br />
* Ruozhou (Joe) Jia (2003) (AoPS assistant instructor)<br />
* Joel Lewis (2003) <br />
* Jonathan Lowd (2003) (AoPS assistant instructor)<br />
* Thomas Mildorf (2004) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Albert Ni (2003) (AoPS instructor)<br />
* Ajay Sharma (2004)<br />
* Bobby Shen (2009)<br />
* Matt Superdock (2009)<br />
* Arnav Tripathy (2006, 2007)<br />
* Qiaochu Yuan (2008)<br />
* Alex Zhai (2007)<br />
<br />
===Perfect AMC 10 scorers===<br />
The [[AMC 10]] is a challenging examination for students in grades 10 and below administered by the [[American Mathematics Competitions]].<br />
* Yongyi Chen (2009)<br />
* Matthew Babbitt (2009)<br />
* Sergei Bernstein (2007)<br />
* Yifan Cao (2005)<br />
* Kevin Chen (2007, 2008, 2009)<br />
* In Young Cho (2007)<br />
* Mario Choi (2007)<br />
* Calvin Deng (2008)<br />
* Billy Dorminy (2007)<br />
* Zhou Fan (2005)<br />
* Albert Gu (2007)<br />
* Robin He (2007)<br />
* Keone Hon (2005)<br />
* Susan Hu (2005)<br />
* Lyndon Ji (2008)<br />
* Sam Keller (2007)<br />
* Vincent Le (2006)<br />
* Daniel Li (2007)<br />
* Johnny Li (2007)<br />
* Kevin Li (2009)<br />
* Patricia Li (2005)<br />
* Carl Lian (2007)<br />
* Sam Lite (2009)<br />
* David Lu (2009)<br />
* Thomas Mildorf (2002) (AoPS assistant instructor)<br />
* Anupa Murali (2008)<br />
* Amrit Saxena (2009)<br />
* Maximilian Schindler (2009)<br />
* Eric Schneider (2009)<br />
* Bobby Shen (2009)<br />
* Lilly Shen (2009)<br />
* Jeffrey Shen (2008)<br />
* Kyle Stankowski (2009)<br />
* Kevin Tian (2009)<br />
* Howard Tong (2005)<br />
* Sam Trabucco (2008)<br />
* Brent Woodhouse (2006, 2007)<br />
* Lawrence Wu (2009)<br />
* Allen Yuan (2009)<br />
* Peijin Zhang (2009)<br />
* Jonathan Zhou (2007)<br />
* Alex Zhu (2009)<br />
<br />
=== Perfect AHSME Scores ===<br />
The [[American High School Mathematics Examination]] (AHSME) was the predecessor of the AMC 12.<br />
* Christopher Chang (1994, 1995, 1996)<br />
* [[Mathew Crawford]] (1994, 1995) (AoPS instructor)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
<br />
== MATHCOUNTS ==<br />
[[MathCounts]] is the premier middle school [[mathematics competition]] in the U.S.<br />
=== National Champions ===<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Albert Ni (2002) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Neal Wu (2005)<br />
* Daesun Yim (2006)<br />
* Kevin Chen (2007)<br />
* Darryl Wu (2008)<br />
* Bobby Shen (2009)<br />
<br />
=== National Top 12 ===<br />
* Ashley Reiter Ahlin (1987) ([[WOOT]] instructor)<br />
* Andrew Ardito (2005, 2006)<br />
* David Benjamin (2004, 2005)<br />
* Nathan Benjamin (2005, 2006)<br />
* Wenyu Cao (2007)<br />
* Christopher Chang (1991, 1992)<br />
* Kevin Chen (2006, 2007)<br />
* Steven Chen (2009)<br />
* Andrew Chien (2003)<br />
* Peter Chien (2004)<br />
* Mario Choi (2007)<br />
* Joseph Chu (2004)<br />
* Alexander Clifton (2009)<br />
* [[Mathew Crawford]] (1990, 1991) (AoPS instructor)<br />
* Calvin Deng (2009)<br />
* Brian Hamrick (2006)<br />
* Adam Hesterberg (2002, 2003)<br />
* Jason Hyun (2008)<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Sam Keller (2006)<br />
* Shaunak Kishore (2003, 2004)<br />
* Kiran Kota (2005)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Karlanna Lewis (2005)<br />
* Daniel Li (2006)<br />
* Patricia Li (2005)<br />
* Ray Li (2009)<br />
* Poh-Ling Loh (2000)<br />
* David Lu (2008)<br />
* Albert Ni (2002) (AoPS assistant instructor)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2008, 2009)<br />
* Elizabeth Synge (2007)<br />
* Jason Trigg (2002)<br />
* [[Sam Vandervelde]] (1985) ([[WOOT]] instructor)<br />
* Victor Wang (2009)<br />
* Neal Wu (2005, 2006)<br />
* Rolland Wu (2006)<br />
* Xiaoyu He (2008)<br />
* David Yang (2009)<br />
* Daesun Yim (2006)<br />
* Darren Yin (2002)<br />
* Allen Yuan (2007)<br />
* Samuel Zbarsky (2008)<br />
* Alex Zhai (2004)<br />
* Mark Zhang (2005)<br />
* Alan Zhou (2009)<br />
<br />
=== Masters Round Champions ===<br />
* Christopher Chang (1991)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Sergei Bernstein (2005)<br />
* Daniel Li (2006)<br />
* Kevin Chen (2007)<br />
* Bobby Shen (2008)<br />
* Maximilian Schindler (2009)<br />
<br />
=== National Test Champions ===<br />
* [[Mathew Crawford]] (1990) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Sergei Bernstein (2005)<br />
* Neal Wu (2006)<br />
* Bobby Shen (2008)<br />
* David Yang (2009)<br />
<br />
== Harvard-MIT Math Tournament ==<br />
<br />
The [[HMMT]] 2007 winning team, the "WOOTlings", consisted entirely of [[WOOT]]ers:<br />
<br />
* Wenyu Cao<br />
* Eric Chang<br />
* Jeremy Hahn<br />
* Alex Kandell<br />
* Adeel Khan<br />
* Sathish Nagappan<br />
* Krishanu Roy Sankar<br />
* Patrick Tenorio<br />
<br />
== ARML ==<br />
<br />
=== ARML winners ===<br />
<br />
=== ARML Top 10 ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Seva Tchernov (2007)<br />
* Arnav Tripathy (2007)<br />
* David Yang (2009)<br />
* Daesun Yim (2008)<br />
<br />
== See also ==<br />
* [[Academic competitions]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
* [[Academic scholarships]]<br />
<br />
<br />
<br />
[[Category:Art of Problem Solving]]</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:AoPS_Community_Awards&diff=34268AoPS Wiki:AoPS Community Awards2010-04-08T05:26:44Z<p>Hamster1800: /* Gold Medalists */</p>
<hr />
<div>This '''AoPS Community Awards''' page is a celebration of the accomplishments of members of the [[AoPS]] community.<br />
<br />
<br />
== IMO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Mathematical Olympiad]].<br />
<br />
=== Participants ===<br />
* Alex Zhai (2008) <br />
* Krishanu Roy Sankar (2008)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Marco Avila (2006)<br />
* John Berman (2009)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Wenyu Cao (2009)<br />
* Sherry Gong (2002, 2003, 2004, 2005, 2007)<br />
* Elyot Grant (2005)<br />
* Darij Grinberg (2006)<br />
* Mahbubul Hasan (2005)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Brian Lawrence (2005, 2007) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Richard Peng (2005, 2006)<br />
* Eric Price (2005)<br />
* David Rhee (2004, 2005, 2006)<br />
* Peng Shi (2004, 2005, 2006)<br />
* Arne Smeets (2003, 2004)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* Yi Sun (2006)<br />
* [[Valentin Vornicu]] (AoPS/MathLinks webmaster)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2005, 2006, 2007, 2008)<br />
* Yufei Zhao (2004, 2005, 2006)<br />
* Tigran Sloyan(2003,2004,2005,2006,2007)<br />
* Marco Avila (2006)<br />
* Vipul Naik (2003,2004)<br />
* Bhargav Narayanan (2007)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
<br />
===Perfect Scorers===<br />
*Brian Lawrence (2005)<br />
*Alex Zhai (2008)<br />
<br />
=== Gold medalists ===<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Darij Grinberg (2006)<br />
