201 Years of Mathematics at West Point

V. Frederick Rickey

West Point Founded 1802

• In 1793 Washington held a Cabinet meeting to discuss an academy. Hamilton and Knox were in favor, Jefferson opposed.

• Jefferson founded the Academy to break the Federalist hold on government and to create a Republican army loyal to him.

George Baron

• Our zeroeth professor of mathematics, hired 16 March 1801

• Founded The Mathematical Correspondent, the first mathematical periodical in the US, 1804

Professor Baron furnished me with Dr. Hutton's Mathematics, and gave me a specimen of his mode of teaching at the blackboard at the academy.

Joseph G. Swift, first graduate of West Point.

Joseph Gardner Swift

• Swift was the first USMA graduate, in 1802

• Superintendent, 1812-1814

American Editions of Hutton

• Edited by Adrain

• A chapter on Descriptive Geometry

• Not attributed to Crozet

Teaching from Hutton in 1814

Jared Mansfield, 1759-1830

• Taught mathematics 1802-1803

• USMA’s first Professor of Philosophy, appointed 1812.

• By Thomas Sully, 1783-1872, in the USMA museum.

Ferdinand Hassler

Published the first book on analytic trigonometry in the US

Claude Crozet

• Brought Descriptive Geometry to the US in 1816.

• Reintroduced the “black board” at USMA.

• Wrote A Treatise on Descriptive Geometry (1821), the first book on the subject in English.

Olivier Models

• Designed for teaching Descriptive Geometry

• Purchased 1857• Made by Fabre de

Lagrange in Paris• 24 of 26 survive

Henry Moore

At Storm King Art Center

Alden Partridge, 1785-1854

• USMA, 1906• First official

“Professor of Mathematics”

• Father of ROTC• Meligned by Cullum

Andrew Ellicott 1754 - 1820

• Laid out DC• Math P at USMA,

1813 – 1820• Nickname: Old infinite

series• Had a slate tied to his

buttonhole• First P to die here

• Ellicott tutored Meriwether Lewis in surveying and navigation

Sylvanus Thayer (1808)

• Assistant Professor of Mathematics, USMA, 1809-1811

• Visited technical and military schools in France and England, 1815-1817

• Superintendent, USMA, 1817-1833

• Founded Thayer School of Engineering at Dartmouth, 1867

• “Father of the Military Academy”

The Thayer Method of Teaching

• Cadets read; no lectures [ ? ]

• Every cadet is graded every day

• Small sections of 10-12

• Sections grouped by performance

Charles Davies (1807-1878)

• USMA 1815• Dept Head 1823-37• Published 49 books• 492 printings/edn’s• By 1875 he was

selling 350,000 books per year

Eight books in Eleven years

• Elements of Descriptive Geometry, 1826• Elements of Geometry and Trigonometry, 1828• Elements of Surveying, 1830• A Treatise on Shades and Shadows, and Linear

Perspective, 1832• The Common School Arithmetic, 1833• Elements of Algebra: Translated from the French of M.

Bourdon, 1835• Elements of the Differential and Integral Calculus, 1836• Elements of Analytical Geometry, 1837

Teach one thing at a time ─ teach that thing thoroughly ─ and as far as possible, teach all its connections with other things.

Charles Davies at the National Meeting of Teachers, Michigan 1852.

Albert E. Church (USMA 1828)

• Professor of Mathematics,

1837-1878†• Widely used textbooks:

• Elements of Differential and Integral Calculus

• Elements of Analytical Geometry

• Elements of Analytical Trigonometry

• Elements of Descriptive Geometry

• Nickname: Old Stinky

Church, the Man

• A kindly, patient teacher

• Worked with weak cadets

• Agonized over cadet failures

Church’s Teaching

• He did not inspire me ─ he had no magnetism ─ he was dry as dust, as his textbooks.

Morris Schaff (USMA 1862)

• The mathematical recitation was a drill room. In my opinion the result was a soldier who knew the maneuvers, but it did not give an independent, self-reliant grasp of the methods of research.

Arthur Hardy (USMA 1869)

Robert Parrott, USMA 1824

Plum Bush InnIn Cold Spring

A SONNET TO "ANALYTICAL"

Of all the girls I ever knew, The one I've most neglected,Is called Miss “Anna Lytical,” For her I've least respected.

Oh! Anna! Anna Lytical I'll never love you more,For you, I fear, will cause my fall, And make me leave the Corps.

And now, -- oh! Anna Lytical I hope that "Albert E.,“Before the "Board," will not give out A word of you to me.

For if he does, now Anna I tremble at the sound,For my examination would Result in being "found.“

Oh! cruel Anna Lytical! With truth I now can say,I fear you'll never let me see My "Graduation day."

Resectioning in 1899This 1890 copy of Davies’ Algebra and Trigonometry was owned by U.S. Grant (USMA 1903). He was first in the second section and then moved to 5th in 1st ─ behind Douglas MacArthur.

