Categories
Courses Curriculum Economists Johns Hopkins Regulations

Johns Hopkins Economics. Ph.D. Regulations, Courses 1880

Johns Hopkins University began instruction October 3, 1876. The class schedule for the entire university could be printed as a single page matrix of hours by days in 1879.

By the academic year 1880-81 Johns Hopkins University had awarded a single Ph.D. in political science, which is where political economy still was classified.

In this posting  we approach the beginning of the Big Bang of graduate education in economics in the U.S.

General Statements for 1880-81
Information for Graduate Students
Enumeration of Classes

 

________________________

[p. 54]

GENERAL STATEMENTS FOR 1880-81.

Instruction is provided for both Collegiate and University students….

Admission of Students.

Arrangements are made for the reception of the following classes of students:

I.
Graduates.

Young men who have already graduated in this or other institutions of acknowledged standing are received on the presentation of their diplomas, after satisfying the chief instructors in the departments of study which they propose to follow that they are qualified to pursue the courses here given. They may be enrolled as candidates for the degree of Doctor of Philosophy or not, at their option. Those whose years and attainments correspond with those of graduates may also be received as special students.

II.
Matriculates.

Students who wish a collegiate training are expected, unless excused for some special reason, to offer themselves for matriculation at the time of their admission. If they can pass satisfactorily in a considerable part of the required studies, but not in all, they may be admitted as candidates for matriculation, but their names will not be printed as enrolled students until the examination is completed. They will not be considered as candidates for more than one academic year.

Students who present themselves with higher attainments than are requisite for matriculation may, upon examination, receive credit for the same, be admitted to advanced classes, and so graduate in less time than would otherwise be requisite.

III.
Non-Matriculates.

  1. Students in subjects preliminary to a medical course…
  2. Young men of collegiate age…sufficiently advanced in character and attainments to be allowed the privilege, and that there is some good reason why they should not offer themselves for matriculation…
  3. Attendants upon lectures. –The University has extended certain privileges to teachers…, to medical students…, and to other persons…[they] are not enumerated as enrolled students.

Fees for Tuition, Etc.

The charges are as follows, payable in advance, unless, for specific reasons satisfactory to the Treasurer, he permits the payment to be deferred:

For Tuition, $80 per annum.

[…]

Board and lodging in private houses near the University, including care of room, fuel and light, may be obtained at five dollars, an upwards, per week. Some students pay even less.

[p. 55]

 

INFORMATION FOR GRADUATE STUDENTS.

Graduate Courses.

Advanced and graduate students are received with or without reference to their being candidates for a degree, and they are permitted to attend such lectures and exercises as they may individually select…

…The University professors are not absorbed in the details of college routine, but are free to give personal counsel and instruction to those who seek it; books and instruments adapted to investigation and advanced work have been liberally provided; the system of Fellowships secures the presence of twenty special students, imbued with the University spirit, most of them looking forward to academic careers; seminaries limited to a few advanced students, under the guidance of a director, have been organized in Greek, Mathematics, Physics, and History; societies devoted to Philology, to Mathematical, Physical, and Natural Science, and to History and Political Science, afford opportunities for the presentation of memoirs and original communications….

The instruction is carried on by such methods (varying of course with individual scholars, and with the different departments of work) as will encourage the student to become an independent and original investigator, while he is growing more and more familiar with the work now in progress elsewhere, and with the results which have been obtained by other scholars in the same field, and while he is adding to his general intellectual culture…

Degree of Doctor of Philosophy.

The Degree of Master of Arts and Doctor of Philosophy will be conferred in conformity with the following regulations:

Every candidate for the degree of A.M: and Ph.D. will be required:

  1. To have obtained the Baccalaureate degree of this University (or to present the diploma of some other college which the Faculty shall accept as equivalent), and to have subsequently devoted not less than two years to University study in the special department of learning which he may have chosen. The appointment to a Fellowship will be regarded by the faculty as equivalent to the attainment of a Bachelor’s Degree, so far as this is a necessary condition of obtaining a higher degree.
  2. To produce a thesis which shall be approved by the Faculty. This thesis must be the result of original investigation in the main subject for examination, and the subject of the thesis must be submitted for approval to the head of the department, or the chief examiner in it, not less than six months before the degree is conferred.
  3. To pass an examination in one main and one or more subsidiary subjects; the choice of which is to be referred by the candidate to the chief examiner, and through him to the Faculty for final approval. The method of examination will vary according to the subject, and will be written, oral, practical, or all three, as may be deemed best.
  4. To enroll himself as a candidate for the degree, at least one year in advance of the time when he proposes to apply for examination.

