AMathematical Primer On Computability

The Book Provides ASelfcontained Introduction To computability Theory For Advanced Undergraduate or Early Graduate Students Of Mathematics and Computer ScienceThe Technical Material is Illustrated With Plenty Of Examples, Problems with Fully Worked Solutions As Well As ARange Of proposed Exercises.part IIs Centered Around Fundamental computability Notions And Results, Starting With the Pillar Concepts Of Computational Model an abstract Highlevel Programming Language, computable Function, Decidable And Listable Set, proper Universal Function, Decision Problem and The Reduction Technique For Transferring decidability And Listability PropertiesThe essential Results Namely Rice?s Theorem, Riceshapiro?s Theorem, Riceshapiromcnaughtonmyhill?s Theorem As Well As Rogers?  Theorem and The Recursion Theorem Are Presented and IllustratedManytoone Reducibility And manytoone Degrees Are InvestigatedAShort introduction To Computation With Oracles Is Also includedComputable As Well As Noncomputable operators Are Introduced As Well As Monotonic and Finitary OperatorsThe  Relationship Between them Is Discussed, In Particular Via Myhillshepherdson?s TheoremKleene?s Least Fixed point Theorem Is Also PresentedFinally, part ITerminates With ABriefi Ng On The Turing computational Model, Turing Reducibility And turing Degrees.part Ii Of The Book Concentrates On Applications of Computability In Several Areas Namely In Logic undecidability Of Arithmetic, Satisfiability In propositional Logic, Decidability In Modal Logic, euclidean Geometry, Graphs And Kolmogorov complexityNevertheless No Previous Knowledge of These Subjects Is RequiredThe Essential Details for Understanding The Applications Are Provided.
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