* Kiran Kedlaya (1990, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Arnav Tripathy (2006)<br />
* Eric Price (2005)<br />
* Yufei Zhao (2005)<br />
* Alex Zhai (2007, 2008)<br />
*Sherry Gong (2007)<br />
*Krishanu Sankar (2008)<br />
* John Berman (2009)<br />
<br />
=== Silver medalists ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Sherry Gong (2004, 2005)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Richard Peng (2005)<br />
* David Rhee (2006)<br />
* Naoki Sato (AoPS instructor)<br />
* Peng Shi (2006)<br />
* Arne Smeets (2004)<br />
* Yi Sun (2006)<br />
* [[Sam Vandervelde]] (1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2006)<br />
* Yufei Zhao (2006)<br />
* Tigran Sloyan(2006,2007)<br />
* Vipul Naik (2003,2004)<br />
* Delong Meng (2009)<br />
* Qinxuan Pan (2009)<br />
* Wenyu Cao (2009)<br />
<br />
=== Bronze medalists ===<br />
* Sherry Gong (2003)<br />
* Elyot Grant (2005)<br />
* Richard Peng (2006)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* [[Valentin Vornicu]] (AoPS/[[MathLinks]] webmaster)<br />
* Yufei Zhao (2004)<br />
* Tigran Sloyan(2004;2005)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
<br />
== IPhO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Physics Olympiad]].<br />
=== Participants ===<br />
* Sherry Gong (2006)<br />
* Yi Sun (2004)<br />
* Arnav Tripathy (2006)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
<br />
=== Gold Medalists ===<br />
* Yi Sun (2004)<br />
* Rahul Singh (2007)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
<br />
=== Silver Medalists ===<br />
* Sherry Gong (2006)<br />
<br />
== IOI Medalists ==<br />
This list is of AoPSers who have won medals at the [[International Olympiad in Informatics]].<br />
<br />
==Gold Medalists ==<br />
* David Benjamin (2008)<br />
* Neal Wu (2008, 2009)<br />
* Brian Hamrick (2009)<br />
<br />
==Silver Medalists ==<br />
* Brian Hamrick (2008)<br />
* Jacob Steinhardt (2008)<br />
* Wenyu Cao (2009)<br />
* Travis Hance (2009)<br />
<br />
==Bronze Medalists ==<br />
* David Benjamin (2007)<br />
<br />
<br />
== USAMO ==<br />
The following AoPSers have won the [[United States of America Mathematical Olympiad]] (USAMO). (Note that the definition of "winner" has changed over the years -- currently it is the top 12 scores on the USAMO, but in the past it has been the top 6 or top 8 scores.)<br />
=== Perfect Scorers ===<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2006) ([[WOOT]] instructor)<br />
<br />
=== Winners ===<br />
* Yakov Berchenko-Kogan (2006)<br />
* Wenyu Cao (2009)<br />
* Sherry Gong (2006, 2007)<br />
* Yi Han (2006)<br />
* Adam Hesterberg (2007)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005, 2006, 2007) ([[WOOT]] instructor)<br />
* Tedrick Leung (2006, 2007)<br />
* Haitao Mao (2007)<br />
* Richard Mccutchen (2006)<br />
* Albert Ni (2005)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
* David Rolnick (2008) (AoPS assistant instructor)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* Krishanu Sankar (2007,2008)<br />
* Peng Shi (2006)<br />
* Jacob Steinhardt (2007)<br />
* Yi Sun (2006)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Sam Vandervelde]] (1987, 1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* David Yang (2009)<br />
* Alex Zhai (2006, 2007,2008)<br />
* Yufei Zhao (2006)<br />
* David Bay Rush (2009)<br />
<br />
== Putnam Fellows ==<br />
The top 5 students (including ties) on the collegiate [[Putnam Exam|William Lowell Putnam Competition]] are named Putnam Fellows.<br />
* David Ash (1981, 1982, 1983)<br />
* Daniel Kane (2003, 2004, 2005) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1994, 1995, 1996) ([[AoPS Foundation]] board member)<br />
* Matthew Ince (2005) (AoPS assistant instructor)<br />
* Alexander Schwartz (2000, 2002)<br />
* Jan Siwanowicz (2001) <br />
* Melanie Wood (2002) ([[WOOT]] instructor)<br />
*Arnav Tripathy (2008)<br />
*Brian Lawrence (2008)<br />
<br />
== Siemens Competition Winners ==<br />
The annual [[Siemens Competition]] (formerly Siemens-Westinghouse) is a scientific research competition.<br />
* Michael Viscardi (1st Individual,2005)<br />
* Lucia Mocz (2nd Team, 2006)<br />
<br />
==Intel STS Finalists==<br />
The annual [[Intel Science Talent Search]] is a science competition seeking to find and reward the most scientifically accomplished seniors.<br />
<br />
* Philip Mocz (2008)<br />
* Yihe Dong (2008)<br />
* Qiaochu Yuan (2008)<br />
* Greg Brockman (2007)<br />
<br />
== Clay Junior Fellows ==<br />
Each year since 2003, the [[Clay Mathematics Institute]] has selected 12 Junior Fellows.<br />
* Thomas Belulovich (2005) (AoPS assistant instructor)<br />
* Atoshi Chowdhury (2003) (AoPS assistant instructor)<br />
* Robert Cordwell (2005)<br />
* Eve Drucker (2003) (AoPS assistant instructor)<br />
* Matthew Ince (2004) (AoPS assistant instructor)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Raju Krishnamoorthy (2005)<br />
* Alison Miller (2003) (AoPS assistant instructor)<br />
* Brian Rice (2003) (AoPS assistant instructor)<br />
* Dmitry Taubinski (2005) (AoPS assistant instructor)<br />
* Ameya Velingker (2005)<br />
<br />
<br />
== Perfect AIME Scores ==<br />
Very few students have ever achieved a perfect score on the [[American Invitational Mathematics Examination]] (AIME)<br />
<br />
* David Benjamin (2006)<br />
* [[Mathew Crawford]] (1992) (AoPS instructor)<br />
* Sam Elder (2008)<br />
* [[Sandor Lehoczky]] (1990) (AoPS author)<br />
* Tedrick Leung (2006)<br />
* Tony Liu (2006)<br />
* Haitao Mao (2008)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* [[Sam Vandervelde]] (1988) ([[WOOT]] instructor)<br />
<br />
== Perfect AMC Scores ==<br />
=== Perfect AMC 12 Scores ===<br />
The [[AMC 12]] is a challenging examination for students in grades 12 and below administered by the [[American Mathematics Competitions]].<br />
* Zachary Abel (2005) (AoPS assistant instructor)<br />
* David Benjamin (2006)<br />
* Wenyu Cao (2009)<br />
* Sam Elder (2008)<br />
* Ruozhou (Joe) Jia (2003) (AoPS assistant instructor)<br />
* Joel Lewis (2003) <br />
* Jonathan Lowd (2003) (AoPS assistant instructor)<br />
* Thomas Mildorf (2004) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Albert Ni (2003) (AoPS instructor)<br />
* Ajay Sharma (2004)<br />
* Bobby Shen (2009)<br />
* Matt Superdock (2009)<br />
* Arnav Tripathy (2006, 2007)<br />
* Qiaochu Yuan (2008)<br />
* Alex Zhai (2007)<br />
<br />
===Perfect AMC 10 scorers===<br />
The [[AMC 10]] is a challenging examination for students in grades 10 and below administered by the [[American Mathematics Competitions]].<br />
* Yongyi Chen (2009)<br />
* Matthew Babbitt (2009)<br />
* Sergei Bernstein (2007)<br />
* Yifan Cao (2005)<br />
* Kevin Chen (2007, 2008, 2009)<br />
* In Young Cho (2007)<br />
* Mario Choi (2007)<br />
* Calvin Deng (2008)<br />