Degrees will be conferred by the Trustees on the recommendation of the Faculty, probably twice a year, in the middle of the winter and at the end of the academic term.

The Diploma will indicate the department of study to which the candidate has directed his attention.

Degrees Conferred.—The degree of Doctor of Philosophy has been conferred on the following named persons, who have passed the required examinations:

 

1878 [4 Ph.D. degrees awarded, one in economics  (no other in economics through 1880)]

Henry C. Adams, A.B., Iowa College, 1874; now Lecturer on Political Economy at Cornell University and at the Johns Hopkins University.

 

[…]

 

ENUMERATION OF CLASSES

Which have been instructed during the Academic Year 1879-80.

[pp. 61]

History and Political Science. (33 Students.)

Seminary of American History (15).

Once weekly, two months: Dr. [Austin] Scott.

Comparative Constitutional History (5).

Once weekly, four months: Dr. H. B. Adams.

History of the Renaissance and Reformation (17).

Daily, first half-year, also ten public lectures: Dr. H. B. Adams.

English Constitutional History, Stubbs’ Select Charters (15).

Once weekly, six months: Dr. H. B. Adams.

Political Economy (13).

Four times weekly, two months : Dr. H. B. Adams.

Money and Banking (12).

Four times weekly, two months: Dr. H. C. Adams.

National Debts.

Nine public lectures: Dr. H. C. Adams.

________________________

Source: Johns Hopkins University. University Circulars. No. 5, May, 1880, pp. 54-55, 61.

Categories
Economists Harvard

Harvard Economics. Daniel Ellsberg profiles Richard Goodwin

A member of the CRIMSON, [Goodwin] left to become one of the founders of a competing newspaper. As a senior, he started a rival to the Advocate, an “intellectual magazine” called the Harvard Critic. “We were far in advance of our time, I will say that for us,” he recalls, speaking of the group’s major project, a Kinsey-type poll of undergraduate sex-life. Aided the a professor of clinical psychology, the staff composed a carefully-worded questionnaire and had 2000 conscientious replies. The date was recorded on IBM cards, and the professor prepared to tabulate it on the University’s IBM machines. At this point the Dean’s Office made the students a sporting offer, one alternative being to publish the results and be expelled. Goodwin shipped the cards back home to Newcastle, Indiana.

Note: this Faculty Profile was written by Daniel Ellsberg who later brought us The Pentagon Papers. The on-line version of the article misspelled Ellsberg’s name.

WONDERING WHAT HAPPENED TO THE PUNCH CARDS….

Source: May 24, 1951: The Harvard Crimson

Categories
Economists Harvard Transcript

Harvard Economics. Richard M. Goodwin, 1949

The economics department of Columbia University set up a search committee  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. The Chairman of the Harvard Economics Department, Harold H. Burbank, suggested a few names to the committee. In this posting I have assembled Burbank’s letter, another by Schumpeter and a data-sheet apparently provided by the Harvard economics department (including a list of graduate courses taken at Harvard) plus a list of Goodwin’s publications as of the end of 1949.

_____________________

HARVARD UNIVERSITY
DEPARTMENT OF ECONOMICS
Office of the Chairman
M-8 Littauer Center
Cambridge 38, Massachusetts

November 28, 1949

Dear Jimmy

I had thought that I might be able to make one or two definite recommendations by this time, but I find that I cannot be at all definite.

