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Books and Book Chapters

  1. Montiel, M. (2018) Mathematical music theory: Integrated course pairing with mathematics and music students from the USA and China in Theoretical and Practical Pedagogy of Mathematical Music Theory: Music for Mathematics and Mathematics for Musicians, From School to Postgraduate Levels, eds. M. Montiel and F. Gómez, World Scientific Publishing Co.
  2. Wilhelmi, M. and Montiel, M. (2018) Muthsics for Clueless: An Experiment with Euclidean Rhythms in Theoretical and Practical Pedagogy of Mathematical Music Theory: Music for Mathematics and Mathematics for Musicians, From School to Postgraduate Levels, eds. M. Montiel and F. Gómez, World Scientific Publishing Co.
  3. Montiel, M. (2017) Manuel M. Ponce’s Sonata No. 2 (1916): An Analysis Using Signature Transformations and Spelled Heptachords In The Musical Mathematical Mind, eds. G. Pareyón, S. Piña-Romero, O. Agustín-Aquino, and E. Lluis-Puebla, Series Computational Music Science, Springer Verlag,
  4. Aceff-Sánchez, F., Agustín, O., du Plessis, J., Lluis-Puebla, E. & Montiel, M. (2012). An Introduction to Group Theory with Applications to Mathematical Music Theory. Bookboon Ventus publishing Aps. ISBN: 978-87-403-0324-7. Online at: http://bookboon.com/en/textbooks/mathematics/an-introduction-to-group-theory
  5. Agustín, O., du Plessis, J., Lluis-Puebla, E. & Montiel, M. (2009). Una Introducción a la Teoría de Grupos con Aplicaciones en la Teoría Matemática de la Música. Online publications of the Mexican Mathematical Society. ISBN: 968-9161-37-7 (online version); 968-9161-38-5 (CD version); 968-9161-36-9 (hard copy version). (textbook) http://www.smm.org.mx/smm/PETextos
  6. Font, V., Montiel, M., Vidakovic, D. & Wilhelmi, M.R. (2011) Dimensional Analogy and Different Coordinate Systems through the Lens of Three Different Theoretical Perspectives. R. Nata (Ed). Progress in Education, Vol. 19, pp. 39-76.Nova Science Publishers, N.Y. (Book Chapter).
  7. Montiel, M. (2004) The Denotator: Its Structure, Construction, and Role in Mathematical Music Theory In Perspectives in Theoretical and Computational Music Theory, 89-105, Guerino Mazzola, Thomas Noll and Emilio Lluis-Puebla (Eds.), Epos, Universitat Osnabruck: Germany, ISBN:3-923486-57-x www.epos.uni-osnabrueck.de/music/books. (book invitation).
  8. Montiel, M. (2002) Contributor to The Topos of Music: Geometric Logic of Concepts, Theory and Performance by Guerino Mazzola, Birkhauser Publishing Company, Berlin: Germany. ISBN-13: 978-3764357313 (book)
  9. Montiel, M. (2018) Mathematical music theory: Integrated course pairing with mathematics and music students from the USA and China in Theoretical and Practical Pedagogy of Mathematical Music Theory: Music for Mathematics and Mathematics for Musicians, From School to Postgraduate Levels, eds. M. Montiel and F. Gómez, World Scientific Publishing Co.

