653870
Description
Mind Map by monkey_prankss, updated more than 1 year ago
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Created by monkey_prankss
about 10 years ago
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Central role of discrete mathematics in information
technology and communications
- OBJECTIVE
- Familiarize students with main mathematical concepts
- Familiarize students with main mathematical concepts
- Computer
- finite structure= finite mathematics
- Language of predicate logic
- Logic & computers
- studies notions, judments and reasoning as well as the laws of correct reasoning
- formal language
- formulas
- formulas
- Intended meaning
- inferences
- inferences
- OBJETIVES
- systematization of what we do daily
- systematization of what we do daily
- APLICATIONS
- switching and logic networks, introduction to PROLOG , verification of correctness of computers programs
- switching and logic networks, introduction to PROLOG , verification of correctness of computers programs
- formal language
- PREDICATE LOGIC
- system of formal logic
- connevtives AND, OR, NOT, IMPLIES, EQUIVALENT and QUANTIFIERS
- associates a truth strcuture
- predicates are statements about objects, their properties and relationship with other objects
- only things can be arguments
- predicates are terms
- only things can be arguments
- predicates are statements about objects, their properties and relationship with other objects
- associates a truth strcuture
- connevtives AND, OR, NOT, IMPLIES, EQUIVALENT and QUANTIFIERS
- system of formal logic
- Fuzzy logic
- generalizes the classical (two-valued) logic and includes many valued logic
- make inferences from information that is imprecise, incomplete, uncertain or paryially true
- imprecise knowledge
- values of functions [ 0,1]
- indicates the degree of membership
- indicates the degree of membership
- values of functions [ 0,1]
- imprecise knowledge
- make inferences from information that is imprecise, incomplete, uncertain or paryially true
- theory of fuzzy subsets
- generalization of the usual sets theory
- contruction of membership
- reflects the context within the concrete problem is being studied
- reflects the context within the concrete problem is being studied
- contruction of membership
- generalization of the usual sets theory
- Random
- results from incertitude
- shows the existence of varios degrees of belonging
- shows the existence of varios degrees of belonging
- results from incertitude
- allows implementing approximat reasoning
- general knowledge
- general knowledge
- computationally simpler and faster than other
- philosophical view
- depends on the semantic interpretation of every fuzzy predicate
- capacity to model linguistic knowledge
- depends on the semantic interpretation of every fuzzy predicate
- generalizes the classical (two-valued) logic and includes many valued logic
- why do we need it ?
- Showing that a problem can be solved by a computer program
- translating problem description into a program language
- arguing that a computer is correct and efficient
- applying the new techniques of programming which require the mastery of different aspects of logic
- Showing that a problem can be solved by a computer program
- studies notions, judments and reasoning as well as the laws of correct reasoning
- Computer organization
- Computer program viewed as a formula
- has
- Formal syntax, proof rules
- Formal syntax, proof rules
- has
- Computer program viewed as a formula
- Logic & computers
- Integrated circuits, transistors,resistors,capacitors, and other electronic components
- transistors act as amplifiers or switches
- switches are combined to form logic gates
- bricks of implementation
- switches are combined to form logic gates
- transistors act as amplifiers or switches
- Boolean alegebra
- finite structure= finite mathematics
- IMPORTANCE
- Knowledge management,software engineering, programing languages/ data structures, hardware topics
- Knowledge management,software engineering, programing languages/ data structures, hardware topics
- GRAPHS & TREES
- Neural nets
- Interconnected assemblies of simple processing elements
- vertices: placed on ordered layers
- arrows: only between a vertex on layer l and a vertex on layer l+1, has weught (+ or -)
- arrows: only between a vertex on layer l and a vertex on layer l+1, has weught (+ or -)
- vertices: placed on ordered layers
- Interconnected assemblies of simple processing elements
- Semantic nets
- vertices: represent objects
- arrows: relationships between objects
- arrows: relationships between objects
- vertices: represent objects
- Bayesian
- acylic graphs
- vertex: represent a random variable
- arrow: conditional dependence
- arrow: conditional dependence
- vertex: represent a random variable
- acylic graphs
- Minimum spanning trees
- sub-graphs of weighted and connected graph
- contain all vertices
- contain all vertices
- sub-graphs of weighted and connected graph
- Binary trees
- mathematical & logical expressions
- possibly involving parentheses
- vertices : represent operators
- leaves: represent values
- leaves: represent values
- vertices : represent operators
- possibly involving parentheses
- mathematical & logical expressions
- Neural nets
- References
- Gersting,J., Mathematical Structures for Computer Science, Freeman& Cie,2003
- Hein,J.L., Discrete Mathematucs, Jones and Bartlett Publishers, 1996.
- Rosen,H.K,Discrete Mathematics,McGraw-Hill,2003
- Reghis,M.Roventa.E,Clasical and Fuzzy Concepsts in Mathematical Logic and Applications, CRCPress 1998
- Zadeh,L.A.,Probability Theory and Fuzzy Logic are Complementary rather than Competitive, Technometrics,August 1995, Vol.37,No.3
- Zadeh,L.A.,Toward a Generalized Theory of Uncertainty(GTU)-An Outline,Information Sciences,Elsevier,Vol.172,pp.1-40,2005
- Gersting,J., Mathematical Structures for Computer Science, Freeman& Cie,2003
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