In 1881 the American philosopher Charles S. Peirce published a remarkable paper in The American Journal of Mathematics called “On the Logic of Number.” Peirce’s paper marked a watershed in nineteenth century mathematics, providing the first successful axiom system for the natural numbers. Awareness that Peirce’s axiom system exists has been gradually increasing but the conventional wisdom among mathematicians is still that the first satisfactory axiom systems were those of Dedekind and Peano. The book analyzes Peirce's paper in depth, placing it in the context of contemporary work, and provides a proof of the equivalence of the Peirce and Dedekind axioms for the natural numbers.

Charles S. Peirce on the Logic of Number

Science & Math

Shields, Paul

Mathematics

Docent Press

<p>The Bible appears to teach that suffering is inevitable; but does suffering originate with, or glorify God? Should enduring chronic sickness be considered an essential part of such suffering? And while God may use it as a punishment to unbelievers and the willfully disobedient, does He send it upon Christians, or should we consider it as being primarily from a diabolical source? Is there a tension between receiving divine healing by faith and relying on medical and surgical means? Is there a reason to expect that healing should occur in a miraculous and instantaneous fashion through a spoken word or a touch, in a similar manner to the healing accounts recorded in the New Testament? A Question of Healing attempts an answer to these fundamental questions about suffering and healing before examining how this theology in turn dictates the practices of those churches and organisations that are engaged in the Christian healing ministry and how the healing ministry operates within local churches, dependent upon those church's beliefs. Paul Shields then goes on to identify some hindrances to healing by addressing further questions such as, What are the issues that limit the success of our healing ministries? How does the attitude of a sick individual hinder or prevent a healing taking place? Is it usually God's will to bring healing or not? A Question of Healing of necessity takes a look at the pastoral problem associated with an individual not being healed, despite the attempts, the faith and often the pronouncements, of the faithful, before finally asking the question: Has the Church uniquely offended the person of the Holy Spirit such that certain of the gifts that He bestows have been effectively withheld? If so, can this condition be restored through renunciation and repentance?The book includes a number of personal testimonies of healing that illustrate the theological arguments being made and also seeks to answers questions such as:Was Jesus ever sick? Did Jesus pray for the sick or simply deal with the disease? Does God deal with injuries differently than sicknesses and diseases?</p>

A Question of Healing: The Failure of Christian Healing?

Religion & Spirituality

Malcolm Down Publishing Limited

Information Theory and Statistics: A Tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an "information geometry" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory. The tutorial does not assume the reader has an in-depth knowledge of Information Theory or statistics. As such, Information Theory and Statistics: A Tutorial, is an excellent introductory text to this highly-important topic in mathematics, computer science and electrical engineering. It provides both students and researchers with an invaluable resource to quickly get up to speed in the field.

Information Theory and Statistics: A Tutorial (Foundations and Trends in Communications and Information The)

Computers & Technology

Csiszár, Imre

Csisz4ar, Imre

Computer Science

Now Publishers

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