American Regions Mathematics League - AbsoluteAstronomy.com

The American Regions Mathematics League (ARML), is an annual high school mathematics team competition held simultaneously at four locations in the United States: the University of Iowa

University of Iowa

The University of Iowa is a public state-supported research university located in Iowa City, Iowa, United States. It is the oldest public university in the state. The university is organized into eleven colleges granting undergraduate, graduate, and professional degrees...

, Penn State

Pennsylvania State University

The Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...

, UNLV

University of Nevada, Las Vegas

University of Nevada-Las Vegas is a public, coeducational university located in the Las Vegas suburb of Paradise, Nevada, USA. The campus is located approximately east of the Las Vegas Strip. The institution includes a Shadow Lane Campus, located just east of the University Medical Center of...

, and the newly added site at the University of Georgia

University of Georgia

The University of Georgia is a public research university located in Athens, Georgia, United States. Founded in 1785, it is the oldest and largest of the state's institutions of higher learning and is one of multiple schools to claim the title of the oldest public university in the United States...

. Past sites have included San Jose

San Jose, California

San Jose is the third-largest city in California, the tenth-largest in the U.S., and the county seat of Santa Clara County which is located at the southern end of San Francisco Bay...

and at Duke University

Duke University

Duke University is a private research university located in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present day town of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco industrialist James B...

.

The contest is largely made possible by the monetary contribution of D. E. Shaw & Co. among other smaller contributors.

Teams consist of 15 members, which usually represent a large geographic region (such as a state) or a large population center (such as a major city). Some math and science magnet schools, such as Thomas Jefferson High School for Science and Technology

Thomas Jefferson High School for Science and Technology

Thomas Jefferson High School for Science and Technology is a Virginia state-chartered magnet school located within Fairfax County, Virginia, United States...

, VA, and the Academy for the Advancement of Science and Technology (AAST), NJ, also field teams. The competition is held on the first Saturday after Memorial Day.

As of 2006, over 100 teams competed with around 1800 students.

ARML problems cover a wide variety of mathematical topics including algebra

Algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

, geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, number theory

Number theory

Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

, combinatorics

Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

, probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

, and inequalities. While part of the competition is short-answer based, there is a cooperative team round, and a proof-based power question (also completed as a team). ARML problems are harder than most high school mathematics competitions.

Competition format

The competition consists of four formal events:

A team round, where the entire team has 20 minutes to solve 10 problems. Each problem is worth 5 points, for a possible total of 50 points
A power question, where the entire team has one hour to solve a multiple-part (usually ten) question requiring explanations and proofs. This is usually an unusual, unique, or invented topic so students are forced to deal with complex new mathematical ideas. Each problem is weighted for a possible 50 points.
An individual round, where each team member answers five groups of two questions each, with ten minutes per pair. Starting in 2009, the individual round expanded from eight questions to ten. Each problem is worth 1 point, for a grand total of 150 points possible for the team.
A relay, where the team is broken into five groups of three. Within each group, the first team member solves a problem and passes the solution to the next team member, who plugs that answer into their question, and so on. The allotted time is six minutes, but extra points are given for solving the problem in three minutes. Solving the relay in 3 minutes gives 5 points, solving it in 6 minutes gives 3 points, making the maximum 50 points possible for the team.

At the end, the student(s) with the highest scores on the individual compete for first place. Each student tied for the highest score is given a single question, and the quickest to get the correct answer wins. In the event of a tie (no one is able to get the correct answer in the given ten minutes), another tiebreaker is given, generally easier than the previous. The tiebreaker results are shared between the four sites to determine the top overall scorer, based on time to get the correct answer. The teams are scored based on the number of points they attained. The maximum being 300 points.

In recent years, there has been a super relay, where two groups of seven team members (fourteen in all) both work to give a correct answer to the fifteenth team member. That last team member substitutes two answers into his problem. For logistical reasons, the Super Relay has never counted towards the team score. It was instituted as a "filler" while scores are tabulated. Candies and other goodies are sometimes rewards for the super relay round. The 2008 super relay at UNLV ended when a team guessed the correct answer. Realizing the likelihood of the fifteenth person receiving two correct answers was small, and knowing their answer to be a small integer, the fifteenth person of some teams began to run answers up to the proctors before the other members of the team finished their problems. This continued until the correct answer was guessed. To fix this, the writers made the final answer for the 2009 super relay a four-digit number. However, the 2008 disaster reoccurred in 2010, when a San Diego team correctly guessed the answer, 24, immediately after the "go" signal.

