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Précis of "The number sense"
"... Number sense " is a shorthand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence ..."
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Cited by 313 (25 self)
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of evidence suggesting that number sense constitutes a domainspecific, biologicallydetermined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence
A mental model for early arithmetic
 Journal of Experimental Psychology: General
, 1994
"... The authors examined young children's ability to solve nonverbal calculation problems in which they must determine how many items are in a hidden array after items have been added into or taken away from it. Earlier work showed that an ability to reliably solve such problems emerges earlier tha ..."
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Cited by 52 (6 self)
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The authors examined young children's ability to solve nonverbal calculation problems in which they must determine how many items are in a hidden array after items have been added into or taken away from it. Earlier work showed that an ability to reliably solve such problems emerges earlier
Validity Checking for Combinations of Theories with Equality
, 1996
"... . An essential component in many verification methods is a fast decision procedure for validating logical expressions. This paper presents the algorithm used in the Stanford Validity Checker (SVC) which has been used to aid several realistic hardware verification efforts. The logic for this decision ..."
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Cited by 163 (30 self)
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for this decision procedure includes Boolean and uninterpreted functions and linear arithmetic. We have also successfully incorporated other interpreted functions, such as array operations and linear inequalities. The primary techniques which allow a complete and efficient implementation are expression sharing
Some systems of second order arithmetic and their use
 in Proceedings of the International Congress of Mathematicians, Vancouver 1974
, 1975
"... The questions underlying the work presented here on subsystems of second order arithmetic are the following. What are the proper axioms to use in carrying out proofs of particular theorems, or bodies of theorems, in mathematics? What are those formal systems which isolate the essential principles ne ..."
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Cited by 48 (2 self)
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The questions underlying the work presented here on subsystems of second order arithmetic are the following. What are the proper axioms to use in carrying out proofs of particular theorems, or bodies of theorems, in mathematics? What are those formal systems which isolate the essential principles
Arithmetic Dynamical Systems
, 2000
"... The main objects of study in this thesis are Z d actions by automorphisms of compact abelian groups, which arise in a natural arithmetic setting. In particular, to a countable integral domain D and units 1 ; : : : ; d 2 D we associate a Z d action by automorphisms of the compact abelian ..."
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Cited by 7 (5 self)
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The main objects of study in this thesis are Z d actions by automorphisms of compact abelian groups, which arise in a natural arithmetic setting. In particular, to a countable integral domain D and units 1 ; : : : ; d 2 D we associate a Z d action by automorphisms of the compact abelian
Register Organization for Media Processing
 HPCA6
, 2000
"... Processor architectures with tens to hundreds of arithmetic units are emerging to handle media processing applications. These applications, such as image coding, image synthesis, and image understanding, require arithmetic rates of up to 10 11 operations per second. As the number of arithmetic uni ..."
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Cited by 126 (11 self)
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Processor architectures with tens to hundreds of arithmetic units are emerging to handle media processing applications. These applications, such as image coding, image synthesis, and image understanding, require arithmetic rates of up to 10 11 operations per second. As the number of arithmetic
Numbers and Arithmetic: Neither Hardwired Nor Out There
, 2009
"... What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions fo ..."
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the inferential organization of the properties and “laws ” of arithmetic emerge metaphorically from everyday meaningful actions. Numbers and arithmetic are thus—outside of natural selection—the product of the biologically constrained interaction of individuals with the appropriate cultural and historical
Query Languages with Arithmetic and Constraint Databases
"... Can we store an innite set in a database? Clearly not, but instead we can store a nite representation of an innite set and write queries as if the entire in nite set were stored. This is the key idea behind constraint databases, which emerged relatively recently as a very active area of database res ..."
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Can we store an innite set in a database? Clearly not, but instead we can store a nite representation of an innite set and write queries as if the entire in nite set were stored. This is the key idea behind constraint databases, which emerged relatively recently as a very active area of database
Hanoi lectures on the arithmetic of hyperelliptic curves
, 2012
"... Manjul Bhargava and I have recently proved a result on the average order of the 2Selmer groups of the Jacobians of hyperelliptic curves of a fixed genus n ≥ 1 over Q, with a rational Weierstrass point [2, Thm 1]. A surprising fact which emerges is that the average order of this finite group is equa ..."
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Cited by 2 (1 self)
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Manjul Bhargava and I have recently proved a result on the average order of the 2Selmer groups of the Jacobians of hyperelliptic curves of a fixed genus n ≥ 1 over Q, with a rational Weierstrass point [2, Thm 1]. A surprising fact which emerges is that the average order of this finite group
HighPrecision Arithmetic: Progress and Challenges
"... For many scientific calculations, particularly those involving empirical data, IEEE 32bit floatingpoint arithmetic produces results of sufficient accuracy, while for other applications IEEE 64bit floatingpoint is more appropriate. But for some very demanding applications, even higher levels of p ..."
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Cited by 1 (0 self)
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For many scientific calculations, particularly those involving empirical data, IEEE 32bit floatingpoint arithmetic produces results of sufficient accuracy, while for other applications IEEE 64bit floatingpoint is more appropriate. But for some very demanding applications, even higher levels
Results 1  10
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