* Billy Dorminy (2007)<br />
* Zhou Fan (2005)<br />
* Albert Gu (2007)<br />
* Robin He (2007)<br />
* Keone Hon (2005)<br />
* Susan Hu (2005)<br />
* Lyndon Ji (2008)<br />
* Sam Keller (2007)<br />
* Vincent Le (2006)<br />
* Daniel Li (2007)<br />
* Johnny Li (2007)<br />
* Kevin Li (2009)<br />
* Patricia Li (2005)<br />
* Carl Lian (2007)<br />
* Sam Lite (2009)<br />
* David Lu (2009)<br />
* Thomas Mildorf (2002) (AoPS assistant instructor)<br />
* Anupa Murali (2008)<br />
* Amrit Saxena (2009)<br />
* Maximilian Schindler (2009)<br />
* Eric Schneider (2009)<br />
* Bobby Shen (2009)<br />
* Lilly Shen (2009)<br />
* Jeffrey Shen (2008)<br />
* Kyle Stankowski (2009)<br />
* Kevin Tian (2009)<br />
* Howard Tong (2005)<br />
* Sam Trabucco (2008)<br />
* Brent Woodhouse (2006, 2007)<br />
* Lawrence Wu (2009)<br />
* Allen Yuan (2009)<br />
* Peijin Zhang (2009)<br />
* Jonathan Zhou (2007)<br />
* Alex Zhu (2009)<br />
<br />
=== Perfect AHSME Scores ===<br />
The [[American High School Mathematics Examination]] (AHSME) was the predecessor of the AMC 12.<br />
* Christopher Chang (1994, 1995, 1996)<br />
* [[Mathew Crawford]] (1994, 1995) (AoPS instructor)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
<br />
== MATHCOUNTS ==<br />
[[MathCounts]] is the premier middle school [[mathematics competition]] in the U.S.<br />
=== National Champions ===<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Albert Ni (2002) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Neal Wu (2005)<br />
* Daesun Yim (2006)<br />
* Kevin Chen (2007)<br />
* Darryl Wu (2008)<br />
* Bobby Shen (2009)<br />
<br />
=== National Top 12 ===<br />
* Ashley Reiter Ahlin (1987) ([[WOOT]] instructor)<br />
* Andrew Ardito (2005, 2006)<br />
* David Benjamin (2004, 2005)<br />
* Nathan Benjamin (2005, 2006)<br />
* Wenyu Cao (2007)<br />
* Christopher Chang (1991, 1992)<br />
* Kevin Chen (2006, 2007)<br />
* Steven Chen (2009)<br />
* Andrew Chien (2003)<br />
* Peter Chien (2004)<br />
* Mario Choi (2007)<br />
* Joseph Chu (2004)<br />
* Alexander Clifton (2009)<br />
* [[Mathew Crawford]] (1990, 1991) (AoPS instructor)<br />
* Calvin Deng (2009)<br />
* Brian Hamrick (2006)<br />
* Adam Hesterberg (2002, 2003)<br />
* Jason Hyun (2008)<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Sam Keller (2006)<br />
* Shaunak Kishore (2003, 2004)<br />
* Kiran Kota (2005)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Karlanna Lewis (2005)<br />
* Daniel Li (2006)<br />
* Patricia Li (2005)<br />
* Ray Li (2009)<br />
* Poh-Ling Loh (2000)<br />
* David Lu (2008)<br />
* Albert Ni (2002) (AoPS assistant instructor)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2008, 2009)<br />
* Elizabeth Synge (2007)<br />
* Jason Trigg (2002)<br />
* [[Sam Vandervelde]] (1985) ([[WOOT]] instructor)<br />
* Victor Wang (2009)<br />
* Neal Wu (2005, 2006)<br />
* Rolland Wu (2006)<br />
* Xiaoyu He (2008)<br />
* David Yang (2009)<br />
* Daesun Yim (2006)<br />
* Darren Yin (2002)<br />
* Allen Yuan (2007)<br />
* Samuel Zbarsky (2008)<br />
* Alex Zhai (2004)<br />
* Mark Zhang (2005)<br />
* Alan Zhou (2009)<br />
<br />
=== Masters Round Champions ===<br />
* Christopher Chang (1991)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Sergei Bernstein (2005)<br />
* Daniel Li (2006)<br />
* Kevin Chen (2007)<br />
* Bobby Shen (2008)<br />
* Maximilian Schindler (2009)<br />
<br />
=== National Test Champions ===<br />
* [[Mathew Crawford]] (1990) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Sergei Bernstein (2005)<br />
* Neal Wu (2006)<br />
* Bobby Shen (2008)<br />
* David Yang (2009)<br />
<br />
== Harvard-MIT Math Tournament ==<br />
<br />
The [[HMMT]] 2007 winning team, the "WOOTlings", consisted entirely of [[WOOT]]ers:<br />
<br />
* Wenyu Cao<br />
* Eric Chang<br />
* Jeremy Hahn<br />
* Alex Kandell<br />
* Adeel Khan<br />
* Sathish Nagappan<br />
* Krishanu Roy Sankar<br />
* Patrick Tenorio<br />
<br />
== ARML ==<br />
<br />
=== ARML winners ===<br />
<br />
=== ARML Top 10 ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Seva Tchernov (2007)<br />
* Arnav Tripathy (2007)<br />
* David Yang (2009)<br />
* Daesun Yim (2008)<br />
<br />
== See also ==<br />
* [[Academic competitions]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
* [[Academic scholarships]]<br />
<br />
<br />
<br />
[[Category:Art of Problem Solving]]</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:AoPS_Community_Awards&diff=34267AoPS Wiki:AoPS Community Awards2010-04-08T05:26:13Z<p>Hamster1800: /* Gold Medalists */</p>
<hr />
<div>This '''AoPS Community Awards''' page is a celebration of the accomplishments of members of the [[AoPS]] community.<br />
<br />
<br />
== IMO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Mathematical Olympiad]].<br />
<br />
=== Participants ===<br />
* Alex Zhai (2008) <br />
* Krishanu Roy Sankar (2008)<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Marco Avila (2006)<br />
* John Berman (2009)<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Wenyu Cao (2009)<br />
* Sherry Gong (2002, 2003, 2004, 2005, 2007)<br />
* Elyot Grant (2005)<br />
* Darij Grinberg (2006)<br />
* Mahbubul Hasan (2005)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Brian Lawrence (2005, 2007) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Richard Peng (2005, 2006)<br />
* Eric Price (2005)<br />
* David Rhee (2004, 2005, 2006)<br />
* Peng Shi (2004, 2005, 2006)<br />
* Arne Smeets (2003, 2004)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* Yi Sun (2006)<br />
* [[Valentin Vornicu]] (AoPS/MathLinks webmaster)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2005, 2006, 2007, 2008)<br />
* Yufei Zhao (2004, 2005, 2006)<br />
* Tigran Sloyan(2003,2004,2005,2006,2007)<br />
* Marco Avila (2006)<br />
* Vipul Naik (2003,2004)<br />
* Bhargav Narayanan (2007)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
<br />
===Perfect Scorers===<br />
*Brian Lawrence (2005)<br />
*Alex Zhai (2008)<br />
<br />
=== Gold medalists ===<br />
* Zarathustra Brady (2006)<br />
* Robert Cordwell (2005)<br />
* Darij Grinberg (2006)<br />
* Kiran Kedlaya (1990, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005) ([[WOOT]] instructor)<br />
* Thomas Mildorf (2005) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Arnav Tripathy (2006)<br />
* Eric Price (2005)<br />
* Yufei Zhao (2005)<br />
* Alex Zhai (2007, 2008)<br />
*Sherry Gong (2007)<br />
*Krishanu Sankar (2008)<br />
* John Berman (2009)<br />
<br />
=== Silver medalists ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Sherry Gong (2004, 2005)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Viktoriya Krakovna (2006)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Richard Peng (2005)<br />
* David Rhee (2006)<br />
* Naoki Sato (AoPS instructor)<br />
* Peng Shi (2006)<br />
* Arne Smeets (2004)<br />
* Yi Sun (2006)<br />
