Harvard-MIT Mathematics Tournament - AbsoluteAstronomy.com

The Harvard–MIT Mathematics Tournament (HMMT) is an annual high school math competition started in 1998. The location of the tournament, in Cambridge, Massachusetts

Cambridge, Massachusetts

Cambridge is a city in Middlesex County, Massachusetts, United States, in the Greater Boston area. It was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders. Cambridge is home to two of the world's most prominent...

, alternates between Harvard University

Harvard University

Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...

(even years) and MIT (odd years). The contest is written and staffed entirely by Harvard and MIT students, and is considered to be one of the most prestigious high school math competitions in the world.

Tournament Format

HMMT is attended by teams of eight students each. Teams can represent a single school, or a regional math team as large as a state. In recent years, teams have represented over 20 states, as well as Africa, Asia, Europe, and South America.

HMMT consists of three rounds: the Individual Round, the Team Round, and the Guts Round. No calculator or computational aids of any kind are allowed during the contest.

Individual Round

The Individual Round consists of exams in Algebra, Combinatorics, and Geometry. Each of the three exams is 50 minutes in length and contains 10 questions. The exams are open-answer; that is, the answers given will be numbers such as 7 or 11/20.

Team Round

For the Team Round, the eight-person teams may decide to compete in the A Team Round or the B Team Round. Each test is a 60 minute collaborative round, consisting of 10-15 questions from any area of elementary mathematics . While the B Team Round is easier, it is weighted only about 50% of the A team test when calculating the overall tournament champions.

The A Team Round is a collaborative event with proof-style problems, arranged into groups of several problems on the same theme. Thorough justifications are required for full credit. The Team Round is worth a total of 400 points, and problems are weighted according to difficulty. The event is similar to an ARML Power Round, but the problems are easier and more numerous. This round is targeted at teams comfortable with rigorous mathematical proofs.

The B Team Round is a collaborative event with a mixture of proof-style and short answer questions. Thorough justifications are required for full credit on the proof questions.

Guts Round

The Guts Round is an 80-minute team event with 36 short-answer questions on an assortment of subjects, of varying difficulty and point values. Each team is seated in a predetermined spot, and the questions are divided into groups of four. At the starting signal, each team sends a runner to an assigned problem station to pick up copies of the first set of four problems for each team member. As soon as a team has answers for one problem set, the runner may bring the answers to the problem station and pick up the next set. It is not expected that students will finish all the problems. Grading is immediate and scores are posted in real time, resulting in an exciting atmosphere for the competitors. The Guts round is worth a total of approximately 400 points.

Other Events

HMMT also features events on the Friday evening prior to the tournament. Some of these events include a dinner and social for students and coaches, and Mini-Events such as math talks about famous problems and math-related games.

Scoring and Awards

HMMT uses a unique scoring algorithm to score the competitors on the Individual Rounds. While the problems on these tests are weighted according to difficulty, they are done so after the testing has completed. As explained here, this helps create a very fair method for weighting problems according to their actual difficulty (as determined by how often and by whom they were solved) as opposed to their perceived difficulty prior to the tournament. The weights assigned to each problem are calculated using a scoring algorithm that takes into account which problems were solved by which students. The weights of the problems on the Team and Guts Rounds are given on the tests.

Prizes are given to the ten highest-scoring individuals overall, the top ten scorers on each of the subject rounds, the ten highest-scoring teams on the Team Round (A and B), and the ten highest-scoring teams on the Guts Round. The top ten teams overall will be named the Sweepstakes winners. The calculation of Sweepstakes scores is roughly half individual round performance and half collaborative round performance.

Difficulty

The difficulty of the competition is compared to that of ARML, the AIME

American Invitational Mathematics Examination

The American Invitational Mathematics Examination is a 15-question 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics contest , and starting in 2010, those who rank in the top 2.5% on the AMC 10.The AIME is the second of two tests used to determine...

, or the Mandelbrot Competition

Mandelbrot Competition

Named in honor of the Mandelbrot set, the Mandelbrot Competition is a mathematics competition founded by Sam Vandervelde, Richard Rusczyk and Sandor Lehoczky that allows high school students to compete individually and in four-person teams.-Competition:...

, though it is considered to be a bit harder than these contests. The contest organizers state that, "HMMT, arguably one of the most difficult math competitions in the United States, is geared toward students who can comfortably and confidently solve 6 to 8 problems correctly on the American Invitational Mathematics Examination (AIME)." As with most high school competitions, knowledge of calculus

Calculus

Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

is not required; however, calculus may be necessary to solve a select few of the more difficult problems on the Individual Rounds.

