Beale, R, and T Jackson, Neural Computing: An Introduction, Adam Hilger 1991 Jacket: '. . . starts from basics and goes on to cover all the most important approaches to the subject. . . . The capabilities, advantages and disadvantages of each model are discussed as are possible applications of each. The relationship of the models developed to the brain and its functions are also explored.' 
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Church, Alonzo, Introduction to Mathematical Logic, Princeton UP 1996 Jacket: 'One of the pioneers of mathematical logic in the twentieth century was Alobzo Church, He introduced such concepts as the lambda calculus, now an essential tool of computer science, and was the founder of the Journal of Symbolic Logic. In Introduction to Mathematical Logic, Church presents a masterful overview of the subject - one which should be read by every researcher and student of logic.' 
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Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. . . . The existence of absolutely unsolvable problems and the Goedel incompleteness theorem are among the results in the theory of computability that have philosophical significance.' 
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Davis, Phillip J, and Reuben Hersh, Descartes Dream: The World According to Mathematics, Penguin 1988 Preface: 'We are concerned with the impact mathematics makes when it is applied to the world that lies outside mathematics itself; when it is used in relation to the world of nature or of human activities. This is sometimes called applied mathematics. This activity has now become so extensive that we speak of the "mathematisation of the world." We want to know the conditions of civilisation that bring it about. We want to know when these applications are effective, when they are ineffective, when beneficial, dangerous or irrelevant. We want to know how they constrain our lives, how they transform our perception of reality.' 
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Davis, Martin, The Undecidable : Basic Papers on Problems Propositions Unsolvable Problems and Computable Functions, Raven Press 1965 Description: '[Includes] ... the basic papers of Gödel, Church, Turing, and Post in which the class of recursive functions was singled out and seen to be just the class of functions that can be computed by terminating processes. Also presented is the work of Church, Turing, and Post in which problems from the theory of abstract computing machines, from mathematical logic, and finally from algebra are shown to be unsolvable in the sense that there is no terminating process for dealing with them. Finally, the book presents the work of Kleene and of Post initiating the classification theory of unsolvable problems. Already the standard reference work on the subject, The Undecidable is also ideally suited as a text or supplementary text for courses in logic, philosophy, and foundations of mathematics.'  
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Frege, Gottlob, The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Nature of Number, Northwestern UP 1980 Jacket: 'The book represents the first philosophically sound discussion of the concept of number in Western civilisation. It influenced profoundly developments in the philosophy of mathematics, general ontology and mathematics.' 
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Hodges, Andrew, Alan Turing: The Enigma, Burnett 1983 Author's note: '. . . modern papers often employ the usage turing machine. Sinking without a capital letter into the collective mathematical consciousness (as with the abelian group, or the riemannian manifold) is probably the best that science can offer in the way of canonisation.' (530) 
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Weizenbaum, Joseph, Computer Power and Human Reason: from Judgement to Calculation, W H Freeman 1976 Jacket: '[This book] has fired enormous controversy and acclaim in America. Here JW, one of the world's top computer scientists, provides is with an insider's critique of computers: what they can already do, what they cannot do and, most controversially, what they should not be used to do. Should we, for example, be working toward the use of computers as substitutes for doctors or psychotherapists?' 
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Alan Turing, On Computable Numbers, with an application to the Entscheidungsproblem, 'The “computable” numbers may be described briefly as the real numbers whose expression: s as a decimal are calculable by finite means. Although the subject of this paper is ostensibly the computable numbers, it is almost equally easy to define and investigate computable functions of an integral variable or a real or computable variable, computable predicates, and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique.' back

Aquinas, Summa, I, 27, 2, Can any procession in God can be called generation?, 'I answer that, The procession of the Word in God is called generation. . . . the procession of the Word in God is generation; for He proceeds by way of intelligible action, which is a vital operation:--from a conjoined principle (as above described):--by way of similitude, inasmuch as the concept of the intellect is a likeness of the object conceived:--and exists in the same nature, because in God the act of understanding and His existence are the same, as shown above (14, 4). Hence the procession of the Word in God is called generation; and the Word Himself proceeding is called the Son.' back