* [[Sam Vandervelde]] (1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* Alex Zhai (2006)<br />
* Yufei Zhao (2006)<br />
* Tigran Sloyan(2006,2007)<br />
* Vipul Naik (2003,2004)<br />
* Delong Meng (2009)<br />
* Qinxuan Pan (2009)<br />
* Wenyu Cao (2009)<br />
<br />
=== Bronze medalists ===<br />
* Sherry Gong (2003)<br />
* Elyot Grant (2005)<br />
* Richard Peng (2006)<br />
* [[Naoki Sato]] (AoPS instructor)<br />
* [[Valentin Vornicu]] (AoPS/[[MathLinks]] webmaster)<br />
* Yufei Zhao (2004)<br />
* Tigran Sloyan(2004;2005)<br />
* Tigran Hakobyan (2007)<br />
* Carmela Lao (2009)<br />
<br />
== IPhO Participants and Medalists ==<br />
This is a list of members of the AoPS community who have competed for their country at the [[International Physics Olympiad]].<br />
=== Participants ===<br />
* Sherry Gong (2006)<br />
* Yi Sun (2004)<br />
* Arnav Tripathy (2006)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
<br />
=== Gold Medalists ===<br />
* Yi Sun (2004)<br />
* Rahul Singh (2007)<br />
* Marianna Mao (2009)<br />
* Anand Natarajan (2009)<br />
* Bowei Liu (2009)<br />
<br />
=== Silver Medalists ===<br />
* Sherry Gong (2006)<br />
<br />
== IOI Medalists ==<br />
This list is of AoPSers who have won medals at the [[International Olympiad in Informatics]].<br />
<br />
==Gold Medalists ==<br />
* David Benjamin (2008)<br />
* Brian Hamrick (2009)<br />
* Neal Wu (2008, 2009)<br />
<br />
==Silver Medalists ==<br />
* Brian Hamrick (2008)<br />
* Jacob Steinhardt (2008)<br />
* Wenyu Cao (2009)<br />
* Travis Hance (2009)<br />
<br />
==Bronze Medalists ==<br />
* David Benjamin (2007)<br />
<br />
<br />
== USAMO ==<br />
The following AoPSers have won the [[United States of America Mathematical Olympiad]] (USAMO). (Note that the definition of "winner" has changed over the years -- currently it is the top 12 scores on the USAMO, but in the past it has been the top 6 or top 8 scores.)<br />
=== Perfect Scorers ===<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1991) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2006) ([[WOOT]] instructor)<br />
<br />
=== Winners ===<br />
* Yakov Berchenko-Kogan (2006)<br />
* Wenyu Cao (2009)<br />
* Sherry Gong (2006, 2007)<br />
* Yi Han (2006)<br />
* Adam Hesterberg (2007)<br />
* Daniel Kane (AoPS assistant instructor)<br />
* Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member)<br />
* Brian Lawrence (2005, 2006, 2007) ([[WOOT]] instructor)<br />
* Tedrick Leung (2006, 2007)<br />
* Haitao Mao (2007)<br />
* Richard Mccutchen (2006)<br />
* Albert Ni (2005)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
* David Rolnick (2008) (AoPS assistant instructor)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* Krishanu Sankar (2007,2008)<br />
* Peng Shi (2006)<br />
* Jacob Steinhardt (2007)<br />
* Yi Sun (2006)<br />
* Arnav Tripathy (2006, 2007)<br />
* [[Sam Vandervelde]] (1987, 1989) ([[WOOT]] instructor)<br />
* Melanie Wood (1998, 1999) ([[WOOT]] instructor)<br />
* David Yang (2009)<br />
* Alex Zhai (2006, 2007,2008)<br />
* Yufei Zhao (2006)<br />
* David Bay Rush (2009)<br />
<br />
== Putnam Fellows ==<br />
The top 5 students (including ties) on the collegiate [[Putnam Exam|William Lowell Putnam Competition]] are named Putnam Fellows.<br />
* David Ash (1981, 1982, 1983)<br />
* Daniel Kane (2003, 2004, 2005) (AoPS assistant instructor)<br />
* Kiran Kedlaya (1994, 1995, 1996) ([[AoPS Foundation]] board member)<br />
* Matthew Ince (2005) (AoPS assistant instructor)<br />
* Alexander Schwartz (2000, 2002)<br />
* Jan Siwanowicz (2001) <br />
* Melanie Wood (2002) ([[WOOT]] instructor)<br />
*Arnav Tripathy (2008)<br />
*Brian Lawrence (2008)<br />
<br />
== Siemens Competition Winners ==<br />
The annual [[Siemens Competition]] (formerly Siemens-Westinghouse) is a scientific research competition.<br />
* Michael Viscardi (1st Individual,2005)<br />
* Lucia Mocz (2nd Team, 2006)<br />
<br />
==Intel STS Finalists==<br />
The annual [[Intel Science Talent Search]] is a science competition seeking to find and reward the most scientifically accomplished seniors.<br />
<br />
* Philip Mocz (2008)<br />
* Yihe Dong (2008)<br />
* Qiaochu Yuan (2008)<br />
* Greg Brockman (2007)<br />
<br />
== Clay Junior Fellows ==<br />
Each year since 2003, the [[Clay Mathematics Institute]] has selected 12 Junior Fellows.<br />
* Thomas Belulovich (2005) (AoPS assistant instructor)<br />
* Atoshi Chowdhury (2003) (AoPS assistant instructor)<br />
* Robert Cordwell (2005)<br />
* Eve Drucker (2003) (AoPS assistant instructor)<br />
* Matthew Ince (2004) (AoPS assistant instructor)<br />
* Nate Ince (2004) (AoPS assistant instructor)<br />
* Hyun Soo Kim (2005) (AoPS assistant instructor)<br />
* Raju Krishnamoorthy (2005)<br />
* Alison Miller (2003) (AoPS assistant instructor)<br />
* Brian Rice (2003) (AoPS assistant instructor)<br />
* Dmitry Taubinski (2005) (AoPS assistant instructor)<br />
* Ameya Velingker (2005)<br />
<br />
<br />
== Perfect AIME Scores ==<br />
Very few students have ever achieved a perfect score on the [[American Invitational Mathematics Examination]] (AIME)<br />
<br />
* David Benjamin (2006)<br />
* [[Mathew Crawford]] (1992) (AoPS instructor)<br />
* Sam Elder (2008)<br />
* [[Sandor Lehoczky]] (1990) (AoPS author)<br />
* Tedrick Leung (2006)<br />
* Tony Liu (2006)<br />
* Haitao Mao (2008)<br />
* [[Richard Rusczyk]] (1989) (AoPS founder)<br />
* [[Sam Vandervelde]] (1988) ([[WOOT]] instructor)<br />
<br />
== Perfect AMC Scores ==<br />
=== Perfect AMC 12 Scores ===<br />
The [[AMC 12]] is a challenging examination for students in grades 12 and below administered by the [[American Mathematics Competitions]].<br />
* Zachary Abel (2005) (AoPS assistant instructor)<br />
* David Benjamin (2006)<br />
* Wenyu Cao (2009)<br />
* Sam Elder (2008)<br />
* Ruozhou (Joe) Jia (2003) (AoPS assistant instructor)<br />
* Joel Lewis (2003) <br />
* Jonathan Lowd (2003) (AoPS assistant instructor)<br />
* Thomas Mildorf (2004) (AoPS assistant instructor)<br />
* Alison Miller (2004) (AoPS assistant instructor)<br />
* Albert Ni (2003) (AoPS instructor)<br />
* Ajay Sharma (2004)<br />
* Bobby Shen (2009)<br />
* Matt Superdock (2009)<br />
* Arnav Tripathy (2006, 2007)<br />
* Qiaochu Yuan (2008)<br />
* Alex Zhai (2007)<br />
<br />
===Perfect AMC 10 scorers===<br />
The [[AMC 10]] is a challenging examination for students in grades 10 and below administered by the [[American Mathematics Competitions]].<br />
* Yongyi Chen (2009)<br />
* Matthew Babbitt (2009)<br />
* Sergei Bernstein (2007)<br />
* Yifan Cao (2005)<br />
* Kevin Chen (2007, 2008, 2009)<br />
* In Young Cho (2007)<br />
* Mario Choi (2007)<br />
* Calvin Deng (2008)<br />
* Billy Dorminy (2007)<br />
* Zhou Fan (2005)<br />
* Albert Gu (2007)<br />
* Robin He (2007)<br />
* Keone Hon (2005)<br />
* Susan Hu (2005)<br />
* Lyndon Ji (2008)<br />
* Sam Keller (2007)<br />
* Vincent Le (2006)<br />