The young man whom I had expected to recommend most strongly is Richard M. Goodwin. Goodwin was graduated from Harvard College in 1934, summa cum laude. After three years at Oxford I had him return to the Department and he has been with us since that time. During the war years he worked with the group in mathematics and physics, improving and consolidating his knowledge of mathematics to a point where it is highly useful in his econonmics. Goodwin is now in the fourth year of his appointment as an assistant professor. Undoubtedly he will be considered for a permanent place here which is probably the best recommendation I can give you. With us he has worked mainly in theory and money and banking and in cycles. I am enclosing a copy of his publications It is true enough that his main interest for the moment is in monetary economics but his interests are so definitely broad that I feel that it would be no great difficulty for him to meet your needs.

[…]

Very sincerely

[signed]

H. H. Burbank

Professor James W. Angell
Department of Economics
Columbia University
New York 27, New York

Source: Columbia University Rare Book and Manuscript Library. Department of Economics Collection, Box 6, Folder “Columbia College”

_____________________

 

Richard Murphey Goodwin

Address:                  7 Revere Street, Cambridge; E1 4-2981

Born:                        1913 in U.S.

Married:                  Yes

Degrees:

A. B. Harvard, 1934
B.A. Oxford, 1936
B. Litt. Oxford, 1937
A.M., Harvard, 1939
Ph.D. Harvard, 1941

Experience:         Annual Instructor, Harvard, 1939-46

Assistant Professor, Harvard, 1946-

Courses:               1937-38

Ec. 116 (Price Theory)           B+
Ec. 103a (Adv. Theory)         A
Ec. 121 (Statistics)                 A+, Exc.
Ec. 145 (Cycles)                      A, A
Ec. 4a (Math. Ec.)                  B+

1938-39

Ec.171 (Com. Dist)                 A

 

Fields of Study:   Theory, Ec. History, Statistics, Cycles; write-off, Commodity Distribution and Prices

Special Field:           Money and Banking

Thesis Topic:           Studies in Money; England and Wales, 1919 to 1938

Generals:                 Passed May 24, 1938 with grade of Good Plus

Specials:                  Passed May 22, 1941 with grade of Excellent Minus

Source: Columbia University Rare Book and Manuscript Library. Department of Economics Collection, Box 6, Folder “Columbia College”

 _____________________

Richard M. Goodwin – Bibliography

“The Supply of Bank Money in England and Wales, 1920-38”, Oxford Economic Papers, no. 5, 1941.

“Keynesian and Other Interest Theories,” Review of [Economic] Statistics, Vol. XXV, No. 1, February, 1943.

“Keynesian Economics,” a review of a book of Mabel Timlin, Review of Economic Statistics, Aug. 1944. Vol. XXVI.

“Innovations and the Irregularity of Economic Cycles,” Review of Economic Statistics, May 1946.

“Dynamical Coupling with Special Reference to Markets Having Production Lags,” Econometrica, July 1947.

“The Multiplier”, an article in the New Economics, edited by S. E. Harris, 1947.

“Secular and Cyclical Aspects of the Multiplier and the Accelerator,” a chapter in Income, Employment and Public Policy – Essays in Honor of Alvin Hansen, 1948.

“The Business Cycle as a Self Sustaining Mechanism,” a paper delivered befoe the Econmetric Society, December, 1948. Abstract published in Econometrica for April 1949.

“Liquidity and Uncertainty”, a discussion paper delivered at the Annual Meeting of the American Economic Association in Cleveland, December 1948. Published in the Proceedings of the convention.

“The Multiplier as Matrix” accepted for publication but not yet published by the Economic Journal of the Royal Economic Society.

A book, “Dynamic Economics”, now in preparation.

Source: Columbia University Rare Book and Manuscript Library. Department of Economics Collection, Box 6, Folder “Columbia College”

 _____________________

JOSEPH A. SCHUMPETER
7 Acacia Street
Cambridge 38, Massachusetts
December 3, 1949

Professor James W. Angell
Executive Officer
Department of Economics
Columbia University
New York 27, N.Y.