Peer Reviewed Published Journal Articles

  1. Maria     Mannone & Mariana Montiel (2022) Atlanta: mathematics     and music,  Journal of Mathematics and the Arts,      DOI: 10.1080/17513472.2022.2137890
  2. Montiel-Hernández , M. (2017). Un experimento piloto sobre la enseñanza interdisciplinaria integrada a nivel universitario: matemáticas y música, Foro de Educación, v. 15, n. 22. FahrenHouse: Salamanca, Spain.
  3. Kastine, J. & Montiel, M. (2016) The S-Canon and the Multi-S-Canon: An Introduction. Journal of Mathematics and Music, Vol. 10, No. 3, 211-225, http://dx.doi.org/10.1080/17459737.2016.1168492
  4. Montiel, M. & Peck, R. (2016) Mathematics and Music: Reports on the American Mathematical Society Special Sessions at the 2016 Spring Southeastern Sectional Meeting and the Forthcoming 2017 Joint Mathematics Meetings. Journal of Mathematics and Music, Vol. 10, No. 3, 245-249, http://dx.doi.org/10.1080/17459737.2016.1261951
  5. Chahine, I. & Montiel, M. (2015). Teaching Modeling in Algebra and Geometry Using Musical Rhythms: Teachers’ Perceptions on Effectiveness. Journal of Mathematics Education, December 2015, Vol. 8, No. 2, pp. 126-138
  6. Montiel, M. & Gómez, F. (2014). Music in the Pedagogy of Mathematics. Journal of Mathematics and Music, Special Issue: Pedagogies of Mathematical Music Theory. Volume 8, Number 2, July 2014.
  7. (2013) Noll, T., Montiel, M. Glarean’s Dodecachordon Revisited. In Mathematics and Computation in Music J. Wild, J.Hust & J. A. Burgoyne (Eds.), pp. 151-166. Lecture Notes in Artificial Intelligence, Subseries of Lecture Notes in Computer Science, Springer Publishing Company. ISBN 978-3-642-39356-3
  8. Norgaard, M., Spencer, J. Montiel, M. (2013). Testing Cognitive Theories: a Probabilistic Based Algorithm for Melody and Rhythm in Jazz Improvisation. Psychomusicology: Music, Mind and Brain special edition on The Improvising Brain. December 2013, Volume 23, Number 4, pages 243-254.
  9. Montiel, M., Wilhelmi, M., Vidakovic, D. & Elstak, I. Vectors, Change of Basis and Matrix Representation: Onto-Semiotic Approach in the Analysis of Creating Meaning. International Journal of Mathematical Education in Science and Technology. Volume 43, Issue 1, January 2012, pages 11-32. Electronic reference: ISSN: 0020-739X , 1464-5211.
  10. Montiel, M., Wilhelmi, M., Vidakovic, D. & Elstak, I. (2011) Dimensional Analogy and Different Coordinate Systems, An Onto-Semiotic Approach. Mediterranean Journal for Research in Mathematics Education Vol 10, No. 1-2, pp. 131-168.
  11. Lacasta, E., Wilhelmi, M. & Montiel, M. (2010). Ostension et Rapport des Professeurs du Secondaire a la Limite de Fonctions. Quaderni di Ricerca in Didattica (Mathematics), n.1, N. 20, 305-328.
  12. Montiel, M., Bhatti, U. (June 15, 2010) Advanced Mathematics Online: Assessing Particularities in the Online Delivery of a Second Linear Algebra Course. Online Journal of Distance Learning Administration. http://www.westga.edu/~distance/ojdla/
  13. Montiel, M., Wilhelmi, M., Vidakovic, D. & Elstak, I. (Nov., 2009) Using the Onto-Semiotic Approach to Identify and Analyze Mathematical Meaning when Transiting between Different Coordinate Systems in a Multivariate Context, Educational Studies in Mathematics. Volume 72, Issue2, pp. 139-160. Electronic reference: Educ Stud Math. DOI 10.1007/s10649-009-9184-2.
  14. Montiel, M., Vidakovic, D., M.,Kabael, T. (2008). The Relationship Between Students' Understanding of Functions in Cartesian and Polar Coordinate Systems. Investigations in Mathematics Learning 1,2, 52-70

