American High School Mathematics Examination

American High School Mathematics Examination
Name	American High School Mathematics Examination
Type	Mathematics competition
Country	United States
Established	1950s
Administered by	Mathematical Association of America
Qualifying for	American Invitational Mathematics Examination

Contents

American High School Mathematics Examination

The American High School Mathematics Examination is a nationwide mathematics contest administered in the United States that serves as a qualifier for the American Invitational Mathematics Examination and is associated with organizations such as the Mathematical Association of America, the American Mathematical Society, the National Council of Teachers of Mathematics, the Institute of Electrical and Electronics Engineers, and the Society for Industrial and Applied Mathematics. It has connections to programs and events like the United States of America Mathematical Olympiad, the International Mathematical Olympiad, the Mathematics Olympiad Summer Program, the Harvard-MIT Mathematics Tournament, and the Princeton University Math Competition, and influences secondary-school pathways linked to institutions such as Massachusetts Institute of Technology, Harvard University, Stanford University, California Institute of Technology, and University of Chicago.

Overview

The examination is structured to identify high-performing students for advancement to national-level contests and recognition by bodies like the American Invitational Mathematics Examination, the United States Mathematical Talent Search, the International Mathematical Olympiad, the British Mathematical Olympiad, and the European Girls' Mathematical Olympiad, while interacting with academic programs at Johns Hopkins University, University of Cambridge, Oxford University, Yale University, and Columbia University. It is administered in coordination with state and regional affiliates such as the California Mathematics Council, the New York State Association of Mathematics Teachers, the Texas Mathworks, the Florida Council of Teachers of Mathematics, and the Illinois Council of Teachers of Mathematics.

The examination’s origins trace to mid-20th-century efforts influenced by events and institutions like the Sputnik crisis, the National Science Foundation, the Atomic Energy Commission, the Carnegie Institution for Science, and the National Defense Education Act. Early organizational roles involved the Mathematical Association of America, individuals associated with the Institute for Advanced Study, and programs linked to the United States Air Force Academy, the United States Naval Academy, and the United States Military Academy. Over decades it intersected with summer programs and contests such as the MathCounts National Competition, the American Regions Mathematics League, the Asian Pacific Mathematics Olympiad, and the International Zhautykov Olympiad.

Question types reflect problem styles found in contests like the United States of America Mathematical Olympiad, the American Invitational Mathematics Examination, the Harvard-MIT Mathematics Tournament, and the Putnam Competition, emphasizing algebra, combinatorics, geometry, and number theory. Typical topics overlap with curricula and texts associated with authors and works such as Paul Halmos, G. H. Hardy, Terence Tao, E. T. Bell, George Pólya, Richard Rusczyk, and textbooks from Cambridge University Press and Princeton University Press. Problems often mirror techniques celebrated in seminars at Institute for Advanced Study, lectures at Massachusetts Institute of Technology, proofs appearing in journals like the American Mathematical Monthly, and solution traditions honored at events like the William Lowell Putnam Mathematical Competition.

Performance on the examination factors into selection for honors such as invitation to the American Invitational Mathematics Examination, qualification for the United States of America Mathematical Olympiad training, selection for the Mathematics Olympiad Summer Program, and awards recognized by institutions including the National Science Foundation, the Guggenheim Foundation, and the American Academy of Arts and Sciences. Top scorers receive distinctions comparable to recognition by the MacArthur Fellowship-associated communities and may be recruited by university programs at Princeton University, Harvard University, Massachusetts Institute of Technology, Stanford University, and California Institute of Technology.

Eligibility and administration involve school systems and organizations such as the Department of Education (United States), the College Board, the Educational Testing Service, state education agencies like the California Department of Education, the New York State Education Department, and district-level boards including the Chicago Public Schools and the Los Angeles Unified School District. Participation pathways connect students to feeder contests including MathCounts, the American Regions Mathematics League, the Kangaroo Math Competition, and local challenges organized by university mathematics departments such as those at University of California, Berkeley, University of Michigan, University of Illinois Urbana-Champaign, and University of Texas at Austin.

The examination’s impact is noted in trajectories leading to competitions like the International Mathematical Olympiad, careers at research institutions such as the Institute for Advanced Study, fellowships from the National Science Foundation, appointments at universities like Princeton University and Harvard University, and contributions to industries associated with Google, Microsoft Research, IBM Research, Bell Labs, and Sandia National Laboratories. Reception in academic media and pedagogy aligns with outlets such as the American Mathematical Monthly, the Notices of the American Mathematical Society, and educational initiatives like the Mathematics Teacher journal.

Preparation resources include textbooks and problem collections from authors and presses such as Richard Rusczyk, Titu Andreescu, Titu Andreescu and Razvan Gelca, Paul Zeitz, John Conway, Terence Tao, Cambridge University Press, Princeton University Press, and course offerings at institutions such as Massachusetts Institute of Technology, Harvard University, Stanford University, University of California, Berkeley, and online platforms affiliated with organizations like the Mathematical Association of America and the Art of Problem Solving. Training pipelines involve programs and camps run by entities like the Math Olympiad Summer Program, the International Mathematical Olympiad Training Program, the Art of Problem Solving Academy, and university outreach from University of Michigan and Johns Hopkins University.

Category:Mathematics competitions in the United States