The Putnam Exam During Year Zero

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

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

3. The Legacy of Putnam • 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

4. The Trouncing… • November 1932 – Army trounced Harvard in football 46-0 • President Lowell proclaimed that Harvard “could just as easily win any contest of a more academic nature”

5. 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

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

7. West Point Curricula • Four semester core curriculum • 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)

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

9. Oscillation Begins… • Resolved Issues • 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

10. Continues… • 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”

11. Continues… • 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

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

13. Completing the Committee • 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

14. 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 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 (1 of 2)

15. 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 Scope of the Examination (2 of 2)

16. Preparations for Battle – West Point • 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.”

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

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

19. 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”

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

22. The Test • Part I – Friday, May 19: 3 hours • 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

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

24. The After Math • 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

25. Putnam’s Legacy • 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

26. 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

27. References: 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. Email: michelle.isenhour@wmich.edu Copy of Briefing Available from: http://www.dean.usma.edu/math/people/rickey/dms/doc/Putnam0-Isenhour.ppt