210 Years of Mathematics
at West Point
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.
List of Math Prof/Dept Heads
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George Baron (1801-2)
Jared Mansfield (1802-3)
William Barron (1802-7)
Ferdinand Hassler (1807-10)
Alden Partridge (1813)
Andrew Ellicot (1813-1820)
David Douglass (1820-1823)
Charles Davies (1823-1837)
Albert Church (1837-1878)
Edgar Bass (1878-1898)
Wright Edgerton (1898-1904)
Charles Echols (1904-1931)
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Harris Jones (1931-1947)
William Bessell (1947-1959)
Charles Nicholas (1959-1967)
John Dick (1967-1974)
Jack Pollin (1974-1985)
David Cameron (1985-1988)
Frank Giordano (1988-1995)
David Arney (1995-2000)
Gary Krahn (2000-2005)
Michael Phillips (2005-Present)
George Baron
• Our zeroeth professor of mathematics,
hired 16 March 1801.
• “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.
• Incident between Swift and Baron led
to Baron’s court-martial and dismissal.
• Founded The Mathematical
Correspondent, the first mathematical
periodical in the US, 1804
Teaching from Hutton in 1814
Ferdinand Hassler
• Acting Professor of
Math 1807-1810.
• Sold large collection
of his books to USMA
library.
• Published the first
book on analytic
trigonometry in the
U.S.
• Superintendent of
U.S. Coast Survey.
Alden Partridge, 1785-1854
• USMA, 1806
• First official “Professor of
Mathematics,” 1812-13
• Professor of Engineering
and acting
Superintendent,
1813-1818
• Father of ROTC
Andrew Ellicott 1754 - 1820
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Laid out Washington, D.C.
Math P at USMA, 1813 – 1820
Nickname: Old infinite series
Wore a slate and sponge tied
to his buttonhole
• Limited math curriculum:
– First year: algebra,
geometry, logarithms
– Second year: algebra,
mensuration, trigonometry,
infinite series
• Ellicott tutored
Meriwether Lewis
in surveying and
navigation
Claude Crozet
• Brought Descriptive
Geometry to the U.S. 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
Examples of Cadet Drawings
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
• “Father of the Military Academy”
Thayer Superintendency
• Developed standardized 4-year curriculum
centered on engineering
• Established standards for admission
• Created student-enforced honor system
• Established Academic Board and
department heads
• Applied military discipline
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 (1798-1876)
• USMA 1815
• Dept Head 1823-37
• Curriculum under Davies:
– First year: algebra,
geometry, trigonometry,
descriptive geometry
– Second year: analytic
geometry, calculus
• Published 49 books
• By 1875 he was selling
350,000 books per year
Eight books in Eleven years
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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.
Professor Albert Church (USMA 1828)
• Professor of Math 1837-1878
• Published 4 textbooks, used in
math program
• Methods of instruction:
repetition, oral recitation of
solutions to problems
• With Professors Mahan and
Bartlett, shaped curriculum of
Academy for more than 30
years
• “He did not inspire me – was
as dry as dust, as his
textbooks.” (Cadet Arthur
Harding)
Edgerton
1898 - 1904
Echols
1904 - 1931
Charles Patton Echols
1867-1940
USMA 1891
• 1891-1894 Served at Engineer School at
Willet's Point, NY
• 1895-1897 Instructor on 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
West Point Admission
Standards
• 1812: Admitted candidates must be “well versed in
reading, writing, and arithmetic.”
• 1901: “Students shall be well versed in reading,
writing,…., arithmetic, algebra through quadratic
equations, plane geometry, descriptive geometry,…”
• Current: “[Candidates] should complete four years of
college preparatory mathematics, to include algebra,
geometry, intermediate algebra, and trigonometry as a
minimum.”
Revised Admission Exam
• Sample questions in 1902:
– There is a number which consists of two digits, such
that if we divide the number by the product of its digits
we obtain a quotient of 5 and a remainder 2, but if we
invert the order of the digits and divide the resulting
number by the product of its digits we obtain a
quotient 2 and a remainder 5. Required the number.
– What number of sides has the polygon the sum of
whose angles is 26 right angles?
The WP Classroom in 1917
• 95 lessons on Calculus, each 1.5 hours
• Students expected to spend 3 hours in
preparation
• Section size of 10 to 14
• Questions are answered, then cadets
recite
• WP was a U.S. leader by teaching
Calculus to sophomores
Superintendency of Douglas
MacArthur (1919-1922)
• Academy in disarray after World
War I
• Modernized curriculum: added
courses in liberal arts,
government, economics
• Mandated competitive sports and
increased physical training
• Restored 4 year course
• Formed Cadet Honor Committee
• Recommended military instructors
attend some graduate school
Math under MacArthur - 1920
• 4th class year: 6 classes a week, 75 minute class
periods, “a brief review of plane geometry and
elementary algebra; completion of algebra in
alternation with geometry and trigonometry;
completion of plane analytical geometry; beginning
of solid analytical geometry.”
