40473_Historia_Matematicas

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UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO 
PROGRAMA ÚNICO DE ESPECIALIZACIONES EN CIENCIAS 
BIOLÓGICAS, FÍSICAS Y MATEMÁTICAS 
ESPECIALIZACIÓN EN MATEMÁTICAS PARA EL BACHILLERATO 
Facultad de Ciencias 
Programa de Actividad académica 
 
Denominación: Historia de las Matemáticas 
Clave: 40473 Semestre: 1 No. Créditos: 6 
Carácter: Obligatorio Horas 
Horas por 
semana 
Horas al 
semestre 
Tipo: Teórica 
Teoría: Práctica: 
3 48 
3 0 
Modalidad: Curso Duración del programa: Semestral 
 
Seriación: No ( X ) Si ( ) Obligatoria ( ) Indicativa ( ) 
Actividad Académica Antecedente: Ninguna 
Actividad Académica Subsecuente: Ninguna 
Objetivo general: 
El alumno comprenderá las ideas, métodos y resultados importantes en el desarrollo de las matemáticas 
a lo largo de la historia. 
Objetivos específicos: 
 Que el participante conozca el desarrollo histórico de algunos de los conceptos y métodos del 
pensamiento matemático. 
 Que el participante valore la importancia de la historia de las matemáticas como instrumento de 
aprendizaje de las matemáticas. 
 Que el participante conozca el uso de las matemáticas como motor del desarrollo cultural y 
material de la humanidad. 
 
Índice temático 
Unidad Tema 
Horas 
Teóricas Prácticas 
1 
Matemáticas griegas 
9 0 
2 
Matemáticas árabes y matemáticas en el Medievo latino 
6 0 
3 
Las matemáticas en el Renacimiento europeo 
6 0 
4 
Las nuevas matemáticas del siglo XVII 
6 0 
5 
El cálculo: tangentes y cuadraturas en el siglo XVII 
12 0 
6 
Geometrías no-euclidianas 
6 0 
7 
Teoría de los conjuntos y fundamentos de las matemáticas 
3 0 
Total de horas: 48 0 
Suma total de horas: 48 
 
Contenido Temático 
Unidad Tema y subtemas 
1 Matemáticas griegas 
1.1 Lógica y matemáticas en Zenón, Platón y Aristóteles 
1.2 Euclides y los Elementos 
1.3 Arquímedes y el método heurístico. El área de la parábola. Ley de la palanca, 
corona de Herón 
1.4 La Aritmética de Diofanto 
1.5 Las Cónicas de Apolonio 
1.6 Geometría, trigonometría y los movimientos planetarios. El caso de Ptolomeo 
2 Matemáticas árabes y matemáticas en el Medievo latino 
2.1 El desarrollo del álgebra: al-Khwarismi y Omar al-Khayyam 
2.2 Las escuelas de ábaco y las matemáticas de los comerciantes 
 
3. Las matemáticas en el Renacimiento europeo 
3.1 Las leyes de la perspectiva de los pintores 
3.2 Los abacistas italianos 
3.3 Solución de ecuaciones: cuadráticas, cúbicas, cuárticas: Tartaglia, Bombelli, 
Cardano 
3.4 El álgebra de Viète y de Stevin. Concepto de número 
4 Las nuevas matemáticas del siglo XVII 
4.1 Fermat, Descartes y el arte analítico. La Geometría 
4.2 Fermat, Mersenne y el renacimiento de la teoría de los números 
4.3 Desargues y la geometría proyectiva 
5 El cálculo: tangentes y cuadraturas en el siglo XVII 
5.1 El método de los indivisibles: Kepler, Cavallieri, Torricelli, Barrow y Newton 
5.2 Tangentes, áreas, volúmenes, series de potencias: Fermat, Wallis, Newton, 
L`Hospital 
5.3 El cálculo diferencial e integral de Newton y Leibniz 
6 Geometrías no-euclidianas 
6.1 Contribuciones de Gauss, Bolya y Lovachevsky 
7 Teoría de los conjuntos y fundamentos de las matemáticas 
7.1 Conjuntos y aritmética: Frege, Cantor y Dedekind 
7.2 El infinito matemático 
 