Asymptotically optimal algorithm - Wikipedia, Asymptotically optimal algorithm - Wikipedia, the free encyclopedia, 'In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor (independent of the input size) worse than the best possible algorithm. It is a term commonly encountered in computer science research as a result of widespread use of big-O notation.' back

Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, 'Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties there is a point x₀ such that f(x₀) = x₀. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a convex compact subset K of Euclidean space to itself. back

Computer programming - Wikipedia, Computer programming - Wikipedia, the free encyclopedia, 'Computer programming (often shortened to programming or coding) is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a program that performs specific operations or exhibits a certain desired behavior. The process of writing source code often requires expertise in many different subjects, including knowledge of the application domain, specialized algorithms and formal logic.' back

Eigenfunction - Wikipedia, Eigenfunction - Wikipedia, the free encyclopedia, ' In mathematics, an eigenfunction of a linear operator, A, defined on some function space is any non-zero function f in that space that returns from the operator exactly as is, except for a multiplicative scaling factor. More precisely, one has Af = λf for some scalar, λ, the corresponding eigenvalue.' back

Hamilton's principle - Wikipedia, Hamilton's principle - Wikipedia, the free encyclopedia, 'In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action . . . It states that the dynamics of a physical system is determined by a variational problem for a functional based on a single function, the Lagrangian, which contains all physical information concerning the system and the forces acting on it.' back

Kurt Gödel I, On formally undecidable propositions of Principia Mathematica and related systems I, '1 Introduction The development of mathematics towards greater exactness has, as is well-known, lead to formalization of large areas of it such that you can carry out proofs by following a few mechanical rules. The most comprehensive current formal systems are the system of Principia Mathematica (PM) on the one hand, the Zermelo-Fraenkelian axiom-system of set theory on the other hand. These two systems are so far developed that you can formalize in them all proof methods that are currently in use in mathematics, i.e. you can reduce these proof methods to a few axioms and deduction rules. Therefore, the conclusion seems plausible that these deduction rules are sufficient to decide all mathematical questions expressible in those systems. We will show that this is not true, but that there are even relatively easy problem in the theory of ordinary whole numbers that can not be decided from the axioms. This is not due to the nature of these systems, but it is true for a very wide class of formal systems, which in particular includes all those that you get by adding a finite number of axioms to the above mentioned systems, provided the additional axioms don’t make false theorems provable.' back

Personally identifiable information - Wikipedia, Personally identifiable information - Wikipedia, the free encyclopedia, 'Personally Identifiable Information (PII), as used in information security, is information that can be used to uniquely identify, contact, or locate a single person or can be used with other sources to uniquely identify a single individual. The abbreviation PII is widely accepted, but the phrase it abbreviates has four common variants based on personal, personally, identifiable, and identifying. Not all are equivalent, and for legal purposes the effective definitions vary depending on the jurisdiction and the purposes for which the term is being used. Although the concept of PII is ancient, it has become much more important as information technology and the Internet have made it easier to collect PII, leading to a profitable market in collecting and reselling PII. PII can also be exploited by criminals to stalk or steal the identity of a person, or to plan a person's murder or robbery, among other crimes. As a response to these threats, many website privacy policies specifically address the collection of PII, and lawmakers have enacted a series of legislation to limit the distribution and accessibility of PII.' back

Transfinite numbers - Wikipedia, Transfinite numbers - Wikipedia, the free encyclopedia, 'Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite. Few contemporary workers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use.' back

Trinity - Wikipedia, Trinity - Wikipedia, the free encyclopedia, 'The Christian doctrine of the Trinity (from Latin trinitas "triad", from trinus "threefold") defines God as three consubstantial persons, expressions, or hypostases: the Father, the Son (Jesus Christ), and the Holy Spirit; "one God in three persons". The three persons are distinct, yet are one "substance, essence or nature" homoousios). In this context, a "nature" is what one is, while a "person" is who one is.' back