Results

The results of HMMT can be seen below:

Year	Overall Champion	Individual Champion	Team Round A Champion	Guts Round Champion
2011	Saratoga High School Saratoga High School Saratoga High School is a high school in Saratoga, California, United States, part of the Los Gatos-Saratoga Joint Union High School District. The school is jointly accredited by the California Department of Education and the Western Association of Schools and Colleges. Student enrollment averages... /SFBA San Francisco Bay Area The San Francisco Bay Area, commonly known as the Bay Area, is a populated region that surrounds the San Francisco and San Pablo estuaries in Northern California. The region encompasses metropolitan areas of San Francisco, Oakland, and San Jose, along with smaller urban and rural areas...	Xiaoyu He	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...	Saratoga High School/SFBA
2010	Phillips Exeter Academy 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...	Ben Gunby	TJHSST 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...	AAST
2009	TJHSST	Ice Pasupat	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... ARML	Lehigh Valley ARML
2008	Phillips Exeter Academy	Brian Hamrick	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... Math Team	Quagga
2007	The WOOT Worldwide Online Olympiad Training The Worldwide Online Olympiad Training program was established in 2005 by Art of Problem Solving, with sponsorship from Google and quantitative hedge fund giant D. E. Shaw & Co., in order to meet the needs of the world's top high school math students. Sponsorship allowed free enrollment for... lings	Arnav Tripathy	The WOOTlings	TJHSST
2006	Phillips Exeter Academy	Nimish Ramanlal	TJHSST	AAST
2005	Phillips Exeter Academy	Thomas Mildorf	TJHSST	Florida Florida Florida is a state in the southeastern United States, located on the nation's Atlantic and Gulf coasts. It is bordered to the west by the Gulf of Mexico, to the north by Alabama and Georgia and to the east by the Atlantic Ocean. With a population of 18,801,310 as measured by the 2010 census, it...
2004	TJHSST	Tiankai Liu	TJHSST	Phillips Exeter Academy
2003	TJHSST	Tony Zhang	TJHSST	AAST
2002	Newton South High School Newton South High School Newton South High School is one of two public high schools in the city of Newton, Massachusetts, the other being Newton North.-Mission statement:Newton South High School, a community of students, parents, faculty, and staff,...	Ricky Liu	Newton South High School	Lexington High School Lexington High School Lexington High School may refer to:Lexington High School — Lexington, AlabamaLexington High School — Lexington, Illinois*Lexington High School — Lexington, Massachusetts...
2001	Lexington High School	Ricky Liu	Lexington High School	Newton South High School
2000	Newton South High School	Ricky Liu	Newton South High School	Newton South High School
1999	Newton South High School	n/a	Newton South High School	n/a
1998	Lexington High School	n/a	Lexington High School	n/a

HMNT

HMNT, the Harvard-MIT November Tournament, has been held since 2008 at MIT for teams of six students within a 125-mile radius of Cambridge, Massachusetts. The tournament is similar in style to HMMT, and is organized by the same Harvard and MIT students as HMMT. Instead of three topic tests, HMNT has two Individual Rounds: a General Test (ten questions from Algebra, Geometry, and Combinatorics) and a Theme Test (ten questions, many of which are tied together by a common theme). Additionally, the Team Round is entirely short answer, instead of proof-based. HMNT is considered to be an easier alternative to HMMT; while schools may compete at both tournaments, no students may compete at both HMNT and HMMT in the same school year as of 2011-12. The results of HMNT can be seen below:

Year	Overall Champion	Individual Champion	Team Round Champion	Guts Round Champion
2011	Phillips Exeter Academy	Forest Tong	Lexington High School	Brookline High School Brookline High School Brookline High School is a four-year public high school in the town of Brookline, Massachusetts, in the United States.As of the 2007-08 school year, the school had an enrollment of 1,826 students and 136 teachers , for a student-teacher ratio of 13.4 to 1 teacher.-Education:Almost every senior in...
2010	Phillips Exeter Academy	Ravi Jagadeesan	Phillips Exeter Academy	Lexington High School
2009	ABRHS Acton-Boxborough Regional High School Acton-Boxborough Regional High School is an open enrollment high school in Acton, Massachusetts. It serves the Massachusetts towns of Acton and Boxborough, with roughly 500 students per grade level in grades 9 through 12. ABRHS has consistently ranked among the top secondary schools in Massachusetts...	Xiaoyu He	Phillips Exeter Academy	ABRHS
2008	Western Mass Western Massachusetts Western Massachusetts is a loosely defined geographical region of the U.S. state of Massachusetts which contains the Berkshires, the Pioneer Valley, and some or all of the Swift River Valley. The region is always considered to include Berkshire, Franklin, Hampshire, and Hampden counties, and the... ARML	Sam Trabucco	Western Mass ARML	Westford Academy Westford Academy Westford Academy is the public high school for the town of Westford, Massachusetts. It was founded in 1792, and is one of the oldest public high schools in the United States. Westford Academy was originally established as a private school and was changed to a public school in 1928...