Private and confidential:

Dear Angell:

I greatly regret my inability to thank you, before leaving New York, for your hospitality and to have a chat with you. Now there is nothing confidential in this. What is strictly confidential however is a topic which I wished to bring up in that chat. The next year will terminate the five-year appointment of one of our best young men, Assistant Professor Richard Goodwin. According to our practice, the question of his promotion to permanent office is going to be discussed presently and I have no hope of securing a majority for him that the administration will consider adequate. This is not because any one has any fault to find with him personally but simply because other people have other candidates. You know how that is. Myself, I believe that Goodwin’s work in the field of dynamic models (and in particular four of his ten published articles) is of striking force and originality and also promises well for the future. In addition, I know that he is an excellent teacher. On the undergraduate level he runs personally and independently our biggest course, namely, the course on Money and Banking (But I do not count the general introductory course because it is run by sections). On the graduate level I have much admired his ability to express convey difficult material to an audience not really in command of the requisite technique. Therefore I am, myself, strongly in favor of promoting him but since I do not anticipate success I am anxious to sound you confidentially as regards possibilities at Columbia. An appointment might be combined with work at the National Bureau and would not therefore burden your budget very much immediately. Of course you will realize that the matter is strictly confidential but I would very much like to have your opinion.

Cordially yours,

[signed]
Joseph A. Schumpeter

JAS/jcs

[handwritten note by Schumpeter at bottom of page] I have talked to Burns

Source: Columbia University Rare Book and Manuscript Library. Department of Economics Collection, Box 6, Folder “Columbia College”

 _____________________

Image Source: Harvard Class of 1951 Yearbook.

Categories
Economists Harvard Research Tip

Harvard Economics. Schumpeter. Harvard Crimson. March 1, 1934

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”.

Categories
Economists Harvard Transcript

Harvard. Wolfgang Stolper’s Coursework. 1934-37

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)
[Taussig, Schumpeter]

Excused

Economics 51
[Business cycles and economic forecasting]

(1 course)
[Schumpeter]

A

Economics 1a1
[Introduction to economic statistics]

(½ course)
Frickey

A

Economics 10a1
[History of commerce, 1450-1750]

(½ course)
[Usher]

A

Economics 10b2
[History of industry and agriculture, 1450-1750]

(½ course)
[Usher]

A minus

Economics 31b2
[Theory of economic statistics]

(½ course)
[Crum]

Excused

1935-36

Mathematics A

(1 course)

C plus

Economics 121
[Monopolistic competition and allied problems in value theory]

(½ course)
[Chamberlin]

A minus

Economics 20
[Economic research]
(1 course)
Mason

A

1936-37

Economics 20
[Economic research]

(1½ courses)
Schumpeter

A

Economics 147a hf
[Seminar: Selected problems in money and banking]

(½ course)
[Harris]

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).

Categories
Chicago Courses Economists Exam Questions Syllabus

Chicago. Course Notes. Theory of Income and Employment. Marschak. 1948.

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.

Categories
Chicago Courses Economists Exam Questions

Chicago. Econ 332. Business Cycle Theory (Lange). Final Exam.1938

 

 

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

  1. State Say’s law and explain under what monetary conditions it does or does not hold good.
  2. (1) What definition of saving makes saving always equal to investment?
    (2) Indicate two definitions of saving such that saving may differ from investment and explain the meaning of this difference in each case.
    (3) Give two possible meanings of the term ‘hoarding.’
  3. Explain briefly Mr. Keynes’ doctrine concerning:
    (1) the effects on employment of a general and uniform change in money wages
    (2) the effects on total employment of relative changes in money wage rates
  4. Is there any theoretical justification for dividing the business cycle into four phases? Discuss the problem on hand of any theory of the business cycle you like to choose.

 

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.

 

Categories
Columbia Courses Economists Harvard Transcript

Columbia. Search Committee Report. 1950

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.

Categories
Columbia Courses Economists

Columbia. Course Descriptions. Hotelling. 1931-1945

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.

_________________________

[1931-32]

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.

 

[1932-33]

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.

 

[1933-34]

[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.

 

[1934-35]

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.

 

[1935-36]

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.

[1936-37]

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.

 

[1937-38]

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]

 

[1938-39]

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.

 

[1939-40]

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.

 

[1940-41]

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.

 

[1941-42]

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.

 

[1942-43]

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.

 

[1943-44]

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.

 

[1944-45]

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]

 

[1945-46]

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.

Categories
Columbia Economists

Columbia Economics. Mathematical Economics. Hotelling. Class Rolls 1931-1944

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).