title: Quantum logic
Jordan operator algebra
MANIAC I
Henry Stapp
Mathematical Foundations of Quantum Mechanics
John von Neumann
John von Neumann Award
Direct integral
Von Neumann entropy
Grete Hermann
sentences: In quantum mechanics, quantum logic is a set of rules for reasoning about propositions that takes the principles of quantum theory into account.
 This research area and its name originated in a 1936 paper by Garrett Birkhoff and John von Neumann, who were attempting to reconcile the apparent inconsistency of classical logic with the facts concerning the measurement of complementary variables in quantum mechanics, such as position and momentum.
In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space.
 When the coefficients are real numbers, the algebras are called Jordan Banach algebras.
 The theory has been extensively developed only for the subclass of JB algebras.
 The axioms for these algebras were devised by .
 Those that can be realised concretely as subalgebras of self-adjoint operators on a real or complex Hilbert space with the operator Jordan product and the operator norm are called JC algebras.
 The axioms for complex Jordan operator algebras, first suggested by Irving Kaplansky in 1976, require an involution and are called JB* algebras or Jordan C* algebras.
 By analogy with the abstract characterisation of von Neumann algebras as C* algebras for which the underlying Banach space is the dual of another, there is a corresponding definition of JBW algebras.
 Those that can be realised using ultraweakly closed Jordan algebras of self-adjoint operators with the operator Jordan product are called JW algebras.
 The JBW algebras with trivial center, so-called JBW factors, are classified in terms of von Neumann factors: apart from the exceptional 27 dimensional Albert algebra and the spin factors, all other JBW factors are isomorphic either to the self-adjoint part of a von Neumann factor or to its fixed point algebra under a period two *-anti-automorphism.
 Jordan operator algebras have been applied in quantum mechanics and in complex geometry, where Koecher's description of bounded symmetric domains using Jordan algebras has been extended to infinite dimensions.
The MANIAC (Mathematical Analyzer, Numerical Integrator, and Computer" or Mathematical Analyzer, Numerator, Integrator, and Computer") was an early computer built under the direction of Nicholas Metropolis at the Los Alamos Scientific Laboratory.
 It was based on the von Neumann architecture of the IAS, developed by John von Neumann.
 As with all computers of its era, it was a one-of-a-kind machine that could not exchange programs with other computers (even other IAS machines).
 Metropolis chose the name MANIAC in the hope of stopping the rash of silly acronyms for machine names, although von Neumann may have suggested the name to him.
Henry Pierce Stapp (born March 23, 1928 in Cleveland, Ohio) is an American mathematical physicist, known for his work in quantum mechanics, particularly the development of axiomatic S-matrix theory, the proofs of strong nonlocality properties, and the place of free will in the "orthodox" quantum mechanics of John von Neumann.
The book Mathematical Foundations of Quantum Mechanics (1932) by John von Neumann is an important early work in the development of quantum theory.
John von Neumann ( ; Hungarian: "Neumann János Lajos" , ] ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, and computer scientist.
 He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, representation theory, operator algebras, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.
The John von Neumann Award, named after John von Neumann is given annually by the Rajk László College for Advanced Studies (Budapest, Hungary), to an outstanding scholar in the exact social sciences, whose works have had substantial influence over a long period of time on the studies and intellectual activity of the students of the college.
 The award was established in 1994 and is given annually.
 In 2013, separately from the annual prize, Kenneth J. Arrow was given the Honorary John von Neumann Award.
In mathematics and functional analysis a direct integral is a generalization of the concept of direct sum.
 The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras.
 The concept was introduced in 1949 by John von Neumann in one of the papers in the series "On Rings of Operators".
 One of von Neumann's goals in this paper was to reduce the classification of (what are now called) von Neumann algebras on separable Hilbert spaces to the classification of so-called factors.
 Factors are analogous to full matrix algebras over a field, and von Neumann wanted to prove a continuous analogue of the Artin–Wedderburn theorem classifying semi-simple rings.
In quantum statistical mechanics, the von Neumann entropy, named after John von Neumann, is the extension of classical Gibbs entropy concepts to the field of quantum mechanics.
 For a quantum-mechanical system described by a density matrix ρ , the von Neumann entropy is
Grete (Henry-)Hermann (March 2, 1901 – April 15, 1984) was a German mathematician and philosopher noted for her work in mathematics, physics, philosophy and education.
 She is noted for her early philosophical work on the foundations of quantum mechanics, and is now known most of all for an early, but long-ignored refutation of a "no-hidden-variable theorem" by John von Neumann.
 The disputed theorem and the fact that Hermann's critique of this theorem remained nearly unknown for decades are considered to have had a strong influence on the development of quantum mechanics.

