Matemáticas Discretas: una perspectiva funcional con Python 3.x
Palabras clave:
Matemáticas, Algorítmos, Programación, Conjuntos, Lógica, Relaciones matemáticas, Funciones matemáticas, Teoría de Grafos, Mathematics, Algorithms, Programming, Python, Sets, Logic, Mathematical relations, Mathematical functions, Graph theorySinopsis
Matemáticas Discretas es una disciplina obligatoria en las Ciencias Computacionales. En este libro se propone un amplio conjunto de definiciones que son propias del área. Se abordan temas de Cálculo Proposicional, Lógica de Predicados, Conjuntos, Relaciones, Funciones y Teoría de Grafos; todos los temas se describen tanto en el lenguaje de matemáticas como en el lenguaje de programación Python 3.
Las definiciones que se ofrecen están escritas principalmente usando el lenguaje de programación Python. Se ha seleccionado este lenguaje de programación por diversas razones, entre estas, porque Python es un lenguaje de propósito general y multiparadigma. Escribir las definiciones matemáticas usando la sintaxis y semántica de Python, acerca a los programadores a la formalidad y abstracción matemática, y acerca a los matemáticos a la efectividad y eficiencia computacional.
Discrete Mathematics: A Functional Perspective with Python 3.x
Discrete mathematics is a compulsory discipline in the Computer Science. This book proposes a wide set of definitions that are specific to the area. It addresses Propositional Calculus, Predicate Logic, Sets, Relations, Functions, and Graph Theory. Every topic is described in mathematical language and Python 3.x programming language.
The definitions offered are mainly written using the Python programming language. This programming language has been selected for many reasons; one of them, because Python is a general purpose and multi-paradigm language. Redact mathematical definitions using Python syntax and semantics brings programmers closer to mathematical formality and abstraction, and mathematicians closer to computational effectiveness and efficiency
Citas
Abelson, H., Sussman, G. J., & Sussman, J. (1996). Structure and Interpretation of Computer Programs (2 ed., p. 657). MIT Press.
Benediktsson, O. (1978). Notes on Argument-parameter Association in Fortran. SIGPLAN Not., 13(1), 16–20. https://doi.org/10.1145/953428.953429
Bondy, J. A., & Murty, U. S. R. (1976). Graph Theory with Applications. North Holland. https://books.google.com.mx/books?id=4bwrAAAAYAAJ
Boole, G. (2009-06-11). The Mathematical Analysis of Logic: Being an Essay Towards a Calculus of Deductive Reasoning. Cambridge Univ PR. http://www.ebook.de/de/product/8770214/george_boole_the_mathematical_analysis_of_logic_being_an_essay_towards_a_calculus_of_deductive_reasoning.html
Chein, M., & Mugnier, M. L. (2009). Graph-Based Knowledge Representation: Computational Foundations of Conceptual Graphs (p. 427). Springer.
Church, A. (1936). An Unsolvable Problem of Elementary Number Theory. American Journal of Mathematics, 58, 345.
Church, A. (1941). The Calculi of Lambda Conversion. Princeton University Press.
Cocchiarella, N. B., & Freund, M. A. (2008). Modal Logic: An Introduction to its Syntax and Semantics. Oxford University Press. https://www.amazon.com/Modal-Logic-Introduction-Syntax-Semantics-ebook/dp/B001E5DW14?SubscriptionId=0JYN1NVW651KCA56C102&tag=techkie-20&linkCode=xm2&camp=2025&creative=165953&creativeASIN=B001E5DW14
Conradie, W., & Goranko, V. (2015). Logic and Discrete Mathematics. A Concise Introduction (p. 450). Wiley & Sons, Limited, John.
Copi, I. M., & Cohen, C. (2013). Introducción a la Lógica ((Español) 2). LIMUSA.
Cuevas Álvarez, A. (2016). Python 3: Curso Práctico. Ra-Ma.
Cunningham, D. W. (2016). Set Theory A First Course (p. 262). Cambridge University Press.
Dantzig, G., Fulkerson, R., & Johnson, S. (1954). Solution of a Large-Scale Traveling-Salesman Problem. Journal of the Operations Research Society of America, 2(4), 393–410. http://www.jstor.org/stable/166695It is shown that a certain tour of 49 cities, one in each of the 48 states and Washington, D. C., has the shortest road distance.
Dasgupta, A. (2014). Set Theory, With al Introduction to Real Points Sets (p. 444). Birkh auser.
