Research Tip:
For the undergraduate point of view and reporting about Harvard developments: The Archive of The Harvard Crimson.
Example: this written portrait of Joseph Alois Schumpeter by a student none-too-happy with the policy views of Harvard’s “Civil War School”.
Frank W. Taussig’s last time teaching the graduate theory course, Economics 11, was in the Fall Semester of 1934. Joseph Schumpeter took over the second half of the course for the Spring Semester of 1935. In Schumpeter’s papers are 3 pages of Taussig’s handwritten notes and carbon copies of reading lists. Note: the folder where the material is found is labelled “Ec 11 Fall 1935” but material from 1934-35 is in it as well.
_________________
[handwritten notes by F. W. Taussig, cf. initials in letter June 9, 1914 to Hunnewell in Lowell Papers, Box 14 Folder 403]
Economics 11 — 1934-35
Topics taken up by F.W.T. [Taussig], in order
Topics not taken up
Theory of Monopoly Price
Austrian Theory of Value
_________________
[handwritten notes by F. W. Taussig]
(1
Ec 11 — ‘34-35
I
Ricardo, chs I Value (omitting the discussion of Adam Smith)
“ II Rent, III Rent of Mines
“ IV
“ V Wages
“ VI Profits
Mill, Bk III chs I, III[,] IV
(Value, omitting ch II, which was considered later in connection with Marshall)
Mill Bk II, ch. XVI ; Bk I, ch. XII (Rent)
“ Bk II, ch XI ; XIII, §§3-4 Wages
“ Bk II, ch XV ; Profits
“ Bk IV, chs IV[,] V, VI ; Profits to a minimum
_________________
[handwritten notes by F. W. Taussig]
(2
Reading List—Econ 11 — 1934-35
Non-competing Groups + Labor Theory of Value
Cairnes[,] Leading Principles. P+I, ch. III
Mill[,] Bk II, ch XIV (Differences of wages), cf. Adam Smith, Bk I, ch. X
Taussig, Principles, ch 47, 48
Marshall, Book VI chs IV, V; Book IV, ch 6
Cf. Marshall second edition, Bk VI, ch I, §3 (p. 557-558)
_________________
[handwritten addition] 3)
[Typed table of readings that is nearly identical to Wolfgang Stolper’s hand-written reading list in his course notes from the Fall Semester 1934. Cf. Duke University, Rubenstein Rare Book & Manuscript Library. Wolfgang F. Stolper Papers, Box 19, Notebook: Taussig Ec 11 Theory, 1934-35]
Economics 11
1934-35
| Demand, Market Value |
Mill, Book III, chs. 1, 2. Marshall, Book III, ch. 3; Book V, chs. 1, 2. Taussig, Quarterly Journal of Economics, May 1921 |
| Normal Value |
Mill, Book III, chs. 3, 4. Marshall, Book V, chs. 3, 4, 5. Viner, Zeitschrift f. Nationaloekonomie, Sept. 1931, vol. I Taussig, Quarterly Journal of Economics, February 1919. Marshall, Appendix H |
| Quasi Rent |
Marshall, Book V, ch. 8; Book V, ch. 9. Fetter, Quarterly Journal of Economics, May 1901 (vol. 15). |
| Increasing Returns |
Marshall, Book V, ch. 12; Book IV, ch. 9, §7; ch. 10, 13. |
| Agricultural Rent, Urban Rent |
Marshall, Book IV, chs. 2, 3; Book V, ch. 10, (omit §§4, 5); Book VI, ch. 9; Book V, ch. 11. Ely, Outlines, 5th ed., ch. 22. |
| Profits | Mill, Book II, ch. 15. Marshall, Book IV, chs. 12, 13; Book VI, chs. 7, 8. Knight, “Risk, Uncertainty and Profits”, chs. 9, 10. Ely, Outlines, ch. 24.L. Robbins, The Representative Firm, Economic Journal (1928) |
| [handwritten addition] | Marshall Bk V, ch. 10 §2 (settlers in a new country); Bk VI, ch V, §7 (rare natural abilities) |
| [handwritten addition] | Schumpeter—Theory of Ec. Development ch. IV |
_________________
[Typed carbon list]
[handwritten addition] 4)
Economics 11
1934-35
Reading
I
Böhm-Bawerk, Positive Theory of Capital
Book II, chs. 1, 2, 4, 6
Book V, chs. 1, 2, 3, 4, 5
Book VI, chs. 1 (pp. 285-286), 2, 4, 5, 6
Book VII, chs. 1, 2, 5
II
Clark, Distribution of Wealth
chs. 6, 7, 8, 9, 20
chs. 11, 12, 13, 21
Marshall, Book IV, ch. 7 (“The Growth of Wealth”—Capital, Saving etc); Book VI, chs. 1, 2
_________________
1934-35
HARVARD UNIVERSITY
ECONOMICS 11
One question may be omitted. Arrange your answers in the order of the questions.
Suppose also that there is free competition as regards the earnings of capital.
On these suppositions what would be the relation between
(a) the values of commodities and their “real cost”
(b) the values of commodities and their money costs;
(c) the values of commodities and their supply prices?
“Internal economies of large-scale production are independent of the size of output of the industry as a whole, and may be accruing to a particular concern whose output is increasing at the same time that the output of the industry as a whole is undergoing a decline.” Why or why not?
(a) “The quasi-rent of farm-buildings.”
(b) “When the artisan or professional man has once obtained the skill required for his work, a part of his earnings are for the future really a quasi-rent of the capital and labor invested in fitting him for his work, in obtaining his start in life, his business connections, and generally his opportunity for turning his faculties to good account; and only the remainder of his income is true earnings of effort. But this remainder is generally a large part of the whole. And here lies the contrast. For when a similar analysis is made of the profits of the business man, the proportions are found to be different; in his case the greater part is quasi-rent.”
(c) “In relation to normal value the earnings of high ability are to one regarded as a quasi-rent rather than as a rent proper.”
(a) that differences in income make it impossible to measure satisfactions;
(b) that each unit of a homogeneous supply yields ipso facto the same satisfaction as every other unit;
(c) that the satisfaction indicated by the high price paid for an article having “prestige value” will disappear when the article becomes cheap
(a) between the intensive and the extensive margins of cultivation for land;
(b) the intensive and the extensive zones of indifference in the application of labor;
(c) the marginal product of labor and the product of marginal labor.
State summarily your opinion of the usefulness of the distinctions as tools of analysis.
Mid-Year. 1935.
No. 37
Source: Harvard University Archives. Joseph Schumpeter Papers. HUC (FP) – 4.62
Box 9 (Lecture Notes), Folder “Ec11 Fall 1935”.
The course “Economics of Socialism” (Economics 11b) was taught during the Spring Semester 1940 by Dr. Paul M. Sweezy. According to the Report of the President of Harvard College and Reports of Departments for 1939-40 (p. 99), sixty students were enrolled: 20 Seniors, 25 Juniors, 6 Sophomores and 9 out-of-course candidates for the Bachelor’s degree.
