Date of Award

4-1928

Degree Type

Bachelors Essay

Degree Name

Bachelor of Science (BS)

Department

Mathematical and Statistical Sciences

First Advisor

Harvey P. Pettit

Second Advisor

John McCormick

Abstract

Jacob Nicolaus Bernoulli (1654-1705) wrote a work on "Ars Conjectandi." It was published eight years after his death. The work consists of four parts. The second part is on permutations and combinations, which Bernoulli used in a proof of the binomial theorem for the case of positive integral exponents. The book contains a formula for the sum of the rth powers of the first n integers. This involves the famous Bernouillian numbers. Bernouilli boasted that by means of his formula he could calculate "Intra semi-quadrantem Horae" the sum of the 10th power: the first thousand integers.

Comments

A thesis submitted to partially fulfill the requirements for The Degree of Bachelor of Science, College of Liberal Arts, Marquette University, Milwaukee, Wisconsin.

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