* Daniel Li (2007)<br />
* Johnny Li (2007)<br />
* Kevin Li (2009)<br />
* Patricia Li (2005)<br />
* Carl Lian (2007)<br />
* Sam Lite (2009)<br />
* David Lu (2009)<br />
* Thomas Mildorf (2002) (AoPS assistant instructor)<br />
* Anupa Murali (2008)<br />
* Amrit Saxena (2009)<br />
* Maximilian Schindler (2009)<br />
* Eric Schneider (2009)<br />
* Bobby Shen (2009)<br />
* Lilly Shen (2009)<br />
* Jeffrey Shen (2008)<br />
* Kyle Stankowski (2009)<br />
* Kevin Tian (2009)<br />
* Howard Tong (2005)<br />
* Sam Trabucco (2008)<br />
* Brent Woodhouse (2006, 2007)<br />
* Lawrence Wu (2009)<br />
* Allen Yuan (2009)<br />
* Peijin Zhang (2009)<br />
* Jonathan Zhou (2007)<br />
* Alex Zhu (2009)<br />
<br />
=== Perfect AHSME Scores ===<br />
The [[American High School Mathematics Examination]] (AHSME) was the predecessor of the AMC 12.<br />
* Christopher Chang (1994, 1995, 1996)<br />
* [[Mathew Crawford]] (1994, 1995) (AoPS instructor)<br />
* [[David Patrick]] (1988) (AoPS instructor)<br />
<br />
== MATHCOUNTS ==<br />
[[MathCounts]] is the premier middle school [[mathematics competition]] in the U.S.<br />
=== National Champions ===<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Albert Ni (2002) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Neal Wu (2005)<br />
* Daesun Yim (2006)<br />
* Kevin Chen (2007)<br />
* Darryl Wu (2008)<br />
* Bobby Shen (2009)<br />
<br />
=== National Top 12 ===<br />
* Ashley Reiter Ahlin (1987) ([[WOOT]] instructor)<br />
* Andrew Ardito (2005, 2006)<br />
* David Benjamin (2004, 2005)<br />
* Nathan Benjamin (2005, 2006)<br />
* Wenyu Cao (2007)<br />
* Christopher Chang (1991, 1992)<br />
* Kevin Chen (2006, 2007)<br />
* Steven Chen (2009)<br />
* Andrew Chien (2003)<br />
* Peter Chien (2004)<br />
* Mario Choi (2007)<br />
* Joseph Chu (2004)<br />
* Alexander Clifton (2009)<br />
* [[Mathew Crawford]] (1990, 1991) (AoPS instructor)<br />
* Calvin Deng (2009)<br />
* Brian Hamrick (2006)<br />
* Adam Hesterberg (2002, 2003)<br />
* Jason Hyun (2008)<br />
* Ruozhou (Joe) Jia (2000) (AoPS assistant instructor)<br />
* Sam Keller (2006)<br />
* Shaunak Kishore (2003, 2004)<br />
* Kiran Kota (2005)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Karlanna Lewis (2005)<br />
* Daniel Li (2006)<br />
* Patricia Li (2005)<br />
* Ray Li (2009)<br />
* Poh-Ling Loh (2000)<br />
* David Lu (2008)<br />
* Albert Ni (2002) (AoPS assistant instructor)<br />
* Maximilian Schindler (2009)<br />
* Bobby Shen (2008, 2009)<br />
* Elizabeth Synge (2007)<br />
* Jason Trigg (2002)<br />
* [[Sam Vandervelde]] (1985) ([[WOOT]] instructor)<br />
* Victor Wang (2009)<br />
* Neal Wu (2005, 2006)<br />
* Rolland Wu (2006)<br />
* Xiaoyu He (2008)<br />
* David Yang (2009)<br />
* Daesun Yim (2006)<br />
* Darren Yin (2002)<br />
* Allen Yuan (2007)<br />
* Samuel Zbarsky (2008)<br />
* Alex Zhai (2004)<br />
* Mark Zhang (2005)<br />
* Alan Zhou (2009)<br />
<br />
=== Masters Round Champions ===<br />
* Christopher Chang (1991)<br />
* Brian Lawrence (2003) ([[WOOT]] instructor)<br />
* Sergei Bernstein (2005)<br />
* Daniel Li (2006)<br />
* Kevin Chen (2007)<br />
* Bobby Shen (2008)<br />
* Maximilian Schindler (2009)<br />
<br />
=== National Test Champions ===<br />
* [[Mathew Crawford]] (1990) (AoPS instructor)<br />
* Adam Hesterberg (2003)<br />
* Sergei Bernstein (2005)<br />
* Neal Wu (2006)<br />
* Bobby Shen (2008)<br />
* David Yang (2009)<br />
<br />
== Harvard-MIT Math Tournament ==<br />
<br />
The [[HMMT]] 2007 winning team, the "WOOTlings", consisted entirely of [[WOOT]]ers:<br />
<br />
* Wenyu Cao<br />
* Eric Chang<br />
* Jeremy Hahn<br />
* Alex Kandell<br />
* Adeel Khan<br />
* Sathish Nagappan<br />
* Krishanu Roy Sankar<br />
* Patrick Tenorio<br />
<br />
== ARML ==<br />
<br />
=== ARML winners ===<br />
<br />
=== ARML Top 10 ===<br />
* Zachary Abel (2006) (AoPS assistant instructor)<br />
* Seva Tchernov (2007)<br />
* Arnav Tripathy (2007)<br />
* David Yang (2009)<br />
* Daesun Yim (2008)<br />
<br />
== See also ==<br />
* [[Academic competitions]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
* [[Academic scholarships]]<br />
<br />
<br />
<br />
[[Category:Art of Problem Solving]]</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=Multiplicative_function&diff=24562Multiplicative function2008-04-04T22:59:10Z<p>Hamster1800: </p>
<hr />
<div>{{WotWAnnounce|week=March 28-April 5}}<br />
<br />
A '''multiplicative function''' <math>f : S \to T</math> is a [[function]] which [[commute]]s with multiplication. That is, <math>S</math> and <math>T</math> must be [[set]]s with multiplication such that <math>f(x\cdot y) = f(x) \cdot f(y)</math> for all <math>x, y \in S</math>, i.e. it preserves the multiplicative structure. A prominent special case of this would be a homomorphism between groups, which preserves the whole group structure (inverses and identity in addition to multiplication).<br />
<br />
Most frequently, one deals with multiplicative functions <math>f : \mathbb{Z}_{>0} \to \mathbb{C}</math>. These functions appear frequently in [[number theory]], especially in [[analytic number theory]]. In this case, one sometimes also defines ''weak multiplicative functions'': a function <math>f: \mathbb{Z}_{>0} \to \mathbb{C}</math> is weak multiplicative if and only if <math>f(mn) = f(m)f(n)</math> for all pairs of [[relatively prime]] [[integer]]s <math>(m, n)</math>.<br />
<br />
Let <math>f(n)</math> and <math>g(n)</math> be multiplicative in the number theoretic sense ("weak multiplicative"). Then the function of <math>n</math> defined by <cmath>\sum_{d|n} f(d) g(\frac{n}{d})</cmath> is also multiplicative; the Mobius inversion formula relates these two quantities.<br />
<br />
Examples in elementary number theory include the identity map, <math>d(n)</math> the number of divisors, <math>\sigma(n)</math> the sum of divisors (and its generalization <math>\sigma_k(n) = \sum_{d|n}d^k</math>, <math>\phi(n)</math> the Euler phi function, <math>\tau(n)</math> the number of divisors (also denoted <math>\sigma_0(n)</math>, $\mu(<br />
{{stub}}</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=Logarithm&diff=22707Logarithm2008-01-20T03:10:24Z<p>Hamster1800: /* Conventions */</p>
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<div>'''Logarithms''' and [[exponents]] are very closely related. In fact, they are [[Function/Introduction#The_Inverse_of_a_Function|inverse]] [[function]]s. This means that logarithms can be used to reverse the result of exponentiation and vice versa, just as addition can be used to reverse the result of subtraction. Thus, if we have <math> a^x = b </math>, then taking the logarithm with base <math> a</math> on both sides will give us <math>x=\log_a{b}</math>.<br />
<br />
We would read this as "the logarithm of b, base a, is x". For example, we know that <math>3^4=81</math>. To express the same fact in logarithmic notation we would write <math>\log_3 81=4</math>.<br />