Also in recent years, a song contest has become an informal event at ARML. Each school is allowed to have any number of their students perform a song related to mathematics, usually a parody of a popular song, with its lyrics replaced.

The format of the ARML competition is based on the NYSML competition

New York State Mathematics League

The New York State Mathematics League competition was originally held in 1973 and has been held annually in a different location each year since. It was founded by Alfred Kalfus. The American Regions Math League competition is based on the format of the NYSML competition....

, but is generally considered more difficult than the NYSML competition. This format also inspired the Great Plains Math League.

History

The New York State Mathematics League

New York State Mathematics League

held its first competition in 1973, a competition intended for New York

New York

New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...

state teams. A team from Massachusetts

Massachusetts

The Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010...

asked to participate in the 1974 NYSML competition, and it took first place. This led to the creation of the Atlantic Regions Mathematics League in 1976, which became the American Regions Mathematics League in 1984.

When the Atlantic Regions Mathematics League was founded, the competition was held at a single eastern site that changed from year to year:

Year	Location
1976	C. W. Post College
1977	Brown University Brown University Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
1978	Rutgers University Rutgers University Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
1979	Brown University Brown University Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
1980	Rutgers University Rutgers University Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
1981	University of Maryland College Park
1982	University of Maryland College Park
1983	Pennsylvania State University Pennsylvania State University The Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...

After 1983, the coordinators decided to keep the competition at Penn State University. ARML expanded to two sites in the late 1980s and to three sites in 1995. In 2008, ARML added a fourth site at the University of Georgia

University of Georgia

in Athens to better accommodate students in the Southeast.

The 2006 competition saw significant expansion. Around 120 teams and a total of around 1800 students competed, which was around 25% larger than during any other year. The Western site at UNLV nearly doubled.