Thomas Selfridge

Albert L. Mills, USMA 1891• Shot in the eye• Awarded the Medal of Honor as a

1st Lt. at San Juan Hill in Cuba• President McKinley liked him• Appointed Superintendent to West

Point by President McKinley, which carried an automatic promotion from 1st Lt. to Col.

• Served 1898-1906• Echols flunked 40% of plebes in

1905• Punishment tour of Europe

Edgerton 1898 - 1904

Echols1904 - 1931

Charles Patton Echols 1867-1940 USMA 1891

• 1891-1894 Served at Engineer School at Willet's Point, NY • 1895-1897 Instructor of Mathematics, USMA • 1897-1898 Assistant Professor of Mathematics• 1898 Commander, Engineer Company in the Philippines • 1898-1904 Associate Professor of Mathematics • 1918:  Special duty as military observer with Allied Armies in France• 1904-1931 Prof Math and Department Head• Murdered in Bryant park

Harris Jones 1892-1977 USMA 1917

• 1918 Commander, Engineer Co, 3rd Division, World War I

• 1918-1922 Instructor of Mathematics, USMA • 1923 MS, Massachusetts Institute of Technology • 1923-1926 Assigned to 8th Engineer Bn, Ft Bliss, TX • 1926-1928 Assistant Director of Public Buildings and Parks,

D.C. • 1928-1931 American Battle Monuments Commission, Paris• 1931-1947 Prof Math and Department Head • 1947-1956 Dean of the Academic Board

William Weston Bessell, Jr.1901-1977 USMA 1920

• 1921-1922 MS, Rensselaer Polytechnic Institute, Troy, NY • 1923-1928 Prof. of Military Science, Rose Polytechnic Institute• 1928-1932 Assistant Professor of Mathematics, USMA • 1936-1939 American Battle Monuments Commission, Paris• 1940-1942 Chief of Military Personnel Branch, Washington,

D.C. • 1943-1946 Army Director, Joint War Plans Committee • 1946-1947 Cmdg General, Antilles Dept, San Juan, Puerto Rico • 1947-1959 Prof Math and Department Head

• Rebuilt Thayer Hall.

• 1959-1965 Dean of the Academic Board

Charles Parsons Nicholas 1903-1985 USMA 1925

• 1927-1928 Inst of English, USMA Preparatory School, Hawaii • 1930-1935 Instructor of Mathematics• 1941-1942 Asso. Prof. of Mathematics• 1947-1948 Deputy Director of Central Intelligence,

National Security Council • 1948-1959 Prof Math and Deputy Head  

• 1959-1967 Prof Math and Department Head

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”

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

Harvard Curricula

• Freshmen– Met for 3 hours per week– Textbooks

• Osgood & Graustein, Plane and Analytic Geometry• Osgood’s Introduction to Calculus

• Sophomores– Under guidance of tutors– Subjects

• Analytic Geometry• Algebra

West Point Curriculum

• 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)

Preparations for Battle at West Point

“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 at 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

The Faculty in 1950

• 2 Professors• 3 Associate Prof.• 4 Assistant Prof.• 29 Instructors

• 37 Total

• 1 PhD• 10 MS• 26 BS

• 31 West Point Grads• 6 Non-grads

The Curriculum in 1950

• Algebra: 50 hours• Slide rule: 5 • Trigonometry: 48• Solid mensuration: 20• Analytic geometry: 106• Calculus: 44

• Calculus: 88• Differential equations: 24• Statistics: 21

The Curriculum in 1960

• Algebra: 27 hours

• Slide rule: 8• Trigonometry: 56• Solid geometry: 29• Analytic geometry: 95• Calculus: 63• Vector analysis: 21

• Calculus: 63• Differential equations: 13• Statistics: 33

Robert Carl Yates, 1904-1963

• PhD, Johns Hopkins, 1930. • COL, Corps of Engineers, 1942-

1954. • Associate Professor of

Mathematics, USMA, 1942-1954 • First PhD in the department.

• Department Head at William and Mary College.

Frank Giordano (USMA 1964)

• Department head 1988-1995

• Reorganized the curriculum in 1991

• Discrete Dynamical Systems• Calculus and Differential Equations• Multivariate Calculus• Probability and Statistics

7 into 4

The two things I was most opposed to at the time were

• Women cadets• Civilian faculty

But they are the two best things that have happened to the Academy.

• COL Gary Krahn

Women at West Point

• 631 applied for the class of 1980 (of 6761)

• 176 were found qualified• 148 offered admissions• 116 entered in June 1976• 87 graduated in June 1980

• Today 15% of the class are women

COL Kathi Snook

• Graduated 1980

• 1987: MA in applied math

• 1987-1991: “rotator” in math

• 1997: Ed.D., Boston University

• 2002: Retired from the Army

Iso Schoenberg (1903-1990)

• First Visiting Professor, 1977-1978

• First civilian in the 20th century

• Penn, Aberdeen, Princeton, Wisconsin

• Splines

The Classroom in 1904

•Questions?