For biographical detail about Paul Sweezy, take to the following link at the Monthly Review website for the Memorial Service for Paul Marlor Sweezy (1910-2004) by (Feb 27, 2004).
Addition April 18, 2017: Final Examination for Sweezy’s course “Economics of Socialism” in 1940.
Fun Fact: John F. Kennedy took this course in the second semester of his senior year according to the copy of his Harvard College record at the John F. Kennedy Presidential Library.
____________________
The first eight weeks (to spring recess) will be devoted to the socialist critique of capitalist economy. The last four weeks will be devoted to the problems of socialist economy. This sheet covers only the first eight weeks.
Assigned readings are taken from the following works:
In addition to the assigned reading every student will be expected to submit before the spring recess a report of about 1500 words on one of the following books:
____________________
FIRST WEEK. Marx and Engels; dialectical materialism and historical materialism; classical economics.
Burns, Handbook of Marxism, Chs. I, XIII, XIV, XX.
Ricardo, Principles, Ch. I (Sections I-V inclusive).
SECOND AND THIRD WEEKS. Commodities; the law of value; suplus value; accumulation; the reserve army of labor.
Marx, Capital, Vol. I, Ch. I (sections 1, 4).
Marx, Value, Price and Profit.
Marx, Capital, Vol. I, Ch. XXIII; Ch. XXIV (sections 1, 2 3); Ch. XXV.
FOURTH WEEK. Law of the falling tendency of the rate of profit; crises.
Marx, Capital, Vol. III, Part III.
Dobb, Political Economy and Capitalism, Ch. IV.
FIFTH WEEK. Value calculation and price calculation.
Marx, Capital, Vol. III, Chs. VIII, IX.
Böhm-Bawerk, Karl Marx and the Close of his System, Chs. II, III.
SIXTH WEEK. Theory of Social Classes and the State.
Lenin, State and Revolution.
SEVENTH WEEK. Monopoly and the Theory of Imperialism.
Lenin, Imperialism.
Dobb, Political Economy and Capitalism, Ch. VII.
Lange, “Marxian Economics and Modern Economic Theory.”
EIGHT WEEK. Review.
Book reports due. No additional assignment.
____________________
Assigned readings are taken from the following works:
NINTH WEEK (April 7-13). Historical sketch of the economics of a socialist society; demand and cost in a socialist economy.
Dickinson, Economics of Socialism, pp. 24-98.
TENTH WEEK (April 14-20). Prices and incomes in a socialist economy.
Dickinson, Economics of Socialism, pp. 98-166.
ELEVENTH WEEK (April 21-27). Special problems of a socialist economy.
Dickinson, Economics of Socialism, pp. 166-226.
TWELFTH WEEK (April 28-May 4). Income distribution in socialist theory and practice.
Assignment to be announced.
READING PERIOD
Read both:
1. Pigou, Socialism vs. Capitalism.
2. Lange and Taylor, On the Economic Theory of Socialism. pp. 55-142.
____________________
Source: Harvard University Archives. Syllabi, course outlines and reading lists in Economics, 1895-2003. HUC 8522.2.1. Box 2, Folder (1939-1940, No. 1).
The picture shows the economics department of Swarthmore ca. 1942:
Standing: John W. Seybold (1916-2004), Frank Pierson (1911-1996)
Seated: Wolfgang F. Stolper (1912-2002), Clair Wilcox (1898-1970), Herbert F. Fraser (1890-1953).
One can read about them and others in One Hundred Years of Economics at Swarthmore by Joshua Hausman (Swarthmore, Class of 2005)
Below is the course record of the first author of the classic paper “Protection and Real Wages,” Review of Economic Studies, 1941. The second author was the economist seen in center of this blog’s rear-view mirror.
____________________________________
HARVARD UNIVERSITY
THE GRADUATE SCHOOL OF ARTS AND SCIENCES
24 UNIVERSITY HALL, CAMBRIDGE, MASSACHUSETTS
May 23, 1938
Transcript of the record of Mr. Friedrich Wolfgang Stolper
|
Course |
1934-35 |
GRADE |
| Economics 11 [Economic theory] |
(1 course) |
Excused |
| Economics 51 [Business cycles and economic forecasting] |
(1 course) |
A |
| Economics 1a1 [Introduction to economic statistics] |
(½ course) |
A |
| Economics 10a1 [History of commerce, 1450-1750] |
(½ course) |
A |
| Economics 10b2 [History of industry and agriculture, 1450-1750] |
(½ course) |
A minus |
| Economics 31b2 [Theory of economic statistics] |
(½ course) |
Excused |
|
1935-36 |
||
| Mathematics A |
(1 course) |
C plus |
| Economics 121 [Monopolistic competition and allied problems in value theory] |
(½ course) |
A minus |
| Economics 20 [Economic research] |
(1 course) Mason |
A |
|
1936-37 |
||
| Economics 20 [Economic research] |
(1½ courses) |
A |
| Economics 147a hf [Seminar: Selected problems in money and banking] |
(½ course) |
A |
Mr. Stolper received the degree of Master of Arts in June, 1935.
The established grades are A, B, C, D, and E.
A grade of A, B, Credit, Satisfactory, or Excused indicates that the course was passed with distinction. Only courses passed with distinction may be counted toward a higher degree.
*Courses marked with an asterisk are elementary and therefore may not be counted toward a higher degree.
[signed] Lawrence S. Mayo
Assistant Dean
Source: Wolfgang F. Stolper papers. Duke University, Rubenstein Rare Book & Manuscript Library, Box 23 c. 1.
Image Source: p. 15 of The Halcyon 1943 (Swarthmore Yearbook).
The Cowles Commission Archive at Yale provides a copy of Income, Employment, and the Price Level: Notes on Lectures Given at the University of Chicago Autumn 1948 and 1949 by Jacob Marschak. Notes edited by David Fand and Harry Markowitz, 1951. Problems, course examination (Fall 1949) and reading list are included.
See the biographical memoir for Jacob Marschak (1898-1977) written by Kenneth Arrow to appreciate the enormous debt modern economics owes to Marschak.
From the Course Announcements this would have been Economics 335, The Theory of Income and Employment offered in Autumn and Spring quarters. The notes explicitly refer to only the Autumn Quarters of 1948 and 1949. Oswald H. Brownlee was listed in the Announcements for the course for the Spring Quarter in 1949.
In the Evsey D. Domar Papers at Duke University’s Rubenstein Library, Box 16 c.1, folder “Final Exams: Johns Hopkins, Stanford, U. of Michigan”, there is a one page mimeographed page of final exam questions for “Economics 335, June 17, 1948” which is the time Domar had an joint appointment Cowles Commission/Department of Economics at the University of Chicago and corresponds to the precise end of the Spring quarter. Thus I consider it highly likely to most probable that Domar taught the Spring term, 1948 of Economics 335.
Image Source: Carl F. Christ. History of the Cowles Commission, 1932-1952.