<br />
<br />
==Conventions==<br />
Depending on the field, the symbol <math>\log</math> without a base can have different meanings. Typically, in mathematics through the level of [[calculus]], the symbol is used to refer to a base 10 logarithm. Thus, <math>\log(100)</math> means <math>\log_{10}(100)=2</math>. Usually, the symbol <math>\ln</math> (an abbreviation of the French "logarithme normal," meaning "natural logarithm") is introduced to refer to the logarithm base [[e]]. However, in higher mathematics such as [[complex analysis]], the base 10 logarithm is typically disposed with entirely, the symbol <math>\log</math> is taken to mean the logarithm base e and the symbol <math>\ln</math> is not used at all. (This is an example of conflicting [[mathematical convention]]s.) In addition, the notation <math>\lg</math> is often used by computer scientists to refer to the logarithm base <math>2</math>.<br />
<br />
==Logarithmic Properties==<br />
We can use the properties of exponents to build a set of properties for logarithms.<br />
<br />
We know that <math>a^x\cdot a^y=a^{x+y}</math>. We let <math> a^x=b</math> and <math> a^y=c </math>. This also makes <math>a^{x+y}=bc </math>. From <math> a^x = b</math>, we have <math> x = \log_a{b}</math>, and from <math> a^y=c </math>, we have <math> y=\log_a{c} </math>. So, <math> x+y = \log_a{b}+\log_a{c}</math>. But we also have from <math>a^{x+y} = bc</math> that <math> x+y = \log_a{bc}</math>. Thus, we have found two expressions for <math> x+y</math> establishing the identity:<br />
<br />
<center><math> \log_a{b} + \log_a{c} = \log_a{bc}.</math></center><br />
<br />
Using the laws of exponents, we can derive and prove the following identities:<br />
<br />
*<math>\log_a b^n=n\log_a b</math><br />
*<math>\log_a b+ \log_a c=\log_a bc</math> (Known as the product property.)<br />
*<math>\log_a b-\log_a c=\log_a \frac{b}{c}</math><br />
*<math>(\log_a b)(\log_c d)= (\log_a d)(\log_c b)</math><br />
*<math>\frac{\log_a b}{\log_a c}=\log_c b</math><br />
*<math>\log_{a^n} b^n=\log_a b</math><br />
<br />
Try proving all of these as exercises.<br />
<br />
Here are some other less useful log properties that follow from these previous ones.<br />
*<math>\log_{a}b=\frac{1}{\log_{b}a}</math> (Known as the inverse property)<br />
*<math>(\log_{a}b)(\log_{b}c)=\log_{a}c</math> (Known as the chain rule.)<br />
*<math>\log_{1/a} b=-\log_a b</math><br />
<br />
== Problems ==<br />
<br />
# Evaluate <math>(\log_{50}{2.5})(\log_{2.5}e)(\ln{2500})</math>.<br />
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# Evaluate <math>(\log_2 3)(\log_3 4)(\log_4 5)\cdots(\log_{2005} 2006)</math>.<br />
<br />
# Simplify <math>\frac 1{\log_2 N}+\frac 1{\log_3 N}+\frac 1{\log_4 N}+\cdots+ \frac 1{\log_{100}N} </math> where <math> N=(100!)^3</math>.<br />
<br />
<br />
== Natural Logarithm ==<br />
The natural logarithm of <math>a</math> is <math>\log_e a=\ln a</math>. The function <math>f(x)=\ln x</math> is the inverse of <math>f(x)=e^x</math>.<br />
<br />
<math>\ln a</math> can also be defined as the area under the curve <math>y=\frac{1}{x}</math> between 1 and a, or <math>\int^a_1 \frac{1}{x}\, dx</math>.<br />
<br />
All logarithms are undefined in nonpositive reals, as they are complex. From the identity <math>e^{i\pi}=-1</math>, we have <math>\ln (-1)=i\pi</math>. Additionally, <math>\ln (-n)=\ln n+i\pi</math> for positive real <math>n</math>.<br />
<br />
== Problems ==<br />
=== Introductory ===<br />
=== Intermediate ===<br />
* The [[sequence]] <math> a_1, a_2, \ldots </math> is [[geometric sequence|geometric]] with <math> a_1=a </math> and common [[ratio]] <math> r, </math> where <math> a </math> and <math> r </math> are positive integers. Given that <math> \log_8 a_1+\log_8 a_2+\cdots+\log_8 a_{12} = 2006, </math> find the number of possible ordered pairs <math> (a,r). </math><br />
[[2006_AIME_I_Problems/Problem_9 | Source]]<br />
=== Olympiad ===<br />
<br />
<br />
[[Category:Definition]]<br />
[[Category:Functions]]</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=Canada/USA_Mathcamp&diff=20358Canada/USA Mathcamp2007-11-30T02:51:22Z<p>Hamster1800: /* Selection */</p>
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<div>{{WotWAnnounce|week=Nov 29-Dec 5}}<br />
<br />
The '''Canada/USA Mathcamp''' is an intensive 5-week-long summer program for mathematically talented high school students, designed to inspire and motivate mathematically talented high school students by exposing them to the beauty and variety of mathematics, to impart valuable knowledge and skills for the pursuit of mathematics in high school, university, and beyond, and to provide a supportive and fun environment for interaction among students who love mathematics.<br />
<br />
The environment of Mathcamp tends to be relaxed in terms of rules; in fact it officially only has four rules (generally involving common sense and respect). Originally it had been stricter, though by 1997 most of the mentors found the structure too rigid and allowed for greater freedom at Mathcamp. <br />
<br />
== History ==<br />
Mathcamp was founded in Vancouver, Canada in 1993 by Dr. George Thomas. At that time, there were only two students. By 1994, there were eleven students. However, by 1996 the enrollment list grew to over 90 students, as Mathcamp had moved to the United States. However, Dr. T (as he is known) left in order to establish [[MathPath]], so Mira Bernstein became the new director. <br />
<br />
So far Mathcamp has been at the University of Toronto, the University of Puget Sound, the University of Washington, Colorado College, Reed College, and Colby College. In 2007, Mathcamp was located at Colby College in Maine; in 2008, it will be located at Reed College in Oregon. The administration believes that Mathcamp will start to periodically cycle through 3 colleges every three years.<br />
<br />
== Selection ==<br />
Students hoping to enroll have to take a 10 question application quiz of open-ended proof questions. Completion of all of the questions is definitely not a requirement; instead the selection process is more interested with the proofs and the manner in which the problems are attacked.<br />
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In addition, two recommendations (personal and academic) are required, as well as a short essay written by the student about why he/she wishes to attend camp. <br />
<br />
The solutions to the application quiz are presented by chosen students sometime during Week 2 or Week 3.<br />
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Once a student has qualified for camp, he or she need not apply for any subsequent years.<br />
<br />
== Course structure ==<br />
