Jacob Bernoulli (6 January 1655 to 16 August 1705) was a Swiss mathematician, whose given name is also written Jakob. He sided with Gottfried Wilhelm Leibniz in the Leibniz-Newton calculus controversy and was an early proponent of Leibnizian calculus, to which he made numerous contributions. A member of the Bernoulli family, he was, along with his brother Johann, one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant e, but his most important contribution was in probability, where he derived the first version of the law of large numbers in his work Ars Conjectandi.
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Jacob Bernoulli
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Source Bernoulli Distribution (Wikipedia)
Source Wikipedia: Bernoulli number
Source e (mathematical constant) (Wikipedia)
Source e (mathematical constant) (Wikipedia)
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Source Wikipedia: Jacob Bernoulli
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Source Jakob Hermann (Wikipedia)
Source Nicolaus I Bernoulli (Wikipedia)
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Source Bernoulli Distribution (Wikipedia)
Source Wikipedia: Bernoulli number
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Source Law of large numbers, Wikipedia
Source Law of large numbers, Wikipedia
Source Law of large numbers, Wikipedia
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1. Wikipedia: Jacob Bernoulli
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Jacob Bernoulli (6 January 1655
Lead
He sided with Gottfried Wilhelm Leibniz during the Leibniz-Newton calculus controversy and was an early proponent of Leibnizian calculus, to which he made numerous contributions.
View the SourceWikipedia: Bernoulli number
Principal Result: Bernoulli Number, Lead sentence of the article on the result
The Bernoulli numbers were discovered around the same time by the Swiss mathematician Jacob Bernoulli, after whom they are named, and independently by Japanese mathematician Seki Takakazu.
Attributed Works: Bernoulli Number, Lead
The Bernoulli numbers were discovered around the same time by the Swiss mathematician Jacob Bernoulli, after whom they are named, and independently by Japanese mathematician Seki Takakazu.
View the SourceBernoulli Distribution (Wikipedia)
Principal Result: Bernoulli Distribution, Lead sentence of the article on the result
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p {\displaystyle p} and the value 0 with probability q = 1 − p {\displaystyle q=1-p} .
Attributed Works: Bernoulli Distribution, Lead section
named after Swiss mathematician Jacob Bernoulli
View the SourceNicolaus I Bernoulli (Wikipedia)
Mentored: Nicolaus I Bernoulli, Body, teacherQuote, Mentored: Nicolaus I Bernoulli, Body, teacher
In 1704 he graduated from the University of Basel under Jakob Bernoulli and obtained his PhD five years later (in 1709) with a work on probability theory in law.
Jakob Hermann (Wikipedia)
Mentored: Jakob Hermann, Body, teacherQuote, Mentored: Jakob Hermann, Body, teacher
He received his mathematical training from Jacob Bernoulli at the University of Basel and graduated with a degree in 1695.
e (mathematical constant) (Wikipedia)
Wikimedia FoundationAttributed Works: e (Euler's Number), Lead
The Swiss mathematician Jacob Bernoulli introduced the constant while studying compound interest.
Attributed Works: Euler's Number, Lead
The Swiss mathematician Jacob Bernoulli introduced the constant while studying compound interest.
View the Source Law of large numbers, Wikipedia
Proofs Credited: Law of Large Numbers, Lead
A special form of the law of large numbers (for a binary random variable) was first proved by Jacob Bernoulli.
Proofs Credited: Weak Law of Large Numbers, Lead section
law of large numbers (for a binary random variable) was first proved by Jacob Bernoulli. It took him over 20 years to develop a sufficiently
Proofs Credited: Strong Law of Large Numbers, Lead section
law of large numbers (for a binary random variable) was first proved by Jacob Bernoulli. It took him over 20 years to develop a sufficiently
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