Riemann dissertation

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Einstein struggled to get a job after his graduation, finally securing a post as ‘assistant examiner’ at the Federal Office for Intellectual Property in Bern. There he initiated a small group named the ‘Olympia Academy’ who got together to discuss science and philosophy. Einstein did his PhD in 1905 with his dissertation being called ‘A New Determination of Molecular Dimensions’. This year was called Einstein’s ‘Miracle Year’ as he not only achieved a PhD but also published four groundbreaking papers on ‘photoelectric effect’, ‘Brownian motion’, ‘special relativity’ and the ‘equivalence of matter and energy’ which brought him fame throughout the scientific world as a leading scientist.
He got the post of lecturer at the University of Bern in 1908 which he gave up for the position of physics docent at the University of Zurich. In 1911 he became a professor at Karl-Ferdinand University in Prague. On his return to Germany in 1914, Einstein was appointed the director of Kaiser Wilhelm Institute for Physics and a professor at the Humboldt University of Berlin. He was also a member of the Prussian Academy of Sciences and in 1916 the President of the German Physical Society. In 1921, he received the Nobel Prize for his contribution to Physics and the Copley Medal from the Royal Society in 1925.

Vygotsky was a pioneering psychologist and his major works span six separate volumes, written over roughly 10 years, from "Psychology of Art" (1925 but not published until 1960s) to "Thought and Language [or Thinking and Speech]" (1934). Vygotsky's interests in the fields of developmental psychology, child development, and education were extremely diverse. His philosophical framework includes insightful interpretations of the cognitive role of mediation tools, as well as the re-interpretation of well-known concepts in psychology such as internalization of knowledge. Vygotsky introduced the notion of zone of proximal development, an innovative metaphor capable of describing the potential of human cognitive development. His work covered such diverse topics as the origin and the psychology of art, development of higher mental functions, philosophy of science and methodology of psychological research, the relation between learning and human development, concept formation, interrelation between language and thought development, play as a psychological phenomenon, learning disabilities, and abnormal human development (aka defectology).

In Riemann's work there are many more interesting developments. He proved the functional equation for the zeta function (already known to Euler), behind which a theta function lies. Also, it gives a better approximation for the prime-counting function π ( x ) {\displaystyle \pi (x)} than Gauss's function L i ( x ) {\displaystyle Li(x)} . Through the summation of this approximation function over the non-trivial zeros on the line with real portion 1/2, he gave an exact, "explicit formula" for π ( x ) {\displaystyle \pi (x)} .

Riemann dissertation

riemann dissertation

In Riemann's work there are many more interesting developments. He proved the functional equation for the zeta function (already known to Euler), behind which a theta function lies. Also, it gives a better approximation for the prime-counting function π ( x ) {\displaystyle \pi (x)} than Gauss's function L i ( x ) {\displaystyle Li(x)} . Through the summation of this approximation function over the non-trivial zeros on the line with real portion 1/2, he gave an exact, "explicit formula" for π ( x ) {\displaystyle \pi (x)} .

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