Deo, N. (2016). Graph Theory with Applications to Engineering & Computer Science. Dover Publications, Inc.
Devlin, K. (2003). Sets, Functions, and Logic (p. 160). Chapman & Hall/CRC.
Erickson, M. J. (2009). Pearls of Discrete Mathematics (p. 270). CRC Press Taylor & Francis Group.
Euler, L. (2012-10). Lettres A Une Princesse D’Allemagne Sur Divers Sujets de Physique Et de Philosophie, Vol. 2. SARASWATI PR. https://www.ebook.de/de/product/20399536/leonhard_euler_lettres_a_une_princesse_d_allemagne_sur_divers_sujets_de_physique_et_de_philosophie_volume_2.html
Ferland, K. K. (2009). Discrete Mathematics An Introduction to Proofs and Combinatorics (p. 714). Houghton Mifflin Company.
Fernández de Castro, M., Preisser, A., Segura, L. F., & Torres Falcón, Y. (2004). Lógica Elemental. Universidad Autónoma Metropolitana. U. Iztapalapa.
Foundation, P. S. (2023). Python Documentation, version 3.11. https://docs.python.org/3/tutorial/classes.html?highlight=class
Garrido, M. (2001). Lógica Simbólica (4 ed., p. 540). Tecnos Grupo Anaya S.A.
Ghallab, M., Nau, D., & Traverso, P. (2004). Automated Planning: Theory & Practice (p. 635). Elsevier - Morgan Kaufmann.
Halmos, P. R. (1974). Naive Set Theory (p. 104). Springer Science+Business Media New York.
Hunt, J. (2020). A Beginners Guide to Python 3 Programming (p. 460). Springer.
Joyner, D. (2002). Adventures in Group Theory; Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys (p. 280). The Johns Hopkins University Press.
Kolman, B., & Busby, R. C. (1984). Estructuras de Matematicas Discretas para Computación (p. 441). Prentice Hall Hispanoamericana, S. A.
LaValle, S. M. (2009). Planning Algorithms. Cambridge University Press.
Lott, S. F. (2019). Mastering Object-Oriented Python (2 ed., p. 992). Packt Publishing.
Lyalin, D. (2020). Applying Euler Diagrams and Venn Diagrams to Concept Modeling. Business Rules Journal Newsletter, 21, 25p. https://www.brcommunity.com/articles.php?id=c021
Michel, A. N., & Herget, C. J. (1981). Applied Algebra and Functional Analysis. Dover Publications.
Muñoz Quevedo, J. M. (2002). Introducción a la Teoría de Conjuntos (p. 303). Universidad Nacional de Colombia.
O’Leary, M. L. (2016). A First Course in Mathematical Logic and Set Theory (p. 443). John Wiley & Sons, Inc.
Rautenberg, W. (2010-07-01). A Concise Introduction to Mathematical Logic. Springer New York. http://www.ebook.de/de/product/19205423/wolfgang_rautenberg_a_concise_introduction_to_mathematical_logic.html
Rendell, C. (2013). Network Topologies : Types, Performance Impact and Advantages/Disadvantages (p. 150). Nova Science Pub Inc.
Rosen, Kenneth. H. (2004). Matemática Discreta y sus Aplicaciones (5 ed., p. 860). McGraw-Hill.
Sainsbury, M. (2000-11-13). Logical Forms: An Introduction to Philosophical Logic (2 ed., p. 436). John Wiley and Sons Ltd. http://www.ebook.de/de/product/3769673/sainsbury_logical_forms.html
Smullyan, R. M. (2014). A Beginner’s Guide to Mathematical Logic. Dover Publications. https://books.google.com.mx/books?id=n6S-AwAAQBAJ
Sowa, J. F. (1991). Principles of Semantic Networks: Explorations in the Representation of Knowledge (p. 500). Morgan Kaufmann Pub.
Stoll, R. R. (1963). Set Theory and Logic (Republished 1979, p. 474). Dover Publications, Inc. New York.
Suppes, P., & Hill, S. (1992). Introducción a la Lógica Matemática (p. 281). Reverté.
Teller, P. (1989). A Modern Formal Logic Primer (Vol. 1). Prentice Hall.
Verblunsky, S. (1951). On the Shortest Path Through a Number of Points. Proceedings of the American Mathematical Society, 2(6), 904–913. http://www.jstor.org/stable/2031707
Descargas
Publicado
June 7, 2023
Categorías
Derechos de autor 2023 Universidad Juárez Autónoma de Tabasco
Licencia
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.