• 3rd class year: 3 classes a week, 75 minute class
periods, “completing solid analytical geometry, and
taking up and completing calculus and least
squares.”
• Prior to this, mathematics had 417 classes at 85
minutes each; now 337 at 75 minutes each.
Descriptive geometry eliminated and calculus
reduced.
Prof. Echols Comments about
cutting Math:
“For technical students who are to become officers,
this course in pure Mathematics is neither too difficult
nor too long. These men will be compelled to study
much and enlarge greatly their knowledge of applied
Mathematics after leaving the Academy.
There is every argument in favor of insuring them a
thorough foundation in pure Mathematics.
Cadets who can’t do this should be sent elsewhere.
We could drop Solid Analytic Geometry and, in the
Calculus, everything pertaining to three dimensions.
I should regret to see these two dimensional
students turned out as graduates of the Military
Academy. I, therefore, recommend once again that he
course in Mathematics remain as at present
constituted.”
Other Curriculum in 1920
• Other subjects studied in first two years:
– 4th class: French, English, Surveying, Military Efficiency and
Conduct
– 3rd class: French, English, History, Drawing, Tactics, Practical
Military Engineering
• Natural and Experimental Philosophy is studied 2nd class
year
– “The Department of Mathematics gives in calculus only the
simplest exercises in velocity, acceleration, etc. that serve to
illustrate the mathematical formulae, leaving to the Departments
of Philosophy and Engineering the more exhaustive theoretical
treatment from the physical point of view.” (Annual
Superintendent’s Report, 1920).
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
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 and 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 – 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
“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.”
Results
“Army ‘Mathletes’ Defeat Harvard 98-112;
Cadet Smith is First in Calculus Affray”
“Crimson Bow to West Point
Mathematicians; Harvard Mathematics
Team Outfigured by West Pointers”
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
• 1959-1965 Dean of the Academic Board
“Prior to 1948, cadets did not study calculus
until the beginning of their 3rd class year; but
in 1948, the course was revised to introduce
calculus the spring term of their 4th class
year. The resulting 4th class calculus course
was an integrated one, introducing the
fundamental ideas of both differential and
integral calculus in order to prepare the
cadets to use these ideas in scientific
applications early in their 3rd class year.”
Robert Carl Yates, 1904-1963
• PhD, Johns Hopkins, 1930.
• COL, Corps of Engineers,
1942-1954.
• Associate Professor of
Mathematics, USMA, 1942 to
1948
• First PhD in the department.
• Department Head at William
and Mary College.
The Curriculum in 1950
First year• Algebra: 50 hours
• Slide rule: 5
• Trigonometry: 48
• Solid mensuration: 20
• Analytic geometry: 106
• Calculus: 44
Second year• Calculus: 88
• Differential equations: 24
• Statistics: 21
The Faculty in 1950
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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 1960
First year
• Algebra: 27 hours
• Slide rule: 8
• Trigonometry: 56
• Solid geometry: 29
• Analytic geometry: 95
• Calculus: 63
• Vector analysis: 21
Second year
• Calculus: 63
• Differential equations: 13
• Statistics: 33
Charles Parsons Nicholas
1903-1985
USMA 1925
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1927-1928
1930-1935
1941-1942
1947-1948
• 1948-1959
Inst of English, USMA Preparatory School, Hawaii
Instructor of Mathematics
Asso. Prof. of Mathematics
Deputy Director of Central Intelligence,
National Security Council
Prof Math and Deputy Head
• 1959-1967
Prof Math and Department Head
Nicholas Introduces Rigor
• In line with national mathematics movements
• Increasing sophistication of science and engineering
textbooks, and need for mathematics in future
coursework
• Rising admission standards
• 7-year sequential upgrade of mathematics program
• Increased statistics, added linear program and
electronic computer work
• Implemented first program of math electives
Curriculum under Nicholas
First year:
• Calculus (109 lessons)
• Analytic Geometry (50)
• Linear Algebra (26)
Second year:
• Calculus (39)
• Differential Equations (26)
• Probability and Statistics
(39)
Frank Giordano (USMA 1964)
• Department head 1988-1995
• Reorganized the curriculum in 1991 (“7 into 4”):
• Discrete Dynamical Systems
• Calculus and Differential Equations
• Multivariate Calculus
• Probability and Statistics
• Added full time civilian professors
– Senior civilians
– Title X
– Davies fellows
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
Iso Schoenberg (1903-1990)
• First Visiting Professor,
1977-1978
• First civilian in the 20th
century
• Penn, Aberdeen,
Princeton, Wisconsin
• Created field of splines
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 ~18% of the class
are women
COL Kathi Snook
• Graduated 1980
• 1987: MA in applied
math
• 1987-1991: “rotator” in
mathematics
• 1997: Ed.D., Boston
University
• 2002: Retired from the
Army
•Questions?
The Classroom in 1904