Bibliografía básica: 
 al-Khuwarizm, Muhammad ibn Musa. The Algebra of Mohammed ben Musa.Adamant Media 
Corporation, 2002. 
 Artmann, B. Euclid, the Creation of Mathematics, New York: Springer Verlag, 1999. 
 Aspray, William and Philip Kitcher. History and Philosophy of Modern Mathematics Greek 
Mathematical Works. (Loeb Classical Library No. 335). Ivor Thomas (trans.) Cambridge: Harvard 
University Press, 1957. 
 (Minnesota Studies in the Philosophy of Science). Univ. of Minnesota Press, 1988. 
 Baron, Margareth E. The Origins of the Infinitesimal Calculus. Dover, 2004. 
 Bos, H. J. Lectures in the History of Mathematics. (History of Mathematics Series). Providence, 
RI: American Mathematical Society, 1993. 
 Bos, Henk. Redefining Geometrical Exactness: Descartes' Transformation of the Early Modern 
Concept of Construction. Springer, 2001. 
 Boyer, Carl B., The History of Calculus and its Conceptual Development, New York: Dover, 1959. 
 Boyer, Carl B., History of Analytic Geometry, Princeton: The Scholar’s Bookshelf, 1988. 
 Boyer, Carl B., Uta C. Merzbach. A History of Mathematics, Wiley, 2011. 
 Burton, David. The History of Mathematics: An Introduction. McGraw-Hill Science, 2010. 
 Edwards, C. H., The Historical Development of the Calculus, New York: Springer Verlag, 1979. 
 Fauvel, John and J.A. van Maanen. History in Mathematics Education - An ICMI Study (New 
ICMI Study Series Volume 6). Springer, 2000. 
 Ferreirós, José. Labyrinth of Thought: A History of Set Theory and Its Role in Modern 
Mathematics, 2nd edition. Birkhäuser Basel, 2007. 
 Field, J. V., The Invention of Infinity. Mathematics and Art in the Renaissance, Oxford: Oxford 
University Press, 1997. 
 Katz, V., A History of Mathematics, an Introduction, New York: Harper Collins College Publishers, 
1998. 
 Knorr, W., Textual Studies in Ancient and Medieval Geometry, Boston: Birkhäuser, 1989. 
 Kwarizmi, al- The Algebra of Mohammed Ben Musa. [1831]. The Elibron Classics, 2005. 
 Miguel, P., González, U., Las Raíces del Cálculo Infinitesimal en el Siglo XVII, Madrid: Alianza 
Editorial, 1992. 
 Rosenfeld, Boris A. A History of Non-Euclidean Geometry. Springer, 1988. 
 Rashed, Roshdi (Editor). Al-Khwarizmi: The Beginnings of Algebra (History of Science and 
Philosophy in Classical Islam). Saqi Books, 2010. 
 Sasak, C. Descartes's Mathematical Thought (Boston Studies in the Philosophy of 
http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&sort=relevancerank&search-alias=books&ie=UTF8&field-author=Muhammad%20ibn%20Musa%20al-Khuwarizmi
http://library.nu/docs/3KFM58JXDE/History%20and%20Philosophy%20of%20Modern%20Mathematics%20%28Minnesota%20Studies%20in%20the%20Philosophy%20of%20Science%29
http://library.nu/docs/3KFM58JXDE/History%20and%20Philosophy%20of%20Modern%20Mathematics%20%28Minnesota%20Studies%20in%20the%20Philosophy%20of%20Science%29
http://library.nu/docs/3KFM58JXDE/History%20and%20Philosophy%20of%20Modern%20Mathematics%20%28Minnesota%20Studies%20in%20the%20Philosophy%20of%20Science%29
http://library.nu/docs/3KFM58JXDE/History%20and%20Philosophy%20of%20Modern%20Mathematics%20%28Minnesota%20Studies%20in%20the%20Philosophy%20of%20Science%29
http://www.amazon.com/s/ref=ntt_athr_dp_sr_2?_encoding=UTF8&sort=relevancerank&search-alias=books&ie=UTF8&field-author=J.A.%20van%20Maanen
http://library.nu/docs/KUMGZWS04L/History%20in%20Mathematics%20Education%20-%20An%20ICMI%20Study%20%28New%20ICMI%20Study%20Series%20Volume%206%29
http://library.nu/docs/KUMGZWS04L/History%20in%20Mathematics%20Education%20-%20An%20ICMI%20Study%20%28New%20ICMI%20Study%20Series%20Volume%206%29
http://library.nu/docs/R9ES0UTP7Z/Labyrinth%20of%20Thought%3A%20A%20History%20of%20Set%20Theory%20and%20Its%20Role%20in%20Modern%20Mathematics
http://library.nu/docs/R9ES0UTP7Z/Labyrinth%20of%20Thought%3A%20A%20History%20of%20Set%20Theory%20and%20Its%20Role%20in%20Modern%20Mathematics
http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&sort=relevancerank&search-alias=books&ie=UTF8&field-author=Roshdi%20Rashed
http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&sort=relevancerank&search-alias=books&ie=UTF8&field-author=C.%20Sasaki
Science). Springer, (2004) 2010. 
 Waerden, B. L. van der, Science Awakening, Amsterdam: Noordhoff, 1954. 
 