In the previous post, we encountered Martin Bronfenbrenner who was the first choice on a short-list for a position to be filled at Columbia College. In his papers archived at the Duke University Economists’ Papers Project we find a mimeographed copy of the exam for Business Cycle Theory, Economics 332 dated December 21, 1938. Since Bronfenbrenner was a graduate student at the University of Chicago then and the course number and title exactly coincide with those of the course offered by Oskar Lange in the Autumn Quarter 1938 that ended precisely on December 21, we can confidently match the exam below to Lange’s Business Cycle Theory course.
From The University of Chicago, Announcements,Vol. XXXVIII, No. 7. The College and the Divisions for the Sessions of 1938-39. (p. 325):
E. FINANCE AND FINANCIAL ADMINISTRATION
[…]
332. Business Cycle Theory.–Historical and systematic analysis of business cycle theory. The main types of explanation. Equilibrium theory and analysis of economic processes. The role of time in the analysis of economic processes. The significance of anticipations. Theoretical and observed fluctuations. The factors which determine the general level of output and employment. The fluctuations of investment and of employment. The role of technical progress. Business-cycle policy. Prerequisite: Economics 211, 301, and 330, or their equivalents. Autumn, 1:30, LANGE.
[Highlighted text was not included in the course description from the 1942 Announcements]
________________________________
December 21, 1938
ECONOMICS 332
Business Cycle Theory
Source: Duke University, Rubenstein Rare Book & Manuscript Library, Martin Bronfennbrenner Papers, 1939-1995, Box 24, c.1, Folder “Exams. Macro-econ cycles & fiscal policy 1951-76. 1 of 3”.
Image source: Wikipedia/commons.
This report is fascinating for a couple of reasons. The search committee understood its task to identify “the names of the most promising young economists, wherever trained and wherever located” from which a short list of three names for the replacement of Louis M. Hacker in Columbia College was selected. Organizationally, Columbia College is where undergraduate economics has been taught so that teaching excellence, including participation in Columbia College’s legendary Contemporary Civilization course sequence, was being sought as well as was potential for significant scholarship. Appendix C provides important information on James Tobin’s graduate economics education. In a later posting, I’ll provide information on others in the long-list of seventeen economists identified by the search committee.
___________________
January 9, 1950
Professor James W. Angell, Chairman
Department of Economics
Columbia University
Dear Mr. Chairman:
The Committee appointed by you to canvass possible candidates for the post in Columbia College that is made available by the designation of Professor Louis M. Hacker as Director of the School of General Studies submits herewith its report.
As originally constituted, this committee was made up of Professors Taylor, Barger, Hart and Haig (chairman). At an early stage the membership was expanded to include Professor Stigler and from the beginning the committee had the advantage of the constant assistance of the chairman of the department.
In accordance with the suggestions made at the budget meeting in November, the committee has conducted a broad inquiry, designed to raise for consideration the names of the most promising young economists, wherever trained and wherever located. In addition to the men known personally to the members of the committee, suggestions were solicited from the authorities at other institutions, including Harvard, Chicago, California and Leland Stanford. By mid December, scrutiny of the records and publications by the committee to the following seventeen:
| Name | Suggested by |
| Alchian, Armen A. | Haley |
| Bronfenbrenner, Martin | Friedman |
| Brownlee, O. H. | Friedman |
| Christ, Carl L. | Angell |
| Dewey, D. J. | Friedman |
| Du[e]senberry, [James] | Stigler |
| Goodwin, Richard M. | Burbank |
| Harberger, J. H. | Friedman |
| Ho[s]elitz, Bert | Friedman |
| Lewis, H. Gregg | Hart |
| Machlup, Fritz | Stigler |
| Nicholls, William H. | Stigler |
| Nutter, J. W. | Friedman |
| Pancoast, Omar | Taylor |
| Schelling, Thomas | Burbank |
| Tobin, James | Burbank |
| Vandermeulen, D. C. | Ellis |
[p. 2]
The meeting of the American Economic Association in New York during the Christmas holidays offered an opportunity to meet many of the men on the above list and to make inquiries regarding them. As a consequence, it has been possible for your committee to make rapid progress with its appraisals. Although the committee is continuing to gather information and data, it is prepared at this time to make a series of definite recommendations, with a high degree of confidence that these recommendations are not likely to be greatly disturbed by its further inquiries.
It is the unanimous opinion of the members of your committee that the most eligible and promising candidate on our list is Martin Bronfenbrenner, associate professor of economics at the University of Wisconsin, at present on leave for special service in Tokyo.
Should Bronfenbrenner prove to be unavailable the committee urges consideration of D. J. Dewey, at present holding a special fellowship at the University of Chicago, on leave from his teaching post at Iowa. As a third name, the committee suggests James Tobin, at present studying at Cambridge, England, on a special fellowship from Harvard.
Detailed information regarding the records of these three men will be found in appendices to this report.
Bronfenbrenner, the first choice of the committee, is 35 years old. He received his undergraduate degree from Washington University at the age of 20 and his Ph.D. from Chicago at 25. During his war service, he acquired a good command of the Japanese language. He taught at Roosevelt College, Chicago, before going to Wisconsin and undergraduate reports of his teaching are as enthusiastic as those of the authorities at Chicago. He happens to be personally well known to two of the members of your committee (Hart and Stigler) and to at last two other member of the department (Shoup and Vickrey), all four of whom commend him in high terms.
The following statement from Hart, dated December 6, 1929, was prepared after a conference with Friedman of Chicago:
“Bronfenbrenner is undoubtedly one of the really powerful original thinkers in the age group between thirty and thirty-five. He has always very much enjoyed teaching; my impression is that his effectiveness has been with the upper half of the student body at Roosevelt College and at Wisconsin. He is primarily a theorist but has a wide range of interest and a great deal of adaptability so it would not be much of a problem to fit him in somewhere [p. 3] in terms of specialization. He would do a good deal to keep professional discussion stirring in the University. My impression is that he tends to be underrated by the market, and that a chance at Columbia College might well be his best opportunity for some time ahead. The difficulty is, of course, that there is no chance of arranging an interview; though Shoup and Vickrey, of course, both saw him last summer.”
In a letter dated December 15, Shoup wrote as follows:
“I have a high regard for Martin Bronfenbrenner’s intellectual capacities, and I think he would fit in well in the Columbia scene. He has an excellent mind and a great intellectual independence. In his writings he sometimes tends to sharp, almost extreme statements, but in my opinion, they almost always have a solid foundation, and in conversation he is always ready to explore all sides of the question. When we had to select someone to take over the tax program in Japan, after the report had been formulated, and oversee the implementation of the program by the Japanese government, it was upon my recommendation that Bronfenbrenner was selected. He arrived in Japan in the middle of August and his work there since that time has confirmed me in my expectations that he would be an excellent selection for the job, even though he did not have very much technical background in taxation. I rank him as one of the most promising economists in his age group in this country, and I should not be surprised if he made one or more major contributions of permanent value in the coming years.
