Author: Irwin Collier

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

Post author By Irwin Collier
Post date 2015-07-17

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.

Tags Arrow, Domar, Marschak

Chicago Courses Economists Exam Questions

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

Post author By Irwin Collier
Post date 2015-07-16

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

State Say’s law and explain under what monetary conditions it does or does not hold good.
(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.’
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
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.

Tags Bronfenbrenner, Lange

Columbia Courses Economists Harvard Transcript

Columbia. Search Committee Report. 1950

Post author By Irwin Collier
Post date 2015-07-15

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.

Tags Alchian, Angell, Barger, Bronfenbrenner, Brownlee, Burbank, Christ, DeweyDJ, Duesenberry, Ellis, Friedman, Goodwin, Haig, Haley, Harberger, HartAG, Hoselitz, LewisHG, Machlup, Nicholls, Nutter, Pancoast, Schelling, Shoup, Stigler, TaylorH, Tobin, Vandermeulen

Columbia Courses Economists

Columbia. Course Descriptions. Hotelling. 1931-1945

Post author By Irwin Collier
Post date 2015-07-15

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.

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.

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.

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.

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]