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]
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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.