Past Team Winners

Year	Team	Score
1976	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1977	Massachusetts Massachusetts The Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010... A
1978	Fairfax Fairfax County, Virginia Fairfax County is a county in Virginia, in the United States. Per the 2010 Census, the population of the county is 1,081,726, making it the most populous jurisdiction in the Commonwealth of Virginia, with 13.5% of Virginia's population... -Montgomery Montgomery County, Maryland Montgomery County is a county in the U.S. state of Maryland, situated just to the north of Washington, D.C., and southwest of the city of Baltimore. It is one of the most affluent counties in the United States, and has the highest percentage of residents over 25 years of age who hold post-graduate...
1979	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1980	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1981	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1982	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1983	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1984	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1985	Montgomery County, Maryland Montgomery County, Maryland Montgomery County is a county in the U.S. state of Maryland, situated just to the north of Washington, D.C., and southwest of the city of Baltimore. It is one of the most affluent counties in the United States, and has the highest percentage of residents over 25 years of age who hold post-graduate... A
1986	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1987	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1988	Chicago Chicago Chicago is the largest city in the US state of Illinois. With nearly 2.7 million residents, it is the most populous city in the Midwestern United States and the third most populous in the US, after New York City and Los Angeles... A
1989	Chicago Chicago Chicago is the largest city in the US state of Illinois. With nearly 2.7 million residents, it is the most populous city in the Midwestern United States and the third most populous in the US, after New York City and Los Angeles... A
1990	Ontario Ontario Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa.... A
1991	Ontario Ontario Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa.... A
1992	Georgia Georgia (U.S. state) Georgia is a state located in the southeastern United States. It was established in 1732, the last of the original Thirteen Colonies. The state is named after King George II of Great Britain. Georgia was the fourth state to ratify the United States Constitution, on January 2, 1788... A
1993	Thomas Jefferson Thomas Jefferson High School for Science and Technology Thomas Jefferson High School for Science and Technology is a Virginia state-chartered magnet school located within Fairfax County, Virginia, United States... A
1994	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1995	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
1996	San Francisco Bay Area A
1997	Minnesota Minnesota Minnesota is a U.S. state located in the Midwestern United States. The twelfth largest state of the U.S., it is the twenty-first most populous, with 5.3 million residents. Minnesota was carved out of the eastern half of the Minnesota Territory and admitted to the Union as the thirty-second state... Gold
1998	Massachusetts Massachusetts The Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010... A
1999	San Francisco Bay Area A
2000	Chicago Chicago Chicago is the largest city in the US state of Illinois. With nearly 2.7 million residents, it is the most populous city in the Midwestern United States and the third most populous in the US, after New York City and Los Angeles... A/San Francisco Bay Area A (tie)
2001	San Francisco Bay Area A
2002	Thomas Jefferson Thomas Jefferson High School for Science and Technology Thomas Jefferson High School for Science and Technology is a Virginia state-chartered magnet school located within Fairfax County, Virginia, United States... A
2003	Thomas Jefferson Thomas Jefferson High School for Science and Technology Thomas Jefferson High School for Science and Technology is a Virginia state-chartered magnet school located within Fairfax County, Virginia, United States... A
2004	Thomas Jefferson Thomas Jefferson High School for Science and Technology Thomas Jefferson High School for Science and Technology is a Virginia state-chartered magnet school located within Fairfax County, Virginia, United States... A
2005	Lehigh Valley Lehigh Valley The Lehigh Valley, known officially by the United States Census Bureau as the Allentown-Bethlehem-Easton, PA-NJ metropolitan area and referred to locally as The Valley and A-B-E, is a metropolitan region consisting of Lehigh, Northampton, Berks, and Carbon counties in eastern Pennsylvania and... Fire	172
2006	North Carolina North Carolina North Carolina is a state located in the southeastern United States. The state borders South Carolina and Georgia to the south, Tennessee to the west and Virginia to the north. North Carolina contains 100 counties. Its capital is Raleigh, and its largest city is Charlotte... A	186
2007	Phillips Exeter Phillips Exeter Academy Phillips Exeter Academy is a private secondary school located in Exeter, New Hampshire, in the United States.Exeter is noted for its application of Harkness education, a system based on a conference format of teacher and student interaction, similar to the Socratic method of learning through asking... Red	171
2008	New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A
2009	Lehigh Valley Lehigh Valley The Lehigh Valley, known officially by the United States Census Bureau as the Allentown-Bethlehem-Easton, PA-NJ metropolitan area and referred to locally as The Valley and A-B-E, is a metropolitan region consisting of Lehigh, Northampton, Berks, and Carbon counties in eastern Pennsylvania and... Fire	215
2010	Lehigh Valley Lehigh Valley The Lehigh Valley, known officially by the United States Census Bureau as the Allentown-Bethlehem-Easton, PA-NJ metropolitan area and referred to locally as The Valley and A-B-E, is a metropolitan region consisting of Lehigh, Northampton, Berks, and Carbon counties in eastern Pennsylvania and... Fire	204
2011	Lehigh Valley Lehigh Valley The Lehigh Valley, known officially by the United States Census Bureau as the Allentown-Bethlehem-Easton, PA-NJ metropolitan area and referred to locally as The Valley and A-B-E, is a metropolitan region consisting of Lehigh, Northampton, Berks, and Carbon counties in eastern Pennsylvania and... Fire	232