BOOK EDITING

  1. Mathematics and     Computation in Music, M. Montiel, O. Agustin-Aquino,     F. Gómez-Martín, Jeremy Kastine, Brent Milam (Eds.), Lecture Notes in     Artificial Intelligence, Subseries of Lecture Notes in Computer Science,     Springer Publishing, 2022
  2. Mathematics and     Computation in Music, M. Montiel, F. Gómez-Martín,     O.  Agustin-Aquino (Eds.), Lecture Notes in Artificial Intelligence,     Subseries of Lecture Notes in Computer Science, Springer Publishing, 2019. https://www.springer.com/gp/book/9783030213916
  3. Mathematical Music Theory:     Algebraic, Geometric, Combinatorial, Topological and Applied Approaches to     Understanding Musical Phenomena, eds. M. Montiel and R. W. Peck, World     Scientific Publishing Co.,2018 https://www.worldscientific.com/worldscibooks/10.1142/10858
  4. Theoretical and Practical     Pedagogy of Mathematical Music Theory: Music for Mathematics     and Mathematics for Musicians, From School to Postgraduate Levels, eds. M. Montiel and     Francisco Gómez, World Scientific Publishing Co.,2018 https://www.worldscientific.com/worldscibooks/10.1142/10665
  5. Mathematics and Computation in Music, O. Agustin-Aquino, E. Lluis-Puebla, M. Montiel (Eds.),     Lecture Notes in Artificial Intelligence, Subseries of Lecture Notes in     Computer Science, Springer Publishing, 2017. https://www.springer.com/gp/book/9783319718262

Peer Reviewed Conference Proceedings

  1. Wilhelmi, M.&Montiel,M. (2019):Integrated Music and Math Projects in SecondaryEducation. Mathematicsand Computation in Music, M. Montiel,F. Gómez-Martín and O. Agustin-Aquino (Eds.), pp. 390-394.Lecture Notesin Artificial Intelligence, Subseries of Lecture Notes in Computer Science,Springer Publishing.Seventh International Conference onMathematics and Computation in Music, June 18-21, 2019.https://www.springer.com/gp/book/9783030213916
  2. Gómez-Tellez, D., Lluis-Puebla, E. &Montiel, M. (2017): A symmetric quantum theory of modulation in ℤ20. Mathematics and Computation in Music, O. Agustin-Aquino, E. Lluis-Puebla, M. Montiel (Eds.), Computational Music Science series, Springer Publishing. Sixth International Conference on Mathematics and Computation in Music, June 26-29 2017
  3. Montiel, M., Wilhelmi, M. (2017): Funciones semióticas para el análisis de procesos de estudio integrados de matemáticas y música en la universidad (Semiotic functions for analysing university courses integrating mathematics and music). Proceedings: Segundo Congreso Internacional Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos 23 a 26 marzo 2017 (Second International Virtual Conference on the Ontosemiotic Approach to Mathematical Knowledge and Instruction, March 23-26, 2017). University of Granada, Spain.
  4. Norgaard, M., Montiel, M., Spencer, J. (2013) Chords not required: Incorporating horizontal and vertical aspects independently in a computer improvisation algorithm. Proceedings of the International Symposium on Performance Science, Vienna, August 29-31 2013.
  5. Spencer, Jonathan, Montiel, M., Norgaard, M. (2013) Testing Cognitive Theories by Creating a Probabilistic Based Algorithm for Melody and Rhythm in Jazz Improvisation. Poster presentation. Fourth International Conference on Mathematics and Computation in Music held at McGill University, Montreal, Canada, June 12-12 2103. Abstract published in J. Wild, J.Hust & J. A. Burgoyne (Eds.), pp. 151-166. Lecture Notes in Artificial Intelligence, Subseries of Lecture Notes in Computer Science, Springer Publishing Company. ISBN 978-3-642-39356-3
  6. Montiel, M. (2011) The RUBATO COMPOSER Software Concept for Learning Advanced Mathematics. Memoirs of the Fourth International Seminar on Mathematical Music Theory. Emilio Lluis-Puebla & Octavio Agustín-Aquino (Eds). Electronic Publications of the Mexican Mathematical Society. 77-96. Available at: http://smm.org.mx/publicaciones/pe/memorias/2011/v4/pdf/smm-pe-memorias-2011-v4.pdf
  7. Montiel, M. (2011) Presentación del Libro: Una Introducción a la Teoría de Grupos con Aplicaciones en la Teoría Matemática de la Música (Presentation of the Book: An Introduction to Group Theory with Applications to Mathematical Music Theory). Memoirs of the Fourth International Seminar on Mathematical Music Theory. Emilio Lluis-Puebla & Octavio Agustín-Aquino (Eds). Electronic Publications of the Mexican Mathematical Society. 163-165. Available at: http://smm.org.mx/publicaciones/pe/memorias/2011/v4/pdf/smm-pe-memorias-2011-v4.pdf
  8. Elstak. I., Vidakovic, D. & Montiel, M. (2010). Navigating Geometries with Different Metrics: College Students' Understanding of Taxicab-Geometry. In: Brosnan, P., Erchick, D. B., & Flevares, L. (Eds.). (2010). Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Vol. VI, pp. 582-589 (peer reviewed). Columbus, OH: The Ohio State University.
  9. Montiel, M.; Wilhelmi, M. R.; Font, V. y Vidakovic, D. (2010). Dimensional analogy and coordinate systems. In Pinto,M.M.F.& Kawasaki, T.F.(Eds.). Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 305-312. Belo Horizonte, Brazil: PME.
  10. Montiel, M., Vidakovic, D., Wilhelmi, M., & Elstak, I. (2009). Using the onto-semiotic approach: Different coordinate systems and dimensional analogy in multivariate calculus. In Swars, S. L., Stinson, D. W., & Lemons-Smith, S. (Eds.), Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education; Vol. 5, pp. 95-103. Atlanta, GA: Georgia State University.
  11. Montiel, M., Wilhelmi, M., Vidakovic, D. & Elstak, I. (2009) Using the Onto-Semiotic Approach to Identify and Analyze Mathematical Meaning in a Multivariate Context. In Durand-Guerrier,V., Soury-Lavergne, S. & Azarello, F. (Eds). Proceedings from the Sixth Conference of European Research in Mathematics Education (CERME); pp. 2286-2295 Leon, France. http://www.inrp.fr/publications/edition-electronique/cerme6/cerme6.pdf
  12. Montiel, M., (2006) Mathematical Fluency Measured with the Four Parameters of Foreign Language Learning: Applications of the Integral in Alatorre, S., Cortina, J.L., Saiz, M, Mendez, A. (Eds), Proceedings from the Twenty Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Merida, Mexico: Universidad Pedagogica Nacional.
  13. Montiel, M., Álgebra y Música, Aportaciones Matematicas (Mathematical Contributions), A publication of the Mexican Mathematical Society, 1997, pp. 117-128.