“He has gone to Japan on a two year appointment, after having obtained a two year leave of absence from the University of Wisconsin. My understanding is that on such an appointment he could come back to the United States at the end of one year, provided he paid his own passage back. It might be possible that even this requirement would be waived, but I have no specific grounds for thinking so. I believe the major part of his work with respect to implementing the tax program will have been completed by next September. If the committee finds itself definitely interested in the possibility of Bronfenbrenner’s coming to Columbia, I should not let the two year appointment stand in the way of making inquiries.”
The breadth and rang of his interests recommend Bronfenbrenner as a person who would probably be highly [p.4] valuable in the general course in contemporary civilization and the quality of his written work suggests high promise as a productive scholar in one or more specialized fields.
Your committee considers that the appropriate rank would be that of associate professor.
Respectfully submitted,
[signed]
Robert M. Haig
______________________________
Appendix A – Martin Bronfenbrenner
The following data regarding Bronfenbrenner are taken chiefly from the 1948 Directory of the American Economic Assoication:
Born: 1914
Education and Degrees:
A.B. Washington University, 1934
Ph.D. University of Chicago 1939
1940-42, George Washington School of Law
Fields: Theory, mathematical economics, statistical methods, econometrics
Doctoral dissertation: Monetary theory and general equilibrium
Publications:
“Consumption function controversy”, Southern Economic Journal, January, 1948
“Price control under imperfect competition”, American Economic Review, March, 1947
“Dilemma of Liberal Economics,” Journal of Political Economy, August, 1946
Additional publications:
“Post-War Political Economy: The President’s Reports”, Journal of Political Economy, October, 1948
Various book reviews including one on W. I. King’s The Keys to Prosperity, Journal of Political Economy, December, 1948, and A. H. Hansen’s Monetary Theory and Fiscal Policy, Annals
Additions to list of publications circulated, January 9, 1950
“The Economics of Collective Bargaining”, Quarterly Journal of Economics, August, 1939.
(with Paul Douglas) “Cross-Section Studies in the Cobb-Douglas Function”, Journal of Political Economy, 1939.
“Applications of the Discontinuous Oligopoly Demand Curve”, Journal of Political Economy, 1940.
“Diminishing Returns in Federal Taxation” Journal of Political Economy, 1942.
“The Role of Money in Equilibrium Capital Theory”, Econometrica (1943).
______________________________
Appendix B – D. J. Dewey
On leave from Iowa.
In 1948 studied at Cambridge, England.
1949-50, at Chicago on special fellowship.
Bibliography:
Notes on the Analysis of Socialism as a Vocational Problem, Manchester School, September, 1948.
Occupational Choice in a Collectivist Economy, Journal of Political Economy, December, 1948.
Friedman and Schultz are highly enthusiastic.
Statement by Hart, dated December 6, 1949:
“Friedman regards Dewey as first rate and points to an article on ‘Proposal for Allocating the Labor Force in a Planned Economy’ (Journal of Political Economy, as far as I remember in July 1949) for which the J.P.E. gave a prize as the best article of the year. I read the article, rather too quickly, a few weeks ago and it is definitely an imaginative and powerful piece of work. How the conclusions would look after a thorough-going seminar discussion, I am not clear; but the layout of questions is fascinating.”
______________________________
Appendix [C] – James Tobin
Statement by Burbank of Harvard, dated December 14, 1949:
“We have known Tobin a good many years. He came to us as a National Scholar, completed his work for the A.B. before the war and had advanced his graduate work very well before he went into the service. He received his Ph.D. in 1947. Since 1947 he has been a Junior Fellow. He was a teaching fellow from 1945 to 1947. He is now in Cambridge, England, and will, I believe, begin his professional work by next fall. Since Tobin has been exposed to Harvard for a very long time I believe that he feels that for his own intellectual good he should go elsewhere. I doubt if we could make a stronger recommendation than Tobin nor one in which there will be greater unanimity of opinion. Certainly he is one of the top men we have had here in the last dozen years. He is now intellectually mature. He should become one of the handful of really outstanding scholars of his generation. His interests are mainly in the area of money but he is also interested in theory and is competent to teach at any level.”
Data supplied by Harvard:
Address: Department of Applied Economics, Cambridge University, England
Married: Yes, one child
Born: 1918, U.S.
Degrees:
A. B. Harvard, 1939 (Summa cum laude)
A.M. Harvard, 1940
Ph.D. Harvard, 1947
Fields of Study: Theory, Ec. History, Money and Banking, Political Theory: write-off, Statistics
Special Field: Business Cycles
Thesis Topic: A Theoretical and Statistical Analysis of Consumer Saving
Experience:
1942-45 U.S. Navy
1945-47 Teaching Fellow, Harvard University
1947- Junior Fellow, Society of Fellows
[p. 2 of Appendix C]
Courses: 1939-40
Ec. 21a (Stat.) A
Ec. 121b (Adv. St.) A
Ec. 133 (Ec. Hist) A
Ec. 147a (M&B Sem) A
Ec. 145b (Cycles) A
Ec. 113b (Hist. Ec.) Exc.
Gov. 121a (Pol.Th.) A
1940-1941
Ec. 121a (Stat.) A
Ec. 164 (Ind. Org.) A
Ec. 20 (Thesis) A
Ec. 118b (App. St.) A
Math 21 A
Ec. 104b (Math Ec.) A
1946-47 Library and Guidance
Generals: Passed May 22, 1940 with grade of Good Plus
Specials: Passed May 9, 1947 with grade of Excellent.
Data from 1948 Directory of American Economic Association:
Harvard University, Junior Fellow
Born: 1918
Degrees: A. B., Harvard, 1939; Ph.D., Harvard, 1947j
Fields: Business fluctuations, econometrics, economic theory, and mathematical economics
Dissertation: A theoretical and statistical analysis of consumer saving.
Publications:
“Note on Money Wage Problem”, Quarterly Journal of Economics, 1941.
“Money Wage Rates and Employment”, in New Economics (Knopf, 1947).
“Liquidity Preference and monetary Policy”, Review of Economics and Statistics, 1947.
[pencil addition] Article in Harris (ed.), The New Economics, 1947.
______________________________
Source: Columbia University Rare Book and Manuscript Library. Department of Economics Collection, Box 6, Folder “Columbia College”
Image Source: The beyondbrics blog of the Financial Times.
Class rolls from Hotelling’s courses on mathematical economics he taught at Columbia have been posted, as have course outlines and a final exam from the course as taught at the University of North Carolina in 1946 and 1950.
_________________________
Economics 311-312—Statistical inference. 3 points each session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.
Summarizing and interpretation of data; probability, mathematical and philosophical; the normal law of error; probable errors; student’s distribution and the work of R. A. Fisher; least squares; fitting trend lines and other empirical curves; their reliability; accuracy of forecasts; tests of stability, homogeneity, and goodness of fit; analysis of variance; simple, partial and multiple correlation coefficients and their interpretation in terms of probability; periodogram analysis.
