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reviews of books on logic and demonstration

Proofs and Logic in Solving Book Reviews are listed all the reviews posted on the web of the Mathematical Association of America (MAA Online ), under section Read This! - The MAA Online book review column on papers whose main theme revolves around logic and demonstration and related disciplines of mathematics, such as the theory to set . To find reviews on other topics in the field of study of mathematics, go to

subject index. Also noteworthy are the web

of MAA Online

, brief monthly columns (on the left drop down menu the portal of entry, are listed under "Publications, Columns "), written by various authors on all sorts of topics related to the broad universe of mathematics, such as Keith Devlin, the oldest of all published under the heading Devlin's Angle ; this author, and the issue of logic and deduction, has something interesting, as are the brief comments The mathematics of human Thought , Laws of Thought and

Are Mathematicians Turning Soft? , among others. Updated (07/01/2005): In this month's (January 2005), removed Last Doubts about the proof of the Four Color Theorem , K. Devlin realizes new contributions in the demonstration by computerized systems, the problem of Four Colors [1 ] [ 2 ] [3

], a classic in the field of deductive logic, the mathematical proof

, topology, and combinatorics, and gives an overview of the various conjectures raised this issue over time. This problem can be defined, briefly, by the following statement:

"In a plane or in an area not need more than four colors to color a map so that two neighboring regions, ie, that share a border and not just a point, are not colored the same color " [Source ] John McCarthy, one of the pioneers of Artificial Intelligence, analyzed, Article Coloring Maps and the Kowalski Doctrine

(1982), a program written in Prolog, and its underlying algorithms, which solved this problem by applying the methodology of logic programming to previous mathematical proofs, reached after the problem statement in the second half of the nineteenth century .