Every day of the week (the weekends are considered to be Sunday and Monday, since field trips organized on Monday will face less crowds) there are four periods of 50 minutes each in which students may take classes. Note that classes are not mandatory, and in fact it is encouraged that students do not fill up there schedules so that they have greater time to ponder about ideas they learned. Afterwards is a 2 hour period known as TAU (Time, Academic -- Unscheduled), where students work on homework and ask questions (to mentors or peers) regarding mathematical topics. <br />
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Then there is Colloquium, a one hour lecture delivered by (normally) an invited mathematician. [[John Conway]] is a distinguished mathematician who typically delivers lectures for an entire week of camp.<br />
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Classes tend to have an emphasis on subjects in mathematics that are normally beyond the scope of high school math; instead, most of the subjects are more likely to be found in college math. <br />
<br />
Outside of courses, field trips are organized for most weekends. There are many other non-mathematical events like game tournaments of various sorts. Games like Mafia, Mao, and Bughouse tend to be highly popular.<br />
<br />
== External links ==<br />
*[http://www.mathcamp.org Website]<br />
*[http://www.artofproblemsolving.com/Forum/index.php?f=314/ Forum on AoPS] Currently moderated by Deputy Director Dave Savitt and mentor Dan Zaharopol <br />
<br />
[[Category:Summer programs]]</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=Generating_function&diff=19574Generating function2007-11-16T03:02:56Z<p>Hamster1800: </p>
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<div>{{WotWAnnounce|week=Nov 15-21}}<br />
<br />
The idea behind '''generating functions''' is to create a [[power series]] whose [[coefficient]]s, <math>c_0, c_1, c_2, \ldots</math>, give the terms of a [[sequence]] which of interest. Therefore the power series (i.e. the generating function) is <math>c_0 + c_1 x + c_2 x^2 + \cdots </math> and the sequence is <math>c_0, c_1, c_2,\ldots</math>.<br />
<br />
== Simple Example ==<br />
<br />
If we let <math>A(k)={n \choose k}</math>, then we have <math>{n \choose 0}+{n \choose 1}x + {n \choose 2}x^2+\cdots+</math><math>{n \choose n}x^n</math>.<br />
<br />
This function can be described as the number of ways we can get <math>{k}</math> heads when flipping <math>n</math> different coins.<br />
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The reason to go to such lengths is that our above polynomial is equal to <math>(1+x)^n</math> (which is clearly seen due to the [[Binomial Theorem]]). By using this equation, we can rapidly uncover identities such as <math>{n \choose 0}+{n \choose 1}+...+{n \choose n}=2^n</math>(let <math>{x}=1</math>), also <math>{n \choose 1}+{n \choose 3}+\cdots={n \choose 0}+{n \choose 2}+\cdots</math>.<br />
<br />
== Convolutions ==<br />
Suppose we have the sequences <math>a_1, a_2, a_3, ...</math> and <math>b_1, b_2, b_3, ...</math>. We can create a new sequence, called the convolution of <math>a</math> and <math>b</math>, defined by <math>c_n = a_0b_n + a_1b_{n-1} + ... + a_nb_0</math>. Generating functions allow us to represent the convolution of two sequences as the product of two power series. If <math>A</math> is the generating function for <math>a</math> and <math>B</math> is the generating function for <math>b</math>, then the generating function for <math>c</math> is <math>AB</math>.<br />
<br />
=== See also ===<br />
<br />
* [[Combinatorics]]<br />
* [[Polynomials]]<br />
* [[Series]]<br />
* [http://www.math.wisc.edu/~propp/491/gfologyLinked.pdf generatingfunctionology] a PDF version</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Chess/Chess_Tournament_Info&diff=18634AoPS Wiki:Chess/Chess Tournament Info2007-10-24T21:56:16Z<p>Hamster1800: </p>
<hr />
<div>__NOTOC__<br />
<small><- [[AoPSWiki:Chess]]</small><br /><br /><br />
:'''Currently: Accepting sign-ups!'''<br />
<br />
:'''<span style="color:blue">Note: The tournament will commence when the game in the Games and Fun Factory is over! Also, this article is more updated than the information in the topic; so if there are any discrepancies, then this probably has the correct information!</span>'''<br />
<br />
===Teams===<br />
Each team will consist of either 4 or 5 players. It is suggested only people who already know each other make teams of 5 people as it can be harder to communicate with more people. Players can agree between themselves and create their own teams. Others who haven't made their own teams will be randomized into teams.<br />
<br />
During the tournament, a team cannot request to have another player added to their team unless one of their players cannot participate anymore. Players cannot switch teams, so choose wisely if you pick your own teams.<br />
<br />
===Rules===<br />
A team must post a move within 2 days after the other team's move. Each time a team fails to do so (unless there is a good reason), a warning will be issued. 5 warnings will result in disqualification.<br />
<br />
The use of computers, chess programs, and other devices that give your team an advantage is not allowed. This rule cannot be strictly enforced, but hopefully people will play fairly as this tournament is for fun only.<br />
<br />
===Tournament Format===<br />
Depending on the amount of players and teams, there will be several rounds of Swiss, followed by single elimination for the final rounds. For the final game, 3 days will be allowed per move.<br />
<br />
===Signing Up===<br />
Before signing up, please make sure you will be able to participate. [[User:I like pie|I_like_pie]] will accept sign ups via post in the [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=164632 original topic], <url>privmsg.php?mode=post&u=22236 PM</url>, or email (nkouevda@gmail.com).<br />
<br />
===List of Players===<br />
35 Players:<br />
#[[User:I like pie|i_like_pie]]<br />
#[[User:7h3.D3m0n.117|7h3.D3m0n.117]]<br />
#cincodemayo5590<br />
#BoesFX<br />
#[[User:Temperal|Temperal]]<br />
#shaggy75<br />
#Tenoreoz<br />
#[[User:H34N1|<nowiki>#</nowiki>H34N1]]<br />
#[[User:abacadaea|abacadaea]]<br />
#[[User:nayel|nayel]]<br />
#not_trig<br />
#bubka<br />
#AnonAmoz<br />
#davidyko<br />
#toadoncart<br />
#Ars<br />
#bos1234<br />
#Hamster1800<br />
#TheDropOutBoy<br />
#mz94<br />
#rem<br />
#ProtestanT<br />
#Farrell<br />
#D3m0n Shad0w<br />
#[[User:Azjps|azjps]]<br />
#[[User:Lawrence Wu|Lawrence Wu]]<br />
#miyomiyo<br />
#ZeroFive1<br />
#chessplayingballer<br />
#[[User:CircleSquared|CircleSquared]]<br />
#Rafaelloaa<br />
#nitish<br />
#DonkeyKong<br />
#moogra<br />
#snee<br />
<br />
===List of Teams===<br />
====Team Alpha (<math>\alpha</math>)====<br />
#i_like_pie - ''<span style="color:blue">Poster</span>''<br />
#7h3.D3m0n.117 - ''<span style="color:blue">Substitute Poster</span>''<br />
#cincodemayo5590<br />
#D3m0n Shad0w<br />
#TheDropOutBoy<br />
<br />
====Team Beta (<math>\beta</math>)====<br />
#Temperal - ''<span style="color:blue">Poster</span>''<br />