Bibliografía complementaria: 
 Aaboe, Asger. Episodes from the Early History of Mathematics (New Mathematical Library 13). 
The Mathematical Association of America, 1997. 
 Dahan-Dalmédico, Amy, Jeanne Peiffer. History of Mathematics: Highways and Byways 
(Spectrum). Mathematical Association of America, 2009. 
 Donovan,M. Suzanne and John D. Bransford, (eds.). How Students Learn: History, 
Mathematics, and Science in the Classroom. Committee on How People Learn. A Targeted 
Report for Teachers, Center for Studies on Behavior and Development, National Research. 
National Academies Press, 2005. 
 Graviner, Judith V. The Origins of Cauchy's Rigorous Calculus. Dover, 2011. 
 Gray, Jeremy. Worlds Out of Nothing: A Course in the History of Geometry in the 19
th
 Century, 
Second Edition (Springer Undergraduate Mathematics Series). Springer, 2010. 
Hodgkin, Luke. A History of Mathematics: From Mesopotamia to Modernity. Oxford University 
Press, USA, 2005. 
 Hoffman, Johan, Claes Johnson, Anders Logg. Dreams of Calculus: Perspectives on 
Mathematics Education. Springer, 2004. 
 Kline, M., El Pensamiento Matemático de la Antigüedad a Nuestros Días, 3 volúmenes. Madrid: 
Alianza Editorial, 1992. 
 Kerkhove, Bart Van. New Perspectives on Mathematical Practices: Essays in Philosophy and 
History of Mathematics, Brussels, Belgium, 26-28 March 2007.World Scientific Publishing 
Company, 2009. 
 Mahoney, M., The Mathematical Career of Pierre de Fermat (1601-1665), Princeton: Princeton 
University Press, 1994. 
 Malet, A., From Indivisibles to Infinitesimals Studies in Seventeenth-Century Mathematization of 
Infinitely Small Quantities, Bellaterra (Barcelona): Universitat Autònoma de Barcelona, 1996. 
 Maor, E., To Infinity and Beyond. A Cultural History of the Infinity, Princeton: Princeton University 
Press, 1991. 
 Martín Casalderrey, Fco. Cardano y Tartaglia. Las matemáticas en el Renacimiento italiano. 
Madrid: Nivola, 2000. 
 Moreno Castillo, Ricardo. Omar Jayyam. Poeta y matemático. Madrid: Nivola, 2002. 
 Nahin, P. J., An Imaginary Tale, the Story of (-1), Princeton, New Jersey: Princeton University 
Press, 1998. 
 Shea ,W. R., The Magic of Numbers and Motion. The Scientific Career of René Descartes, 
Canton, MA: Science History Pub., 1991. 
 Singh, S., Fermat’s Last Theorem, London: Fourth State, 1997. 
 Sedall, Jacqueline. From Cardano's Great Art to Lagrange's Reflections: Filling a Gap in the 
History of Algebra. European Mathematical Society, 2011. 
 Stillwell John. Mathematics and Its History (Undergraduate Texts in Mathematics), 3rd ed. 
http://library.nu/docs/GMK3ZTCSDR/Episodes%20from%20the%20Early%20History%20of%20Mathematics%20%28New%20Mathematical%20Library%2013%29
http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&sort=relevancerank&search-alias=books&ie=UTF8&field-author=Amy%20Dahan-Dalm%26%23233%3Bdico
http://www.amazon.com/s/ref=ntt_athr_dp_sr_2?_encoding=UTF8&sort=relevancerank&search-alias=books&ie=UTF8&field-author=Jeanne%20Peiffer
http://library.nu/docs/BOTY3DRM4C/Worlds%20Out%20of%20Nothing%3A%20A%20Course%20in%20the%20History%20of%20Geometry%20in%20the%2019th%20Century%2C%20Second%20Edition%20%28Springer%20Undergraduate%20Mathematics%20Series%29
http://library.nu/docs/BOTY3DRM4C/Worlds%20Out%20of%20Nothing%3A%20A%20Course%20in%20the%20History%20of%20Geometry%20in%20the%2019th%20Century%2C%20Second%20Edition%20%28Springer%20Undergraduate%20Mathematics%20Series%29
http://library.nu/docs/4PWSNY30G8/A%20History%20of%20Mathematics%3A%20From%20Mesopotamia%20to%20Modernity
http://www.amazon.com/s/ref=ntt_athr_dp_sr_2?_encoding=UTF8&sort=relevancerank&search-alias=books&ie=UTF8&field-author=Claes%20Johnson
http://www.amazon.com/s/ref=ntt_athr_dp_sr_3?_encoding=UTF8&sort=relevancerank&search-alias=books&ie=UTF8&field-author=Anders%20Logg
http://library.nu/docs/S1OAUWTI4F/New%20Perspectives%20on%20Mathematical%20Practices%3A%20Essays%20in%20Philosophy%20and%20History%20of%20Mathematics%2C%20Brussels%2C%20Belgium%2C%2026-28%20March%202007
http://library.nu/docs/S1OAUWTI4F/New%20Perspectives%20on%20Mathematical%20Practices%3A%20Essays%20in%20Philosophy%20and%20History%20of%20Mathematics%2C%20Brussels%2C%20Belgium%2C%2026-28%20March%202007
http://library.nu/docs/TYLKC049M5/Mathematics%20and%20Its%20History%20%28Undergraduate%20Texts%20in%20Mathematics%29
Edition. Springer, 2010. 
 Swetz, F. J., Capitalism and Arithmetic. The New Mathematics of the 15
th
 Century (The Treviso 
Arithmetic, 1478), Lasalle: Open Court, 1989. 
 Szabo, A., The Beginnings of Greek Mathematics, Budapest: Akademiai Kiado, 1978. 
 Tabak, John. Mathematics and the Laws of Nature: Developing the Language of Science (The 
History of Mathematics). Facts on File Math Library, 2004. 
 Tabak, John. Geometry: The Language of Space and Form (History of Mathematics) Facts on 
File Math Library, 2011. 
 Van Heijenoort, J. From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931, 
Cambridge, Mass.: Harvard University Press, 1970. 
 
