Central Role of Discrete Mathematics in IT&C

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Mapa Mental sobre Central Role of Discrete Mathematics in IT&C, criado por Marco Antonio Ar em 20-03-2014.
Marco Antonio Ar
Mapa Mental por Marco Antonio Ar, atualizado more than 1 year ago
Marco Antonio Ar
Criado por Marco Antonio Ar aproximadamente 10 anos atrás
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Resumo de Recurso

Central Role of Discrete Mathematics in IT&C
  1. Some applications of graphs and trees
    1. Neural nets (NN)
      1. Semantic Nets (SN)
        1. Bayesian (Causal) Networks (BN)
          1. Minimum Spanning Trees
            1. Binary Trees
              1. Compression of data using Huffman algorithm
                1. Creating a totally ordered list and searching items
                  1. The reverse Polish notation
                    1. Decision trees (DT)
                    2. Some Applications in ITC
                      1. Language of Predicate Logic Computer Organization
                        1. Knowledge Management
                          1. Database Systems
                            1. Software Engineering
                              1. Programming Languages/Data Structures
                                1. Programming Languages/Data Structures
                                  1. Hardware Topics
                                2. Boolean Algebra
                                  1. Computers are built up from integrated circuits
                                    1. transistors switches are combined to form logic gates
                                      1. theoretical basis for computer logic design
                                        1. Combinatorial circuits are circuits in which the results of an operation depend only of the present inputs to the operation
                                        2. Logic
                                          1. science that studies by means of mathematical tools the notions
                                            1. Two parts of formal logic
                                              1. Inferences (derivations of new formulas from old ones).
                                                1. Formulas (certain strings of symbols),
                                              2. Objectives of studying logic
                                                1. applications of formal logic in information technology
                                                  1. Switching and logic networks
                                                    1. Introduction to PROLOG a programming language based on logic
                                                      1. Verification of correctness of computer programs
                                                      2. Predicate logic
                                                        1. “and”, “or”, “not”, “implies”, “equivalent”
                                                        2. Fuzzy logic
                                                          1. Is a logical system that generalizes the classical (two-valued) logic and includes many-valued logic
                                                        3. Fuzzy Logic (FL) versus Probability Theory (PT)
                                                          1. PT is the theory of random events
                                                            1. PT does not support the concept of fuzzy event
                                                              1. PT offers no techniques for dealing with fuzzy quantifiers like many, most, several, few
                                                                1. PT does not provide a system for computing with fuzzy probabilities expressed as likely, unlikely, not very likely
                                                                  1. PT is not sufficient expressive as a meaningrepresentation language
                                                                    1. PT cannot handle some kind of approximate reasoning
                                                                    2. FL deals with the uncertainty resulting from the imprecision of meaning of a concept expressed by a linguistic term in a natural language
                                                                      1. The fuzzy logic inference is based not only on the structure of the statements
                                                                        1. The fuzzy logic inference is approximate
                                                                          1. Fuzzy logic is not a logic but an entire family
                                                                            1. Fuzzy logic is not complete.
                                                                              1. In fuzzy logic many partially inconsistent propositions can be derived.
                                                                                1. Fuzzy logic deals with fuzzy predicates
                                                                                  1. Fuzzy logic allows implementing approximate reasoning.
                                                                                2. Reference Eugene Roventa, & Tiberiu Spircu (2008). The central role of discrete mathematics in the context of information technology and communications, Retrieved from http://0-ieeexplore.ieee.org.millenium.itesm.mx/xpl/articleDetails.jsp?tp=&arnumber=4531270&contentType=Conference+Publications&searchField%3DSearch_All%26queryText%3Ddiscrete+mathematics

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