Prerequisite: Calculus. A knowledge of determinants is desirable.
Economics 313-314—Mathematical economics. 3 points each session. Professor H. Hotelling.
M. and W. at 4:10. 302 Fayerweather.
Supply and demand functions; monopoly; competition; duopoly; utility; taxation; tariffs; index numbers; exhaustible resources; dynamical economics.
Prerequisite: Calculus.
Economics 311—Statistical inference. 3 points Winter Session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.
Summarizing and interpretation of data; probable errors; significance of means, of differences of variances; and of least-square determinations; accuracy of forecasts; Student’s distribution and R. A. Fisher’s extensions; comparison of observed with theoretical frequencies; tests of independence, homogeneity and goodness of fit. Proofs of the formulae are considered. Examples are drawn from a variety of fields, both within and outside of the social sciences.
Prerequisite: Calculus is a prerequisite. Mathematics 101 (Probability. Professor B. O. Koopman. Tu. and Th., 2:10-3) must be taken simultaneously. Mathematics 57 (Higher algebra. Professor L. P. Siceloff. M., W., and F. at 11) should also be taken at the same time if the student is to go on with Economics 312 or undertake research in statistics, unless he is already familiar with determinants and quadratic forms.
Graduate credit in economics will be allowed for Mathematics 57 and 101, which are required for this work in statistics.
Economics 312—Modern statistical theory. 3 points Spring Session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.
Correlation, simple, partial and multiple, with exact and approximate tests of significance; comparison and analysis of variances; the theory of estimation and efficiency; frequency curve fitting; analysis of time series; periodicity. Recent discoveries will be discussed.
Prerequisites: Economics 311 and Mathematics 57 and 101.
Economics 313-314—Mathematical economics. 3 points each session. Professor H. Hotelling.
M. and W. at 4:10. 302 Fayerweather.
Supply and demand functions; monopoly; competition; duopoly; utility; taxation; tariffs; index numbers; exhaustible resources; dynamical economics.
Prerequisite: Calculus. Mathematics 57 will also be found helpful, though it is not a required prerequisite.
[Starting this year the two courses in Statistics were moved from “Research Courses” to “General Courses” as reflected in the course numbering. Note the label “Statistics” instead of “Economics” before the course numbers]
Statistics 111—Statistical inference. 3 points Winter Session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.
Summarizing and interpretation of data; probable errors; significance of means, of differences of variances; and of least-square determinations; accuracy of forecasts; Student’s distribution and R. A. Fisher’s extensions; comparison of observed with theoretical frequencies; tests of independence, homogeneity and goodness of fit. Proofs of the formulae are considered. Examples are drawn from a variety of fields, both within and outside of the social sciences.
Calculus is a prerequisite. Mathematics 101 (Probability. Professor B. O. Koopman. Tu. and Th., 2:10-3) should be taken simultaneously. Mathematics 57 (Higher algebra. Professor L. P. Siceloff. M., W., and F. at 11) should also be taken at the same time if the student is to go on with Statistics 312 or undertake research in statistics, unless he is already familiar with determinants and quadratic forms.
Graduate credit in economics will be allowed for Mathematics 57 and 101, which are required for this work in statistics.
Statistics 112—Statistical inference. 3 points Spring Session. Professor H. Hotelling.
M. and W. at 10. 412 Fayerweather.
Correlation, simple, partial and multiple, with exact and approximate tests of significance; comparison and analysis of variances; the theory of estimation and efficiency; frequency curve fitting; analysis of time series; periodicity. Recent discoveries will be discussed.
Prerequisites: Economics 111 and Mathematics 57 and 101 or equivalent knowledge.
Economics 117-118—Mathematical economics. 3 points each session. Professor H. Hotelling. [Starting this year Mathematical Economics was moved from “Research Courses” to “General Courses” as reflected in the course numbering.]
M. and W. at 4:10. 418 Business.
Supply and demand functions; monopoly; competition; duopoly; utility; taxation; tariffs; index numbers; exhaustible resources; dynamical economics.
Prerequisite: Calculus. Mathematics 57 will also be found helpful, though it is not a required prerequisite. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 101.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 412 Fayerweather.
Summarizing and interpretation of data; probable errors; significance of means, of differences of variances; and of least-square determinations; accuracy of forecasts; student’s [sic] distribution and R. A. Fisher’s extensions; comparison of observed with theoretical frequencies; tests of independence, homogeneity and goodness of fit. Proofs of the formulae are considered. Examples are drawn from a variety of fields, both within and outside of the social sciences.
Calculus is a prerequisite. Mathematics 101 (Probability. Professor B. O. Koopman. Tu. and Th., 2:10-3) should be taken simultaneously. Mathematics 57 (Higher algebra. Professor L. P. Siceloff. M., W., and F. at 11) should also be taken at the same time if the student is to go on with Statistics 312 or undertake research in statistics, unless he is already familiar with determinants and quadratic forms.
Graduate credit in economics will be allowed for Mathematics 57 and 101, which are required for this work in statistics.
Statistics 112—Statistical inference. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 412 Fayerweather.
Correlation, simple, partial and multiple, with exact and approximate tests of significance; comparison and analysis of variances; the theory of estimation and efficiency; frequency curve fitting; analysis of time series; periodicity. Recent discoveries will be discussed.
Prerequisites: Economics [sic, Statistics] 111 and Mathematics 57 and 101 or equivalent knowledge.
Statistics 301—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
[According to Bulletin 1935-36 this course was given in 1934-1935 but not given in 1935-1936]
Economics 117-118—Mathematical economics. 3 points each session. Professor Hotelling.
M. and W. at 4:10. 418 Business.
The fundamentals of economics as a set of problems in maxima and minima. The maximizing of utility or of profits by individuals and the consequent equations of general equilibrium; the nature and interrelations of utility, curves and surfaces of indifference, demand and supply functions, consumers’ surplus, and welfare. Monopoly and various forms of competition. The extent to which selfish activities of individuals promote the general welfare; contrasts and resemblances of a planned society with the outcome of competition. Interrelation of prices. Taxation. Dynamical economics: cycles, lagging effects, and exhaustible resources.
The theory of maxima and minima of functions of n variables, with and without restraining conditions; the elements of the calculus of variations; tensors. The effects of variation of parameters on maximizing conditions are applied to discover consequences of taxation and other interferences.
A thorough knowledge of calculus, with something of differential equations, is an essential prerequisite. Mathematics 57 (Higher algebra; M., W., and F. at 11) is highly desirable. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 101.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 4:10 611 Business.
Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability.
Prerequisites: Calculus and Mathematics 101 (probability); but the latter may be taken simultaneously. Mathematics 57 (higher algebra) is recommended.
Graduate credit in economics will be allowed for Mathematics 57, and Mathematics 101.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 412 Fayerweather.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Diverse applications, both to social and to natural sciences.
The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111, Mathematics 57, and Mathematics 101 or equivalent knowledge.
Statistics 114 [new course]—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W. at 4:10. 611 Business.
