The Putnam Exam During Year Zero USMAHarvard Math

The Putnam Exam During Year Zero USMA-Harvard Math Competition of 1933 Presented By: CPT Michelle Isenhour Western Michigan University

Putnam Mathematical Competition l Conducted by the MAA l Began in 1938 and has prospered since l Named after the late William Lowell Putnam l 12 questions in two three-hour sessions l Individual and team awards

The Legacy of Putnam l l 1921 – Putnam suggested the development of academic competition 1928 – English competition between Harvard and Yale (Harvard won) Yale and Princeton declined further competitions in English Cambridge declined competition in Economics

The Trouncing… l November 1932 – Army trounced Harvard in football 460 l President Lowell proclaimed that Harvard “could just as easily win any contest of a more academic nature”

The Challenge… “…I would very much like to test our method of teaching mathematics against that of your institution. I, frankly, think our method is superior to yours, and would like to try it out. ” -Major General Connor, Superintendent of the United States Military Academy in a 1932 letter to President Lowell

Preparations for the Competition l Rules delegated to department heads – – l Lieutenant Colonel Harris Jones, USMA Professor William C. Graustein, Harvard Exchanged information about curricula, pedagogy, and students

West Point Curricula l Four semester core curriculum – – l Freshmen: 8 hours per week Sophomores: 4 hours per week Subjects – – Algebra and Trigonometry Solid and Analytic Geometry Differential and Integral Calculus Least Squares (upper 1/3 of class)

Harvard Curricula l Freshmen – – Met for 3 hours per week Textbooks l l l Osgood and Graustein, Plane and Analytic Geometry Osgood’s Introduction to Calculus Sophomores – – Under guidance of tutors Subjects l l Analytic Geometry Algebra

Oscillation Begins… l Resolved Issues – – l Topics examined: analytic geometry and calculus Sophomores examined in May 1933 Unresolved Issues – – – West Point wanted 20 -25 contestants, Harvard 10 Home Team and Host Length of Test

Continues… l LTC Jones, USMA – – Offered to lower the number of contestants to 15 and have his team travel to Harvard for the test on 20 May Suggested one three-hour test claiming six-hours would “convert and interesting contest into dull drudgery and kill the enthusiasm of the competition”

Continues… l Professor Graustein, Harvard – – – Established the number per side as 10 No expectation that the Military Academy would bear any part of the expense Two three-hour sessions with the second more challenging Twice as much calculus as analytic geometry and include theoretical questions on test Allow formula cards, logarithm tables, and Pierce’s Integral Tables as references Harvard would be happy to travel to West Point

…and Ends l LTC Jones, USMA – – Agreed to two-part test and use of Pierce’s Integral Tables Scoring would be that used in cross-country meets

Completing the Committee l l President of the MAA – the body which stands for collegiate mathematics in this country Professor Arnold Dresden seemed almost ‘ordained’ for the job and accepted the invitation

Scope of the Examination (1 of 2) l Plane Analytic Geometry – – Distance from a point to a line Conics – Derivation of equations in rectangular and polar coordinates General equation of the second degree; simplification by translations and rotation of coordinate axes Locus problems involving applications of the above l Solid Analytic Geometry – – Equations of straight lines and planes Distance from point to a plane or line Equations of spheres, cylinders, cones, surfaces of revolution Elementary properties of quadric surfaces

Scope of the Examination (2 of 2) l Calculus – – – Curve tracing Velocity, acceleration, rates Radius and center of curvature Evolutes Taylor’s Theorem, functions of one variable Series – tests for convergence, expansion of functions, integration – – Applications to mechanics, center of gravity, moment of inertia, radius of gyration, attraction, fluid pressure, work Elementary differential equations, first order, linear equations with constant coefficients, orthogonal trajectories, simple equations of higher order

Preparations for Battle – West Point l West Point Team Statement “We are really series about this contest. We really mean it. We’re just dyne to meet those dumb Harvard guys, and we’re determinant to win. We all hope to make our integral signs. ”

Preparations for Battle – West Point l From March 15 – May 20 – – – Excused from parade 3 days a week Excused from intramural athletics Drilled in extra mathematics two afternoons a week

Preparations for Battle - Harvard l l Confident of Victory Took a lighter approach Met with coach about four times Assumed Harvard intellects would easily carry the day

Pre-game Publicity Sports section of New York Times “Sports of the Times” column by John Kieran on May 18, 1933 “The Coordinate Clash, or Block that Abscissa”

Other Headlines l “Army meets Harvard in Mathematical ‘Go’” l “Squads at West Point Begin Contest in Calculus and Analytic Geometry” l “Harvard and West Point Line up on the Geometry Field”

The Test l Part I – Friday, May 19: 3 hours – – – l 11 problems: 6 analytic geometry, 2 differential calculus, 3 integral calculus Part II – Saturday, May 20: 3 hours 11 problems: 1 logarithms, 3 analytic geometry, 6 differential calculus, 1 integral calculus Not as difficult, nor as challenging, as the first National Putnam Examination given on April 16, 1938

And the Winner is… l “Crimson Bow to West Point Mathematicians” l “Harvard Mathematics Team Outfigured by West Pointers”

The After Math l All members of the Army team finished in the top 20 of their graduating class; seven of the ten spent over 20 years in the Army; most later became professors and obtained their Ph. D. None were mathematicians; all were engineers

Putnam’s Legacy l l Harvard-USMA competition was not repeated Putnam’s sons, George and August, consulted with George Birkhoff of Harvard to keep the dream alive Birkhoff and colleagues from the department wrote the first national examination in 1938 Set up continuing principles for the competition – – – Teams consist of three people Tests are administered by the MAA Prizes are distributed to several top teams and individuals

Conclusion “Through the efforts of Birkhoff and many others, and the experience garnered from the Harvard-USMA Competition of 1933, the annual William Lowell Putnam Mathematics Competition came into existence in 1938 and has prospered in the 50 years since. ” -David C. Arney and George Rosenstein “USMA-Harvard Math Competition”, 2000

Arney, David C. and George Rosenstein. “USMA-Harvard Math Competition. ” Available from http: //www. dean. usma. edu/math/about/history/mathcomp. htm Arney, David C. “Army Beats Harvard. ” Math Horizons. Sept. 1994: 14 – 17. Kieran, John. “The Coordinate Clash, or Block That Abscissa!” New York Times 18 Mar. 1933: 17. “Army ‘Mathletes’ Defeat Harvard, 98 -112; Cadet Smith is First in Calculus Affray. ” New York Times 5 June 1933: 4. References: Email: michelle. isenhour@wmich. edu Copy of Briefing Available from: http: //www. dean. usma. edu/math/people/rickey/dms/doc/Putnam 0 -Isenhour. ppt