#<nowiki>#</nowiki>H34N1 - ''<span style="color:blue">Substitute Poster</span>''<br />
#CircleSquared<br />
#abacadaea<br />
<br />
====Team Gamma (<math>\gamma</math>)====<br />
#nayel - ''<span style="color:blue">Poster</span>''<br />
#BoesFX - ''<span style="color:blue">Substitute Poster</span>''<br />
#mz94<br />
#shaggy75<br />
<br />
====Team Delta (<math>\delta</math>)====<br />
#AnonAmoz - ''<span style="color:blue">Poster</span>''<br />
#nitish - ''<span style="color:blue">Substitute Poster</span>''<br />
#Rafaelloaa<br />
#Lawrence Wu<br />
<br />
====Team Epsilon (<math>\varepsilon</math>)====<br />
#not_trig - ''<span style="color:blue">Poster</span>''<br />
#Hamster1800 - ''<span style="color:blue">Substitute Poster</span>''<br />
#-- OPEN --<br />
#-- OPEN --<br />
<br />
[[Category: AoPSWiki Games]]</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=United_States_of_America_Computing_Olympiad&diff=18270United States of America Computing Olympiad2007-10-17T21:54:42Z<p>Hamster1800: No more level 1</p>
<hr />
<div>The '''United States Computing Olympiad''' includes a series of seven internet programming contests and a training camp, used to eventually choose the team that will represent the US in the [[International Olympiad in Informatics]] (IOI).<br />
<br />
==Training Pages==<br />
<br />
==Internet Competitions==<br />
There are seven Internet Competitions held each year, including the qualification contest, and USACO's flagship contest, the US Open, which tests the programmer's ability to write correct programs, with restrictions on runtime and memory usage.<br />
<br />
These Internet Competitions have different level, Gold (the most difficult), Silver, and Bronze (the least difficult).<br />
<br />
===Qualification Round===<br />
The qualification round is held in the October of each season, to give participants the chance of being in the Gold or Silver divisions. This contest does not count for deciding who goes to the training camp or not however.<br />
<br />
There are other ways to qualify for the Silver or Gold divisions, including doing well on a previous contest.<br />
<br />
===Regular Contests===<br />
Regular contests take place each month from November through March. These contests are generally 3-5 problems lasting 3 hours. Competitors may participate at any time over a weekend for three hours as long as those hours are continuous. Preliminary results get mailed to individuals on the Tuesday after the contest, and an analysis mode is released. The preliminary results contain the results from testing that competitor's programs. In analysis mode, competitors may submit code for testing. If they feel that their code was graded incorrectly, they may ask for a retest at this time. The Thursday of that same week, overall results are released. These include problem weights, overall score, rankings, and who gets to move up to the next competition.<br />
<br />
===US Open===<br />
<br />
==Training Camp==</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=United_States_of_America_Computing_Olympiad&diff=17246United States of America Computing Olympiad2007-09-30T19:13:48Z<p>Hamster1800: </p>
<hr />
<div>{{WotWAnnounce|week=Sep 27-Oct 3}}<br />
<br />
The '''United States Computing Olympiad''' includes a series of seven internet programming contests and a training camp, used to eventually choose the team that will represent the US in the [[International Olympiad in Informatics]] (IOI).<br />
<br />
==Training Pages==<br />
<br />
==Internet Competitions==<br />
There are seven Internet Competitions held each year, including the qualification contest, and USACO's flagship contest, the US Open, which tests the programmer's ability to write correct programs, with restrictions on runtime and memory usage.<br />
<br />
These Internet Competitions have different level, Gold (the most difficult), Silver, and Bronze (the least difficult). There is also a level 1 contest for those who are taking a first-level computer science course.<br />
<br />
===Qualification Round===<br />
The qualification round is held in the October of each season, to give participants the chance of being in the Gold or Silver divisions. This contest does not count for deciding who goes to the training camp or not however.<br />
<br />
There are other ways to qualify for the Silver or Gold divisions, including doing well on a previous contest.<br />
<br />
===Regular Contests===<br />
Regular contests take place each month from November through March. These contests are generally 3-5 problems lasting 3 hours. Competitors may participate at any time over a weekend for three hours as long as those hours are continuous. Preliminary results get mailed to individuals on the Tuesday after the contest, and an analysis mode is released. The preliminary results contain the results from testing that competitor's programs. In analysis mode, competitors may submit code for testing. If they feel that their code was graded incorrectly, they may ask for a retest at this time. The Thursday of that same week, overall results are released. These include problem weights, overall score, rankings, and who gets to move up to the next competition.<br />
<br />
===US Open===<br />
<br />
==Training Camp==</div>Hamster1800https://artofproblemsolving.com/wiki/index.php?title=2007_USAMO_Problems/Problem_5&diff=147282007 USAMO Problems/Problem 52007-04-26T02:44:01Z<p>Hamster1800: Moved the solution to above the box</p>
<hr />
<div>== Problem ==<br />
<br />
Prove that for every nonnegative integer <math>n</math>, the number <math>7^{7^n}+1</math> is the product of at least <math>2n+3</math> (not necessarily distinct) primes.<br />
<br />
== Solution ==<br />
<br />
Let <math>\displaystyle{a_{n}}</math> be <math>7^{7^{n}}+1</math>. We prove the result by induction.<br />
<br />
The result holds for <math>\displaystyle{n=0}</math> because <math>\displaystyle{a_0 = 2^3}</math> is the product of <math>\displaystyle{3}</math> primes. Now we assume the result holds for <math>\displaystyle{n}</math>. Note that <math>\displaystyle{a_{n}}</math> satisfies the recursion<br />
<br />
<br />
<math>\displaystyle{a_{n+1}= (a_{n}-1)^{7}+1} = a_{n}\left(a_{n}^{6}-7(a_{n}-1)(a_{n}^{2}-a_{n}+1)^{2}\right)</math>.<br />
<br />
<br />
Since <math>\displaystyle{a_n - 1}</math> is an odd power of <math>\displaystyle{7}</math>, <math>\displaystyle{7(a_n-1)}</math> is a perfect square. Therefore <math>\displaystyle{a_{n}^{6}-7(a_{n}-1)(a_{n}^{2}-a_{n}+1)^{2}}</math> is a difference of squares and thus composite, i.e. it is divisible by <math>\displaystyle{2}</math> primes. By assumption, <math>\displaystyle{a_n}</math> is divisible by <math>\displaystyle{2n + 3}</math> primes. Thus <math>\displaystyle{a_{n+1}}</math> is divisible by <math>\displaystyle{2+ (2n + 3) = 2(n+1) + 3}</math> primes as desired.<br />
<br />
{{USAMO newbox|year=2007|num-b=4|num-a=6}}</div>Hamster1800