The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. The analysis of variance and covariance to segregate factors producing significant variation. Recent discoveries in statistical theory.
Prerequisites: Statistics 111, Mathematics 57 and Mathematics 101.
[Statistics 301—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
Given in 1934-1935; not to be given in 1935-1936]
Economics 117 [Course reduced to a single semester]—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 507 Business.
The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Theory of interest, depreciation, exhaustible resources. Contrasts and resemblances of a planned society with the outcome of competition. Dynamical economics: cycles and lagging effects.
The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions. Elements of the calculus of variations.
Prerequisite: A thorough knowledge of calculus. Mathematics 57 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 101.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 4:10 611 Business.
Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability.
Prerequisites: Calculus and Mathematics 101 (probability); but the latter may be taken simultaneously. Mathematics 57 (higher algebra) is recommended.
Graduate credit in economics will be allowed for Mathematics 57, and Mathematics 101.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 412 Fayerweather.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Diverse applications, both to social and to natural sciences.
The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111, Mathematics 57, and Mathematics 101 or equivalent knowledge.
Statistics 114 [new course]—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W. at 4:10. 611 Business.
The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. The analysis of variance and covariance to segregate factors producing significant variation. Recent discoveries in statistical theory.
Prerequisites: Statistics 111, Mathematics 57 and Mathematics 101.
[Statistics 302—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
Not listed in Bulletin 1936-1937]
Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. M. in 401 Fayerweather and W. in 412 Fayerweather.
The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.
The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.
Prerequisite: A thorough knowledge of calculus. Mathematics 57 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 101.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 5:10 228 Pupin.
Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability.
Prerequisites: Calculus and Mathematics 101 (probability); but the latter may be taken simultaneously. Mathematics 57 (higher algebra) is recommended.
Graduate credit in economics will be allowed for Mathematics 57, and Mathematics 101.
[Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
Not given in 1937-38]
[Statistics 114—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
Not given in 1937-38]
Statistics 301—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
Hours to be arranged.
Prerequisites: Statistics 111, 112, and 114, or similar knowledge of statistical theory.
[Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
Not given in 1937-38]
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W. at 5:10 412 Fayerweather.
Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability. The characteristic function.
Prerequisites: A thorough knowledge of calculus and Mathematics 107 (probability); but the latter may be taken simultaneously, or a knowledge of elementary probability supplemented by readings may be substituted for Mathematics 107. Mathematics 58 (higher algebra) is recommended.
Graduate credit in economics will be allowed for Mathematics 58, and Mathematics 107.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W. at 11. 412 Fayerweather.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences.
The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see Mathematics 58 and 107.
Statistics 114—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W. at 5:10. 412 Fayerweather.
The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. The analysis of variance and covariance to segregate factors producing significant variation. Recent discoveries in statistical theory. The efficient design of investigations.
Prerequisites: Same as for Statistics 112.
[Statistics 301—Seminar in advanced mathematical statistics. 3 points Winter Session. Professor Hotelling.
Not given in 1938—1939]
Prerequisites: Statistics 111, 112, and 114.
Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 11. M. in 412 Fayerweather.
The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.
The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.
Prerequisite: A thorough knowledge of calculus. Mathematics 58 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 58 and Mathematics 107.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling and Dr. Wald.
M. and W. at 5:10 412 Fayerweather.
Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability. The characteristic function.
Prerequisites: A thorough knowledge of calculus and Mathematics 107 (probability); but the latter may be taken simultaneously, or a knowledge of elementary probability supplemented by readings may be substituted for Mathematics 107. Mathematics 58 (higher algebra) is recommended.
Attention is called also to Mathematics 108 (calculus of finite differences, given by Professor Koopman, M. and W., 1:45-3). Graduate credit in economics will be allowed for Mathematics 58, 107, and 108.
Numerical methods, including the use of punched-card equipment, may be learned in Astronomy 110.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling and Dr. Wald.
M. and W. at 5:10. 412 Fayerweather.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences.
The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see Mathematics 58 and 107.
Statistics 114—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling and Dr. Wald.
M. and W. at 11. 224 Pupin.
The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. The analysis of variance and covariance to segregate factors producing significant variation. Recent discoveries in statistical theory. The efficient design of investigations.
Prerequisites: Same as for Statistics 112.
Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professor Hotelling and Dr. Wald.
Tu. at 8 p.m. 304 Fayerweather.
Prerequisites: Statistics 111, 112, and 114.
Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling and Dr. Wald.
M. and W. at 11. M. 228 Pupin.
The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.
The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.
Prerequisite: A thorough knowledge of calculus. Mathematics 58 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 58 and Mathematics 107.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W., at 5:30—6:20. 410 Fayerweather.
Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability. The characteristic function.
Prerequisites: A thorough knowledge of calculus and Mathematics 107 (probability); but the latter may be taken simultaneously, or a knowledge of elementary probability supplemented by readings may be substituted for Mathematics 107. Mathematics 58 (higher algebra) is recommended.
Graduate credit in economics will be allowed for Mathematics 58 and 107.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 410 Fayerweather.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences.
The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see Mathematics 58 and 107.
Statistics 114—Correlation, analysis of variance, and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W., 5:30—6:20. 410 Fayerweather.
The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies.
Prerequisites: Same as for Statistics 112.
Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professor Hotelling and Dr. Wald.
Tu. at 8 p.m. 304 Fayerweather.
Prerequisites: Statistics 111, 112, and 114.
Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 401 Fayerweather.
The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.
The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.
Prerequisite: A thorough knowledge of calculus. Mathematics 58 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 58 and Mathematics 107.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W., at 5:40—6:30. 305 Schermerhorn.
Summarizing and interpretation of data. Frequency distributions. Significance of the normal distribution. Accuracy of means and of differences of means. Relations of statistics and probability. The characteristic function.
Prerequisites: A thorough knowledge of calculus and Mathematics 107 (probability); but the latter may be taken simultaneously, or a knowledge of elementary probability supplemented by readings may be substituted for Mathematics 107. Mathematics 57 (higher algebra) is recommended.
Graduate credit in economics will be allowed for Mathematics 57 and 107.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
M. and W., at 5:40—6:30. 305 Schermerhorn.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences.
The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see Mathematics 58 and 107.
Statistics 114—Correlation and the χ2 test. 3 points Spring Session. Professor Hotelling.
M. and W. at 10. 410 Fayerweather.
The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies.
Prerequisites: Same as for Statistics 112.
Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professor Hotelling and Dr. Wald.
Tu. at 8 p.m. 304 Fayerweather.
Prerequisites: Statistics 111, 112, and 114.
Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 410 Fayerweather.
The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.
The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.
Prerequisite: A thorough knowledge of calculus. Mathematics 57 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 57 and Mathematics 107.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
M. and W., at 5:40—6:30. 305 Schermerhorn.
The fundamental course prerequisite to all others in mathematical statistics. An introduction to the modern theory of inference from observations, leading to the combination of observations in such ways as to make inferences valid and efficient. Relations of statistics and probability. Significance of the normal distribution. Accuracy of means and differences of means. The characteristic function.
