Pensamiento matemático

PRINCIPIA
INTRODUCCIÓN AL PENSAMIENTO MATEMÁTICO,
ARITMÉTICA Y GEOMETRÍA
JOSÉ ALFREDO DEL OSO ACEVEDO
ISAÍ MORENO ROQUE
RAFAEL TORRES SIMÓN
MYRNA VELARDE SALDAÑA
INTRODUCCIÓN AL
PENSAMIENTO MATEMÁTICO,
ARITMÉTICA Y GEOMETRÍA
José Alfredo Del Oso Acevedo
Isaí Moreno Roque
Rafael Torres Simón
Myrna Velarde Saldaña
Academia de Matemáticas
Colegio de Ciencia y Tecnología
Programa de Integración
TALLER DE MATEMÁTICAS
COORDINACIÓN ACADÉMICA
UNIVERSIDAD AUTÓNOMA DE LA CIUDAD DE MÉXICO
Esther Orozco Orozco
RECTORA
Facundo González Bárcenas
COORDINADOR ACADÉMICO
Carlos Ruano Cavazos
COORDINADOR DEL COLEGIO DE CIENCIA Y TECNOLOGÍA
©
Principia. Introducción al pensamiento matemático, aritmética y geometría,
primera edición, 2006
primera reimpresión, 2007
segunda reimpresión, 2009
tercera reimpresión, 2010
©
José Alfredo Del Oso Acevedo, Isaí Moreno Roque, Rafael Torres Simón
y Myrna Velarde Saldaña
D.R.
Universidad Autónoma de la Ciudad de México
Av. División del Norte 906, Col. Narvarte Poniente,
Delegación Benito Juárez, C.P. 03020, México, D.F.
ISBN: 968-5720-76-2
Academia de Matemáticas, Colegio de Ciencia y Tecnología, Programa de Integración,
Coordinación Académica, UACM
Materiales Educativos: [email protected]
Responsable de la edición: Ana Beatriz Alonso
Diseño de la portada: Aarón Aguilar. Diagramas elaborados por integrantes de la UACM.
Imágenes tomadas de images.google.comFRQREMHWLYRVGLGiFWLFRV\VLQ¿QHVGHOXFUR
Material educativo universitario de distribución gratuita para estudiantes de la UACM.
Prohibida su venta
Hecho e impreso en México / Printed in Mexico
La Ley de la Universidad Autónoma de la Ciudad de México, en su Exposición de
motivos, establece:
“7. Contribuir al desarrollo cultural, profesional y personal de los
estudiantes:
(...) El empeño de la Universidad Autónoma de la Ciudad de México deberá
ser que todos los estudiantes que a ella ingresen concluyan con éxito sus
estudios. Para ello deberá construir los sistemas y servicios que éstos
necesiten para alcanzar este propósito de acuerdo con su condición de vida
y preparación previa. (...).” 1
De igual manera, en su Título I, Capítulo II, Artículo 6, Fracción IV, dice:
“Concebida como una institución de servicio, la Universidad brindará a los
estudiantes los apoyos académicos necesarios para que tengan éxito en sus
estudios. (...).” 2
Atendiendo a este mandato, los profesores - investigadores de la UACM preparan
materiales educativos como herramienta de aprendizaje para los estudiantes de
los cursos correspondientes, respondiendo así al principio de nuestra casa de
estudios de proporcionarles los soportes necesarios para su avance a lo largo de
la licenciatura.
Universidad Autónoma de la Ciudad de México
Nada humano me es ajeno
__________________
1
Ley de la Universidad Autónoma de la Ciudad de México, publicada en la *DFHWD2¿FLDOGHO
Distrito Federal el 5 de enero de 2005, reproducida en el Taller de Impresión de la UACM, p. 14.
2
Ídem., p. 18.
Imagen de la portada:
El Triángulo de Penrose, también llamado tribar, es un objeto imposible.
Fue creado por el artista sueco Oscar Reutersvärd en 1934,
y popularizado en los años 1950s por el matemático inglés Roger Penrose.
El tribar aparenta ser un objeto sólido hecho con tres barras cuadradas
que forman un triángulo; sin embargo, su fabricación en el espacio Euclideano
o tridimensional no es posible: sólo puede ser concebido mediante el dibujo
en dos dimensiones.
Imagen tomada de en.wikipedia.org
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Esta obra se terminó de imprimir
en el mes de agosto de 2009
en el taller de impresión de la
Universidad Autónoma de la Ciudad de México
con un tiraje de 3500 ejemplares.
Principia es un libro dirigido, en general, a todo aquel que le interese adentrarse en la matemática a un nivel básico universitario, y
especialmente a los estudiantes de la Universidad Autónoma de la
Ciudad de México que cursan el módulo inicial del Programa de
Integración.
La propuesta metodológica se basa en la comprensión de los principios matemáticos como elementos esenciales para el entendimiento
de un universo tan maravilloso como vasto. Privilegia, antes que el
conocimiento, el pensamiento y la imaginación; el uso creativo de
la razón.
Siguiendo la ¿losofía del matemático Pólya, quien habla de la “excitación del descubrimiento”, Principia se estructura bajo la consigna de aprender por medio del razonamiento y la resolución de
problemas. Cada sección, tanto la de aritmética como la de geometría, y en particular la de razonamiento inductivo, incluyen ejercicios y notas históricas amenas que permiten que el lector perciba
la génesis de algunos tópicos matemáticos.
Introducir al lector en este mundo y despojarlo de sus miedos, ayudarlo a comprender lo que ocurre de manera natural y sumergirlo en su goce y disfrute son los propósitos fundamentales de esta
obra.