Sugerencias didácticas: 
Exposición oral ( X ) 
Exposición audiovisual ( ) 
Ejercicios teóricos o prácticos ( X ) 
Seminarios ( ) 
Lecturas obligatorias ( X ) 
Trabajo de investigación ( X ) 
Prácticas de taller o laboratorio ( ) 
Prácticas de campo ( ) 
Otras:(especificar) ( ) 
 
Mecanismos de evaluación del aprendizaje de los 
alumnos: 
Exámenes parciales ( X ) 
Examen final ( ) 
Trabajos y tareas ( X ) 
Exposición de tema ( X ) 
Participación en clase ( X ) 
Asistencia ( X ) 
Otras: 
(especificar) ( ) 
 
Línea de investigación: 
Enseñanza de las Matemáticas 
Perfil profesiográfico: 
Especialista en Matemáticas con experiencia docente en la enseñanza a nivel bachillerato 
 
 
http://library.nu/docs/NKOMTZI26U/Mathematics%20and%20the%20Laws%20of%20Nature%3A%20Developing%20the%20Language%20of%20Science%20%28The%20History%20of%20Mathematics%29
http://library.nu/docs/NKOMTZI26U/Mathematics%20and%20the%20Laws%20of%20Nature%3A%20Developing%20the%20Language%20of%20Science%20%28The%20History%20of%20Mathematics%29
http://library.nu/docs/GNUA1KEY2M/Geometry%3A%20The%20Language%20of%20Space%20and%20Form%20%28History%20of%20Mathematics%29