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 George Baron (1801-2) Jared Mansfield (1802-3) William Barron (1802-7) Ferdinand Hassler ( ) Alden Partridge (1813) Andrew Ellicot ( ) David Douglass ( ) Charles Davies ( ) Albert Church ( ) Edgar Bass ( ) Wright Edgerton ( ) Charles Echols ( ) Harris Jones ( ) William Bessell ( ) Charles Nicholas ( ) John Dick ( ) Jack Pollin ( ) David Cameron ( ) Frank Giordano ( ) David Arney ( ) Gary Krahn ( ) Michael Phillips (2005-Present)

George Baron Our zeroeth professor of mathematics, hired 16 March “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 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, USMA, 1806 First official “Professor of Mathematics,” Professor of Engineering and acting Superintendent, Father of ROTC

Andrew Ellicott 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 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, Visited technical and military schools in France and England, Superintendent, USMA, “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 Sections grouped by performance.

Charles Davies ( ) USMA 1815 Dept Head 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 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 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 Echols

Charles Patton Echols USMA Served at Engineer School at Willet's Point, NY Instructor on Mathematics, USMA Assistant Professor of Mathematics 1898 Commander, Engineer Company in the Philippines Associate Professor of Mathematics 1918 Special duty as military observer with Allied Armies in France 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 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 ( ) 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 th 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.” 3 rd 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: –4 th class: French, English, Surveying, Military Efficiency and Conduct –3 rd class: French, English, History, Drawing, Tactics, Practical Military Engineering Natural and Experimental Philosophy is studied 2 nd 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 USMA Commander, Engineer Co, 3rd Division, World War I Instructor of Mathematics, USMA 1923 MS, Massachusetts Institute of Technology Assigned to 8th Engineer Bn, Ft Bliss, TX Assistant Director of Public Buildings and Parks, D.C American Battle Monuments Commission, Paris Prof Math and Department Head 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 ; Cadet Smith is First in Calculus Affray” “Crimson Bow to West Point Mathematicians; Harvard Mathematics Team Outfigured by West Pointers”

William Weston Bessell, Jr USMA MS, Rensselaer Polytechnic Institute, Troy, NY Prof. of Military Science, Rose Polytechnic Institute Assistant Professor of Mathematics, USMA American Battle Monuments Commission, Paris Chief of Military Personnel Branch, Washington, D.C Army Director, Joint War Plans Committee Cmdg General, Antilles Dept, San Juan, Puerto Rico Prof Math and Department Head Dean of the Academic Board

“Prior to 1948, cadets did not study calculus until the beginning of their 3 rd class year; but in 1948, the course was revised to introduce calculus the spring term of their 4 th class year. The resulting 4 th 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 3 rd class year.”

Robert Carl Yates, PhD, Johns Hopkins, COL, Corps of Engineers, 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 Professors 3 Associate Prof. 4 Assistant Prof. 29Instructors 37 Total 1 PhD 10 MS 26BS 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 USMA 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 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 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 ( ) First Visiting Professor, First civilian in the 20 th 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 graduated in June 1980 Today ~18% of the class are women

COL Kathi Snook Graduated : MA in applied math : “rotator” in mathematics 1997: Ed.D., Boston University 2002: Retired from the Army

The Classroom in 1904 Questions?