From Discrete Mathematics to AI applications: A progression path for

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From Discrete Mathematics to AI applications:

A progression path for an undergraduate program in math

Abdul Huq

Middle East College of Information Technology, Sultanate of

Oman huq@mecit.edu.om

and

Narayanan T. Ramachandran

Middle East College of Information Technology, Sultanate of

Oman narayanan@mecit.edu.om

1

Approaches to AI

 Can be approached in different ways..

AI as a branch of Computer Science

AI’s strong links with Math

 May be thought of as Applied Math

 Clarification of Theoretical issues

2

AI and Math

 The term AI has its roots in Math

 Dominant role played by Mathematicians in the establishment of CS disciplines: Introduced by John McCarthy,Prof. of Math, Dartmouth

College

 There are Math departments with AI Groups

 Use of technology in traditionally strong

Mathematical subjects

3

Proposed approach

Math

Modules

Computer

Science

Modules

Discrete Math and Logic

Formal

Specification

Automata &

Formal Lang.

4

Three essential aspects

fundamental concepts of AI computational language concepts that support AI and applications of AI

5

Component mapping with essential aspects

fundamental concepts of AI computational language concepts that support AI and applications of AI

Discrete Math and Logic

Automata & Formal Lang.

Formal Specification

Prolog

Expert

System

Natural

Lang.

Proces sing

Automatic

Theorem

Proving

Robotics

6

Discrete Math

 Data Structures

 Discrete Structures

- Sets

- Sequences

- Relations

7

Logic

 Propositional Logic

 Predicate Logic

 Logics of higher order

 Fuzzy Logic

 Useful in Knowledge Representation

 There are researchers who consider logic as the most important factor in developing strategic, fundamental advances

8

VDM

 A formal specification language

 Specifies what needs to be done rather than how it is to be done

 Based on predicate logic

 Useful in program development and proving correctness of programs

9

Prolog

 Based on predicate logic

 A logic programming language

 Automatic Theorem Proving

 Developed into a general purpose programming language for AI applications

10

Key Features

Ensure a firm understanding of the basic tools and techniques that are required for AI applications

Instill knowledge in a spectrum of related subjects

Encourage Creativity in the process of developing solutions to a variety of problems

Provide opportunities to convert complex scenarios into various solvable parts and identify a solution from a list of known options

Increase ability to search for solutions

Develop computational skills that are needed in the industry

Develop the ability to reason logically, analytically and critically

Ensure that there is clear understanding of the role of AI specialists

Provide the necessary skills to appreciate different AI concepts, their use and rationale

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Categories of modules

Fundamentals

Computation

• Applications

• General Education

• Additional Modules

Projects

12

Categories of modules : Fundamentals

Graph Theory

Combinatorics

Discrete Math

Logic

Operating Systems

Operations Research

Introduction to AI

13

Categories of modules :

Computation

 Data Structures

 Algorithms

 Formal Specification

 Prolog

 Theory of computation

14

Categories of modules :

Applications

 Pattern Recognition

 Expert Systems

 Natural Language Processing

 Automatic Theorem Proving

 Robotics

 Machine Intelligence

 Human Computer Interaction

15

Categories of modules :

General Education

 English

 Biology

 Philosophy

 Pyschology

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Additional Modules

Calculus

Mathe. Statistics

Numerical Methods

Hardware Networking

Systems Software

Computer Architecture

DBMS

Physics

Computer vision

Fuzzy set &fuzzy logic

17

Structure of the programme

 Four year/8 semester

 15 weeks/sem

 No. of modules??

 Credit points??

 Exit points??

18

Pedagogy

 Group work

 Task based

 Effort based

 Individual effort

 Self study

 Blend of theory and practice

 Exposure to real life problems

19

Learning outcomes of the programme

On completion of the programme, student will be able to:

 Formulate AI problems Mathematically

 Apply standard Mathematical methods

 Write code to implement solution procedures

 Search for information in tackling advanced problems

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