Peer Reviewed Encyclopedia Entries

  1. Montiel, M. (2012). Mathematics: Discovery or Invention. Encyclopedia of Mathematics and Society, Salem Press.
  2. Montiel, M. (2012). Theoretical Mathematics. Encyclopedia of Mathematics and Society, Salem Press.

Translations

  1. English to Spanish translation of the book: Nonnegative Matrices by Alexander Graham for the Economics Department of the National Autonomous University of Mexico (UNAM) (1995).
  2. Spanish to English translation of the article: Wilhelmi, M. R., Godino, J. D.; Lacasta, E. (2007). Configuraciones epistémicas asociadas a la noción de igualdad de números reales. Reserches en Didactique des Mathématiques, 27(1), 77–120. [Revised English version, by M. Montiel (2011): 'Epistemic configurations associated to the notion of equality in real numbers', Quaderni di Ricerca in Didattica (Mathematics) 21, 53–82. Retrieved from: http://math.unipa.it/~grim/Wilhelmi_Q21.pdf]
  3. Spanish to English translation of the book Introducción a la Teoría de Grupos con Aplicaciones en la Teoría Matemática de la Música. (An Introduction to Group Theory with Applications to Mathematical Music Theory). Agustín, O., du Plessis, J., Lluis-Puebla, E. & Montiel, M. (2012)

 Outreach Publications

  1. Montiel, M. (2020), Escuchemos las     matemáticas. De conceptos matemáticos a estructuras musicales: ejemplos     para el aula. Cartapacio de Ciencias, vol 07, Almonte,     España.
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