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Stewart's theorem (plane geometry) Stinespring factorization theorem (operator theory) Stirling's theorem (mathematical analysis) Stokes's theorem (vector calculus, differential topology) Stolper–Samuelson theorem ; Stolz–Cesàro theorem ; Stone's representation theorem for Boolean algebras (mathematical logic)
The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.
This was stated and proved without attribution in Burnside's 1897 textbook, [6] but it had previously been discussed by Augustin Cauchy, in 1845, and by Georg Frobenius in 1887. Cayley–Hamilton theorem. The theorem was first proved in the easy special case of 2×2 matrices by Cayley, and later for the case of 4×4 matrices by Hamilton.
Euler's theorem; Five color theorem; Five lemma; Fundamental theorem of arithmetic; Gauss–Markov theorem (brief pointer to proof) Gödel's incompleteness theorem. Gödel's first incompleteness theorem; Gödel's second incompleteness theorem; Goodstein's theorem; Green's theorem (to do) Green's theorem when D is a simple region; Heine–Borel ...
It contains many important results in plane and solid geometry, algebra (books II and V), and number theory (book VII, VIII, and IX). [52] More than any specific result in the publication, it seems that the major achievement of this publication is the promotion of an axiomatic approach as a means for proving results.
It is traditionally divided into three topics: plane geometry (books 1–6), basic number theory (books 7–10) and solid geometry (books 11–13)—though book 5 (on proportions) and 10 (on irrational lines) do not exactly fit this scheme. [39] [40] The heart of the text is the theorems scattered throughout. [35]
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions ( theorems ) from these.
These treatises attempt to construct a rigorous foundation for calculus and use historical materialism to analyze the history of mathematics. Marx's contributions to mathematics did not have any impact on the historical development of calculus, and he was unaware of many more recent developments in the field at the time, such as the work of ...
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