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From Discrete Mathematics to AIFrom Discrete Mathematics to AI

applications:applications:A progression path for an undergraduateA progression path for an undergraduate

program in math program in math

Abdul HuqAbdul HuqMiddle East College of Information Technology, Sultanate ofMiddle East College of Information Technology, Sultanate of

OmanOmanhuq@mecit edu omhuq@mecit edu om

andand!arayanan T "amachandran!arayanan T "amachandran

Middle East College of Information Technology, Sultanate ofMiddle East College of Information Technology, Sultanate ofOmanOman

narayanan@mecit edu omnarayanan@mecit edu om

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A##roaches to AIA##roaches to AI

Can be approached in different ways..Can be approached in different ways..

AI as a branch of Computer ScienceAI as a branch of Computer Science

AI s strong lin!s with MathAI s strong lin!s with MathMay be thought of as Applied MathMay be thought of as Applied Math

Clarification of "heoretical issuesClarification of "heoretical issues

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AI and MathAI and Math

"he term AI has its roots in Math"he term AI has its roots in MathDominant role played by Mathematicians inDominant role played by Mathematicians inthe establishment of CS disciplines:the establishment of CS disciplines:Introduced by #ohn McCarthy$%rof. of Math$Introduced by #ohn McCarthy$%rof. of Math$Dartmouth CollegeDartmouth College

"here are Math departments with AI &roups"here are Math departments with AI &roups

'se of technology in traditionally strong'se of technology in traditionally strongMathematical sub(ectsMathematical sub(ects

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$ro#osed a##roach$ro#osed a##roach

MathModules

Computer ScienceModules

Discrete Mathand LogicFormalSpecificationAutomata &Formal Lang.

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Three essential as#ectsThree essential as#ects

fundamentalconcepts of AI

computational language conceptsthat support AI and

applications of AI

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Com#onent ma##ing %ith essentialCom#onent ma##ing %ith essentialas#ectsas#ects

fundamentalconcepts of AI

computational languageconcepts

that support AI and

applications of AI

&iscrete Math and 'ogic&iscrete Math and 'ogic

Automata ( )ormal 'angAutomata ( )ormal 'ang

)ormal S#ecification)ormal S#ecification$rolog$rolog

ExpertSystem

NaturalLang.Proces

sing

Automatic

!heoremPro"ing

#o$otics

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&iscrete Math&iscrete Math

Data StructuresData Structures

Discrete StructuresDiscrete Structures

) Sets) Sets ) Se*uences) Se*uences

) +elations) +elations

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'ogic'ogic

%ropositional ,ogic%ropositional ,ogic

%redicate ,ogic%redicate ,ogic

,ogics of higher order ,ogics of higher order Fu--y ,ogicFu--y ,ogic

'seful in nowledge +epresentation'seful in nowledge +epresentation

"here are researchers who consider logic as"here are researchers who consider logic asthe most important factor in de/elopingthe most important factor in de/elopingstrategic$ fundamental ad/ancesstrategic$ fundamental ad/ances

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*&M*&M

A formal specification languageA formal specification language

Specifies what needs to be doneSpecifies what needs to be done

rather than how it is to be donerather than how it is to be done

0ased on predicate logic0ased on predicate logic

'seful in program de/elopment and pro/ing'seful in program de/elopment and pro/ing

correctness of programscorrectness of programs

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$rolog$rolog

0ased on predicate logic0ased on predicate logic

A logic programming languageA logic programming language

Automatic "heorem %ro/ingAutomatic "heorem %ro/ingDe/eloped into a general purposeDe/eloped into a general purpose

programming language for AI applications programming language for AI applications

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ey Featuresey Features

nsure a firm understanding of the basic tools and techni*ues thatnsure a firm understanding of the basic tools and techni*ues thatare re*uired for AI applicationsare re*uired for AI applicationsInstill !nowledge in a spectrum of related sub(ectsInstill !nowledge in a spectrum of related sub(ectsncourage Creati/ity in the process of de/eloping solutions to ancourage Creati/ity in the process of de/eloping solutions to a/ariety of problems/ariety of problems

%ro/ide opportunities to con/ert comple2 scenarios into /arious%ro/ide opportunities to con/ert comple2 scenarios into /arioussol/able parts and identify a solution from a list of !nown optionssol/able parts and identify a solution from a list of !nown optionsIncrease ability to search for solutionsIncrease ability to search for solutionsDe/elop computational s!ills that are needed in the industryDe/elop computational s!ills that are needed in the industryDe/elop the ability to reason logically$ analytically and criticallyDe/elop the ability to reason logically$ analytically and critically

nsure that there is clear understanding of the role of AI specialistsnsure that there is clear understanding of the role of AI specialists%ro/ide the necessary s!ills to appreciate different AI concepts$ their%ro/ide the necessary s!ills to appreciate different AI concepts$ theiruse and rationaleuse and rationale

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Categories of modulesCategories of modules

3Fundamentals3Computation3 Applications

3General Education 3 Additional Modules3 Projects

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Categories of modules :Categories of modules : Fundamentals Fundamentals

&raph "heory&raph "heoryCombinatoricsCombinatoricsDiscrete MathDiscrete Math

,ogic,ogic4perating Systems4perating Systems4perations +esearch4perations +esearchIntroduction to AIIntroduction to AI

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Categories of modules :Categories of modules : ComputationComputation

Data StructuresData Structures

AlgorithmsAlgorithms

Formal SpecificationFormal Specification%rolog%rolog

"heory of computation"heory of computation

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Categories of modules :Categories of modules : Applications Applications

%attern +ecognition%attern +ecognition

2pert Systems2pert Systems

5atural ,anguage %rocessing 5atural ,anguage %rocessingAutomatic "heorem %ro/ingAutomatic "heorem %ro/ing

+obotics+obotics

Machine IntelligenceMachine Intelligence6uman Computer Interaction6uman Computer Interaction

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Categories of modules :Categories of modules : General EducationGeneral Education

nglishnglish

0iology0iology

%hilosophy%hilosophy%yschology%yschology

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Additional Modules Additional Modules

CalculusCalculusMathe. StatisticsMathe. Statistics

5umerical Methods 5umerical Methods

6ardware 5etwor!ing6ardware 5etwor!ingSystems SoftwareSystems SoftwareComputer ArchitectureComputer ArchitectureD0MSD0MS%hysics%hysicsComputer /isionComputer /isionFu--y set 7fu--y logicFu--y set 7fu--y logic

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Structure of the #rogrammeStructure of the #rogramme

Four year89 semester Four year89 semester

1 wee!s8sem1 wee!s8sem

5o. of modules;; 5o. of modules;;Credit points;;Credit points;;

2it points;;2it points;;

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$edagogy$edagogy

&roup wor! &roup wor! "as! based"as! based

ffort basedffort basedIndi/idual effortIndi/idual effortSelf studySelf study

0lend of theory and practice0lend of theory and practice2posure to real life problems2posure to real life problems

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'earning outcomes of the'earning outcomes of the#rogramme#rogramme

4n completion of the programme$ student will be4n completion of the programme$ student will beable to:able to:

Formulate AI problems MathematicallyFormulate AI problems MathematicallyApply standard Mathematical methodsApply standard Mathematical methods