Past Individual Winners

Year	Team
1981	Benji Fisher (New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A)
1982	Noam Elkies Noam Elkies Noam David Elkies is an American mathematician and chess master.At age 14, Elkies received a gold medal with a perfect score at the International Mathematical Olympiad, the youngest ever to do so... (New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A)
1983	David Zuckerman (New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A)
1984	Mike Reid (New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A)
1985	Ken Fan (Montgomery County, Maryland Montgomery County, Maryland Montgomery County is a county in the U.S. state of Maryland, situated just to the north of Washington, D.C., and southwest of the city of Baltimore. It is one of the most affluent counties in the United States, and has the highest percentage of residents over 25 years of age who hold post-graduate... A)
1986	John Overdeck (Howard County Howard County, Maryland -2010:Whereas according to the 2010 U.S. Census Bureau:62.2% White17.5% Black0.3% Native American14.4% Asian0.0% Native Hawaiian or Pacific Islander3.6% Two or more races2.0% Other races5.8% Hispanic or Latino -2000:... A)
1987	Danny Cory North Carolina
1988	Michael Zieve (Greater Richmond)
1989	Sam Vandervelde
1990	Akira Negi (North Carolina North Carolina North Carolina is a state located in the southeastern United States. The state borders South Carolina and Georgia to the south, Tennessee to the west and Virginia to the north. North Carolina contains 100 counties. Its capital is Raleigh, and its largest city is Charlotte... )
1991	Andrew Schultz (Chicago Chicago Chicago is the largest city in the US state of Illinois. With nearly 2.7 million residents, it is the most populous city in the Midwestern United States and the third most populous in the US, after New York City and Los Angeles... A)
1992	Robert Kleinberg (Upstate New York Upstate New York Upstate New York is the region of the U.S. state of New York that is located north of the core of the New York metropolitan area.-Definition:There is no clear or official boundary between Upstate New York and Downstate New York... )
1993	Jeremy Bem (Upstate New York Upstate New York Upstate New York is the region of the U.S. state of New York that is located north of the core of the New York metropolitan area.-Definition:There is no clear or official boundary between Upstate New York and Downstate New York... )
1994	Noam Shazeer (Massachusetts Massachusetts The Commonwealth of Massachusetts is a state in the New England region of the northeastern United States of America. It is bordered by Rhode Island and Connecticut to the south, New York to the west, and Vermont and New Hampshire to the north; at its east lies the Atlantic Ocean. As of the 2010... A)
1995	Daniel Stronger (New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A)
1996	Nathan Curtis (Thomas Jefferson Thomas Jefferson High School for Science and Technology Thomas Jefferson High School for Science and Technology is a Virginia state-chartered magnet school located within Fairfax County, Virginia, United States... A)
1997	Davesh Maulik (Nassau Nassau County, New York Nassau County is a suburban county on Long Island, east of New York City in the U.S. state of New York, within the New York Metropolitan Area. As of the 2010 census, the population was 1,339,532... A)
1998	Gabriel Carroll (San Francisco Bay Area A)
1999	Gabriel Carroll (San Francisco Bay Area A)
2000	Tiankai Liu (San Francisco Bay Area A)
2001	Gabriel Carroll (San Francisco Bay Area A)
2002	Ruozhou Jia (Chicago Chicago Chicago is the largest city in the US state of Illinois. With nearly 2.7 million residents, it is the most populous city in the Midwestern United States and the third most populous in the US, after New York City and Los Angeles... A)
2003	Anders Kaseorg (North Carolina North Carolina North Carolina is a state located in the southeastern United States. The state borders South Carolina and Georgia to the south, Tennessee to the west and Virginia to the north. North Carolina contains 100 counties. Its capital is Raleigh, and its largest city is Charlotte... A)
2004	Aaron Pixton (Upstate New York New York New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east... A)
2005	Ryan Ko (Phillips Exeter Phillips Exeter Academy Phillips Exeter Academy is a private secondary school located in Exeter, New Hampshire, in the United States.Exeter is noted for its application of Harkness education, a system based on a conference format of teacher and student interaction, similar to the Socratic method of learning through asking... A)
2006	Samuel Dittmer (Indiana Indiana Indiana is a US state, admitted to the United States as the 19th on December 11, 1816. It is located in the Midwestern United States and Great Lakes Region. With 6,483,802 residents, the state is ranked 15th in population and 16th in population density. Indiana is ranked 38th in land area and is... Gold)
2007	Tao Ran Chen (New York City New York City New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and... A)
2008	Qin Xuan Pan (Montgomery Montgomery County, Maryland Montgomery County is a county in the U.S. state of Maryland, situated just to the north of Washington, D.C., and southwest of the city of Baltimore. It is one of the most affluent counties in the United States, and has the highest percentage of residents over 25 years of age who hold post-graduate... A)
2009	Alex Song (Ontario Ontario Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa.... West)
2010	Ben Gunby (Georgetown Day School Georgetown Day School Georgetown Day School is a pre-K-12 private preparatory school in Washington, D.C..-History:GDS was founded in 1945 as the first integrated school in the District of Columbia.-Academics:... B)
2011	Alex Song (Ontario Ontario Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa.... West)

External links

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