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At the time structures such as Lie algebras and hyperbolic quaternions drew attention to the need to expand algebraic structures beyond the associatively multiplicative class. In a review Alexander Macfarlane wrote: "The main idea of the work is not unification of the several methods, nor generalization of ordinary algebra so as to include them, but rather the comparative study of their several structures." In a separate review, G. B. Mathews wrote, "It possesses a unity of design which is really remarkable, considering the variety of its themes."

What did Lie algebras and hyperbolic quaternions demonstrate a need for?
Answer: the need to expand algebraic structures beyond the associatively multiplicative class
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In the 1820s, Boston's population grew rapidly, and the city's ethnic composition changed dramatically with the first wave of European immigrants. Irish immigrants dominated the first wave of newcomers during this period, especially following the Irish Potato Famine; by 1850, about 35,000 Irish lived in Boston. In the latter half of the 19th century, the city saw increasing numbers of Irish, Germans, Lebanese, Syrians, French Canadians, and Russian and Polish Jews settled in the city. By the end of the 19th century, Boston's core neighborhoods had become enclaves of ethnically distinct immigrantsItalians inhabited the North End, Irish dominated South Boston and Charlestown, and Russian Jews lived in the West End. Irish and Italian immigrants brought with them Roman Catholicism. Currently, Catholics make up Boston's largest religious community, and since the early 20th century, the Irish have played a major role in Boston politicsprominent figures include the Kennedys, Tip O'Neill, and John F. Fitzgerald.

What was the estimated population of Irish people living in Boston in 1850?
Answer: about 35,000
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The company originated in 1911 as the Computing-Tabulating-Recording Company (CTR) through the consolidation of The Tabulating Machine Company, the International Time Recording Company, the Computing Scale Company and the Bundy Manufacturing Company. CTR was renamed "International Business Machines" in 1924, a name which Thomas J. Watson first used for a CTR Canadian subsidiary. The initialism IBM followed. Securities analysts nicknamed the company Big Blue for its size and common use of the color in products, packaging and its logo.

What does IBM stand for?
Answer:
International Business Machines