A thorough knowledge of calculus is an essential prerequisite. Unless a previous study has been made of mathematical probability, Mathematics 107 (probability) should be taken simultaneously. Mathematics 167 is also recommended to be taken simultaneously in order to get an acquaintance with matrix algebra for use in more advanced statistics courses and in mathematical economics.
Graduate credit in economics will be allowed for Mathematics 107 and 167. For these courses see the Announcement of the Division of Mathematical and Physical Sciences.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
Tu. and Th. at 10. 410 Fayerweather.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences. The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see under Statistics 111.
Statistics 114—Correlation and the χ2 test. 3 points Spring Session. Professor Hotelling.
Tu. and Th., 5:40—6:30. 410 Fayerweather.
The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies.
Prerequisites: Same as for Statistics 112.
Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professors Hotelling and Wald.
W. at 8 p.m. 304 Fayerweather.
Prerequisites: Statistics 111, 112, and 114.
Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
M. and W. at 10. 410 Fayerweather.
The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.
The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.
Prerequisite: A thorough knowledge of calculus. Mathematics 167 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 167 and Mathematics 107.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
Tu. and Th., at 5:40—6:30. 305 Schermerhorn.
The fundamental course prerequisite to all others in mathematical statistics. An introduction to the modern theory of inference from observations, leading to the combination of observations in such ways as to make inferences valid and efficient. Relations of statistics and probability. Significance of the normal distribution. Accuracy of means and differences of means. The characteristic function.
A thorough knowledge of calculus is an essential prerequisite. Unless a previous study has been made of mathematical probability, Mathematics 107 (probability) should be taken simultaneously. Higher algebra is also recommended to be taken simultaneously in order to get an acquaintance with matrix algebra for use in more advanced statistics courses and in mathematical economics.
Graduate credit in economics will be allowed for Mathematics 107 and 57. For these courses see the Announcement of the Division of Mathematical and Physical Sciences.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
Tu. and Th., at 5:40—6:30. 410 Fayerweather.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences. The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see under Statistics 111.
Statistics 114—Correlation and the χ[2] test. 3 points Spring Session. Professor Hotelling.
Tu. and Th. at 10. 410 Fayerweather.
The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies.
Prerequisites: Same as for Statistics 112.
Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professors Hotelling and Wald.
Hours to be arranged.
Prerequisites: Statistics 111, 112, and 114.
Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
Tu. and Th. at 10. 410 Fayerweather.
The consequences of the simultaneous attempts by different persons to maximize their respective profits or degrees of satisfaction. Utility, indifference curves, demand, supply and cost functions, monopoly and various forms of competition, interrelations of prices, taxation. Contrasts and resemblances of a planned society with the outcome of competition. Overhead and marginal costs.
The theory of maxima and minima of functions of n variables, with and without constraining conditions, is developed beyond the treatments in calculus books to include the second-order conditions.
Prerequisite: A thorough knowledge of calculus. Mathematics 167 (higher algebra) is highly desirable. Graduate credit in economics is allowed for Mathematics 167 and Mathematics 107.
Statistics 111—Statistical inference. 3 points Winter Session. Professor Hotelling.
Tu. and Th., at 5:40—6:30. 305 Schermerhorn.
The fundamental course prerequisite to all others in mathematical statistics. An introduction to the modern theory of inference from observations, leading to the combination of observations in such ways as to make inferences valid and efficient. Relations of statistics and probability. Significance of the normal distribution. Accuracy of means and differences of means. The characteristic function.
A thorough knowledge of calculus is an essential prerequisite. Unless a previous study has been made of mathematical probability, Mathematics 107 (probability) should be taken simultaneously. Higher algebra is also recommended to be taken simultaneously in order to get an acquaintance with matrix algebra for use in more advanced statistics courses and in mathematical economics.
Graduate credit in economics is allowed for these mathematics courses, for which see the Announcement of the Division of Mathematical and Physical Sciences.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Hotelling.
Tu. and Th at 10. 410 Fayerweather.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences. The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see under Statistics 111.
Statistics 114—Correlation and the χ[2] test. 3 points Spring Session. Professor Hotelling.
Tu. and Th., at 5:40—6:30. 410 Fayerweather.
The multivariate normal distribution. Simple, partial, multiple, and vector correlation. Rank correlation and the problem of non-normal populations. Tests of independence, homogeneity, and goodness of fit for tables of frequencies. Contingency tables.
The distribution of the correlation coefficient is derived and is used to illustrate various logical and mathematical questions of more general application.
Prerequisites: Same as for Statistics 112.
Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professors Hotelling and Wald.
Hours to be arranged.
Prerequisites: Statistics 111, 112, and 114.
[Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
Not given in 1944-1945]
Statistics 111a and 111b—Probability and statistical inference. 3 or 6 points Winter Session. Professor Hotelling.
Tu. and Th., at 5:40—6:30 and 7:30—8:20. 305 Schermerhorn.
The fundamental prerequisite to all other courses in mathematical statistics. Statistics 111a (Probability) covers the first half of the session and Statistics 111b (Statistical inference) the second half. Students may register for the first half alone, or, if they have completed a course in mathematical probability, for the second half alone. Those intending to study both parts should register for both at the beginning of the session. Registration for Statistics 111b should be completed not later than November 15.
The classical mathematical theory of probability is developed in the first half, starting from a critical treatment of the basic concepts and including permutations and combinations, the binomial, Poisson and normal distribution, the Law of Great Numbers, the principal limit theorems, geometrical probability, and the characteristic function. The second half introduces the use of observations to estimate unknown quantities and to test hypotheses, and deals with criteria of valid, efficient, and exact estimation, with illustrations drawn from physical, biological, and social sciences. The method of maximum likelihood is considered. The Student distribution and the variance distribution are derived and applied to various situations. Moments, cumulants, and other quantities are considered in their two meanings as parameters of a “population,” or probability distribution, and as estimates of parameters based on a “sample” of observations.
A thorough knowledge of calculus is an essential prerequisite. Students are advised to study Mathematics 167 simultaneously to obtain a knowledge of matrix algebra for use in more advanced statistics courses and in mathematical economics.
Statistics 112—Least squares and the treatment of time series. 3 points Spring Session. Professor Wald. [Note change in instructor.]
Tu. and Th at 10. 410 Fayerweather.
The classical method of least squares and modern modifications and developments, with stress on the interpretation of results in terms of probability. Applications to social and to natural sciences. The problems of observations ordered in time. Correlation and regression of time series. Seasonal variation and secular trend. Methods of correcting lack of independence and avoiding fallacies. Periodogram analysis. Recent discoveries and improvements.
Prerequisites: Statistics 111b, and a knowledge of higher algebra (e.g., Bôcher’s) and of probability. For these see under Statistics 111a and 111b.
[Statistics 114—Correlation and the χ[2] test. 3 points Spring Session. Professor Hotelling.