Question: Question: The book Mathematical Foundations of Quantum Mechanics, released in which year, by John von Neumann? 

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Supporting Information: Paragraph 0 

 In quantum mechanics, quantum logic is a set of rules for reasoning about propositions that takes the principles of quantum theory into account.
 This research area and its name originated in a 1936 paper by Garrett Birkhoff and John von Neumann, who were attempting to reconcile the apparent inconsistency of classical logic with the facts concerning the measurement of complementary variables in quantum mechanics, such as position and momentum. 

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Paragraph 1 

 In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space.
 When the coefficients are real numbers, the algebras are called Jordan Banach algebras.
 The theory has been extensively developed only for the subclass of JB algebras.
 The axioms for these algebras were devised by .
 Those that can be realised concretely as subalgebras of self-adjoint operators on a real or complex Hilbert space with the operator Jordan product and the operator norm are called JC algebras.
 The axioms for complex Jordan operator algebras, first suggested by Irving Kaplansky in 1976, require an involution and are called JB* algebras or Jordan C* algebras.
 By analogy with the abstract characterisation of von Neumann algebras as C* algebras for which the underlying Banach space is the dual of another, there is a corresponding definition of JBW algebras.
 Those that can be realised using ultraweakly closed Jordan algebras of self-adjoint operators with the operator Jordan product are called JW algebras.
 The JBW algebras with trivial center, so-called JBW factors, are classified in terms of von Neumann factors: apart from the exceptional 27 dimensional Albert algebra and the spin factors, all other JBW factors are isomorphic either to the self-adjoint part of a von Neumann factor or to its fixed point algebra under a period two *-anti-automorphism.
 Jordan operator algebras have been applied in quantum mechanics and in complex geometry, where Koecher's description of bounded symmetric domains using Jordan algebras has been extended to infinite dimensions. 

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Paragraph 2 

 The MANIAC (Mathematical Analyzer, Numerical Integrator, and Computer" or Mathematical Analyzer, Numerator, Integrator, and Computer") was an early computer built under the direction of Nicholas Metropolis at the Los Alamos Scientific Laboratory.
 It was based on the von Neumann architecture of the IAS, developed by John von Neumann.
 As with all computers of its era, it was a one-of-a-kind machine that could not exchange programs with other computers (even other IAS machines).
 Metropolis chose the name MANIAC in the hope of stopping the rash of silly acronyms for machine names, although von Neumann may have suggested the name to him. 

--------------------------------

Paragraph 3 

 The book Mathematical Foundations of Quantum Mechanics (1932) by John von Neumann is an important early work in the development of quantum theory. 

--------------------------------

Paragraph 4 

 John von Neumann ( ; Hungarian: "Neumann János Lajos" , ] ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, and computer scientist.
 He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, representation theory, operator algebras, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics. 

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Paragraph 5 

 The John von Neumann Award, named after John von Neumann is given annually by the Rajk László College for Advanced Studies (Budapest, Hungary), to an outstanding scholar in the exact social sciences, whose works have had substantial influence over a long period of time on the studies and intellectual activity of the students of the college.
 The award was established in 1994 and is given annually.
 In 2013, separately from the annual prize, Kenneth J. Arrow was given the Honorary John von Neumann Award. 

--------------------------------

Paragraph 6 

 In mathematics and functional analysis a direct integral is a generalization of the concept of direct sum.
 The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras.
 The concept was introduced in 1949 by John von Neumann in one of the papers in the series "On Rings of Operators".
 One of von Neumann's goals in this paper was to reduce the classification of (what are now called) von Neumann algebras on separable Hilbert spaces to the classification of so-called factors.
 Factors are analogous to full matrix algebras over a field, and von Neumann wanted to prove a continuous analogue of the Artin–Wedderburn theorem classifying semi-simple rings. 

--------------------------------

Paragraph 7 

 In quantum statistical mechanics, the von Neumann entropy, named after John von Neumann, is the extension of classical Gibbs entropy concepts to the field of quantum mechanics.
 For a quantum-mechanical system described by a density matrix ρ , the von Neumann entropy is 

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Answer: 1932