Not given in 1945-1946]
Statistics 302—Seminar in advanced mathematical statistics. 3 points Spring Session. Professor Wald. [Note change in instructor.]
Tu., 8-10 p.m. 618 Business.
Prerequisites: Statistics 111a and b, 112, and 114.
[Economics 117—Mathematical economics. 3 points Winter Session. Professor Hotelling.
Not given in 1945-1946]
___________________
Source: Columbia University. Bulletin of Information. History, Economics, Public Law, and Social Science [1931-32—1940-41]; History, Economics, Public Law, and Sociology [1941-42—1945-46]. Courses offered by the Faculty of Political Science.
Image source: From a photo of the Institute of Statistics leadership around 1946: Gertrude Cox, Director, William Cochran, Associate Director-Raleigh and Harold Hotelling, Associate Director-Chapel Hill. North Carolina State University.
Hotelling’s students included the communist and later Soviet agent Victor Perlo (1932-33) and three Nobel prize winners in economics, Milton Friedman (1933-34), William Vickrey (Winter session 1935-36) and Kenneth Arrow (Winter session 1940-41). Friedman’s and Arrow’s student notes for this course with Hotelling can be found at the Hoover Archives and the Duke Economist Papers Project, respectively.
Course outlines and a final examination for Hotelling’s course as taught at the University of North Carolina in 1946 and 1950 has been posted. Here is a link to the posting of a list of statistics and economics courses taught at Columbia by Harold Hotelling.
____________________________
|
Econ 312. Mathematical Economics |
Winter Session, 1931-32 |
| Benitz, Paul A. | |
| Kelly, Thomas H. | |
| Metzger, Henry W. | |
| Pabst, William R., Jr. | |
| Wu, Kan | |
| Columbia College | Madow, William |
| School of Business | Otto, Erich A. |
| School of Business | Stein, Arthur |
| Econ 314. Mathematical Economics | Spring Session, 1931-32 |
| Benitz, Paul A. | |
| Duncan, Acheson Johnston | |
| Kelly, Thomas H. | |
| Pabst, William R. (Jr) | |
| Metzger, Henry W. | |
| Econ 313. Mathematical Economics | Winter session, 1932-33 |
| Lawson, Alfred | |
| Perlo, Victor | |
| Preinreich, Gabriel A.D. | |
| Weyl, Nathaniel | |
| Econ 314. Mathematical Economics | Spring Session, 1932-33 |
| Perlo, Victor | |
| Preinreich, Gabriel A. D. | |
| Weyl, Nathaniel | |
| Econ 117. Mathematical Economics | Winter session, 1933-34 |
| Dodwell, David W. | |
| Edmondson, Susanna P. | |
| Friedman, Milton | |
| Goldberg, Henry | |
| Madow, William G. | |
| Vass, Laurence C. | |
| School of Business | Osborne, Ernest L. |
| Econ 118. Mathematical Economics | Spring Session, 1933-34 |
| Edmondson, Susanne P. | |
| Friedman, Milton | |
| Goldberg, Henry | |
| Vass, Laurence C. | |
| Econ 117. Mathematical Economics | Winter Session, 1934-35 |
| Bonis, Austin J. | |
| Frankel, Lester R. | |
| Wright, Charles A. | |
| Econ 118. Mathematical Economics | Spring Session, 1934-35 |
| Bonis, Austin J. | |
| Frankel, Lester R. | |
| Machol, Richard M. | |
| Richards, Margaret H. | |
| Romig, Harry G. | |
| Solomons, Leonard M. | |
| Wright, Charles A. | |
| Econ 117. Mathematical Economics | Winter Session, 1935-36 |
| Bennett, Rollin F. | |
| Fabricant, Solomon | |
| Hilfer, Irma | |
| Jacobson, Katharine | |
| Norton, John D. | |
| Vickrey, William | |
| Wallis, W. Allen | |
| Econ 117. Mathematical Economics | Class rolls not found for 1936-37 |
| Econ 117. Mathematical Economics | Not offered 1937-38 |
| Econ 117. Mathematical Economics | Winter Session, 1938-39 |
| Dejongh, Theunis W | |
| Durand, David | |
| Friedman, Irma D. | |
| Geisler, Murray A. | |
| Gould, Jacob M. | |
| King, Frederick G. | |
| Schwartz, Seymour | |
| Shulman, Harry | |
| Columbia College | Klarman, Herbert |
| Teachers College | Recht, Leon Samuel |
| Econ 117. Mathematical Economics | Winter Session, 1939-40 |
| Bennett, Blair M. | |
| Nassimbene, Raymond | |
| Pascale, Henry | |
| Columbia College | Schwartz, Harry |
| Econ 117. Mathematical Economics | Winter Session, 1940-41 |
| Arrow, Kenneth J. | |
| Berger, Richard | |
| Cohen, Leo | |
| Divatia, Makarand V. | |
| Fischer, Harry S. | |
| Haines, Harold | |
| Konijn, Hendrik S. | |
| Peiser, Donald E. | |
| School of Business | Ballentine, George A. |
| Econ 117. Mathematical Economics | Winter Session, 1941-42 |
| Diamond, Harold S. | |
| Peach, Paul | |
| Ravitsky, Inda | |
| Reder, Melvin W. | |
| Sievers, Allen M. | |
| School of Business | Cooper, William W. |
| School of Business | Morrison, Lachlan |
| Econ 117. Mathematical Economics | Winter Session, 1942-43 |
| Boyd, Elizabeth N. | |
| D’Errico, John E. | |
| Simpson, Elizabeth T. | |
| Simpson, William B. | |
| Columbia College | Tenenbaum, Warren S. |
| School of Business | Lopata, Simon |
| Econ 117. Mathematical Economics | Winter Session, 1943-44 |
| Hsieh, Kia | |
| Lindsey, Fred D. | |
| Owlett, Ann M. | |
| Straus, Everett M. | |
| Ullman, Joseph L. | |
| School of Business |
Varon, Frank R. |
Source: Assembled from the student registration cards. Columbia University. Rare Book & Manuscript Library. Hotelling Papers, Box 48, Folder Mathematical Economics (1).
This set of pictures was found in Box 2, Folder “Photographs” of the Franklin Henry Giddings papers, 1890-1931, Columbia University, Rare Book & Manuscript Library. Judging from the college/university affiliations given (about a two year window) and the fact that the Seventh Annual Meeting of the American Economic Association was held with Columbia College, New York City, December 26-29, 1894, my first guess was that this was related to the AEA event and put together by the local organizers.
However we can be certain that this handsome collection of portraits was published instead as a supplement to the University Extension Bulletin. Exactly these eight economists are the “corps of lecturers” for the University Extension Summer Meeting held July 2-28, 1894 at the University of Pennsylvania as described in The University Extension Bulletin, Vol. I, No. 8 (May 10, 1894). Further it is announced: “We present our readers also with a supplement with portraits of the lecturers in the Economics Department.” Here at haithitrust.org is that supplement.
