Publicaciones (publications)
Publicaciones de los Profesores Investigadores del Departamento de Matemáticas y Estadística.Libros
Calculus off the Beaten Path: A Journey Through Its Fundamental IdeasAuthor: Ignacio Zalduendo. Springer Undergraduate Mathematics Series, 1st. edition, (2022).
This textbook provides a gentle overview of fundamental concepts related to one-variable calculus. The original approach is a result of the author’s forty years of experience in teaching the subject at universities around the world. In this book, Dr. Zalduendo makes use of the history of mathematics and a friendly, conversational approach to attract the attention of the student, emphasizing what is more conceptually relevant and putting key notions in a historical perspective. Such an approach was conceived to help them to overcome potential difficulties in teaching and learning of this subject ― caused, in many cases, by an excess of technicalities and computations.
Besides covering the core of the discipline ― real number, sequences and series, functions, derivatives, integrals, convexity and inequalities ― the book is enriched by “side trips” to relevant subjects not usually seen in traditional calculus textbooks, touching on topics like curvature, the isoperimetric inequality, Riemann’s rearrangement theorem, Snell’s law, Buffon’s needle problem, Gregory’s series, random walk and the Gauss curve, and more. An insightful collection of exercises and applications completes this book, making it ideal as a supplementary textbook for a calculus course or the main textbook for an honors course on the subject.
This textbook provides a gentle overview of fundamental concepts related to one-variable calculus. The original approach is a result of the author’s forty years of experience in teaching the subject at universities around the world. In this book, Dr. Zalduendo makes use of the history of mathematics and a friendly, conversational approach to attract the attention of the student, emphasizing what is more conceptually relevant and putting key notions in a historical perspective. Such an approach was conceived to help them to overcome potential difficulties in teaching and learning of this subject ― caused, in many cases, by an excess of technicalities and computations.
Besides covering the core of the discipline ― real number, sequences and series, functions, derivatives, integrals, convexity and inequalities ― the book is enriched by “side trips” to relevant subjects not usually seen in traditional calculus textbooks, touching on topics like curvature, the isoperimetric inequality, Riemann’s rearrangement theorem, Snell’s law, Buffon’s needle problem, Gregory’s series, random walk and the Gauss curve, and more. An insightful collection of exercises and applications completes this book, making it ideal as a supplementary textbook for a calculus course or the main textbook for an honors course on the subject.
Matemática para Iñaki. Author: Ignacio Zalduendo. Fondo de Cultura Económica, México, (2017).
Quien abra este libro quizá no creerá que se trata de uno de divulgación: verá que hay ejercicios y problemas, y encontrará que todo lo que se afirma va acompañado de una demostración.
No hay duda, en cambio, de que se trata de un libro que invita al lector a adentrarse en el pensamiento matemático a través de sus conceptos más elementales, aquello que conforman la base firme de la edificación matemática: los números naturales y la aritmética; el punto y la recta; los ángulos, las funciones circulares y las ecuaciones; las permutaciones y la probabilidad.
Ignacio Zalduendo escribió este libro para Iñaki y para todo aquel que aun tiene viva su curiosidad, disfruta de los desafíos y encuentra placer en el descubrimiento que llega después de pasar un rato pensando con lápiz y papel en mano. En esto se resume, a fin de cuentas, la matemática.
Quien abra este libro quizá no creerá que se trata de uno de divulgación: verá que hay ejercicios y problemas, y encontrará que todo lo que se afirma va acompañado de una demostración.
No hay duda, en cambio, de que se trata de un libro que invita al lector a adentrarse en el pensamiento matemático a través de sus conceptos más elementales, aquello que conforman la base firme de la edificación matemática: los números naturales y la aritmética; el punto y la recta; los ángulos, las funciones circulares y las ecuaciones; las permutaciones y la probabilidad.
Ignacio Zalduendo escribió este libro para Iñaki y para todo aquel que aun tiene viva su curiosidad, disfruta de los desafíos y encuentra placer en el descubrimiento que llega después de pasar un rato pensando con lápiz y papel en mano. En esto se resume, a fin de cuentas, la matemática.
Stochastic Optimization in Insurance: A Dynamic Programming Approach. Authors: Pablo Azcue and Nora Muler. Springer Briefs in Quantitative Finance, Springer, (2014).
- A concise viscosity solution approach in insurance control problems.
- Provides existence and structure of optimal strategies.
- Offers systematic construction of the optimal value functions.
Publicaciones recientes
Optimal dividend strategies for a catastrophe insurer. Authors: Pablo Azcue, Nora Muler and Hansjoerg Albrecher. Frontiers of Mathematical Finance, doi: 10.3934/fmf.2024008, (2024).
Level Sets Semimetrics for Probability Measures with applications in hypothesis testing. Authors: Gabriel Martos Venturini, Alberto Muñoz, and Javier Gonzalez. Methodology and Computing in Applied Probability, 25, issue 1, art. 21, (2023).
Density kernel depth for outlier detection in functional data. Authors: Gabriel Martos Venturini, Nicolás Hernández and Alberto Muñoz. International Journal of Data Science and Analytics, 16, 481–488, (2023).
- Optimal dividends under a drawdown constraint and a curious square-root rule. Authors: Nora Muler, Hansjörg Albrecher and Pablo Azcue. Finance & Stochastics, 27, 341-400, (2023).
- Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis. Authors: Nora Muler, Pablo Azcue, Xiaoqing Liang and Virginia R. Young. SIAM Journal on Financial Mathematics, 14, no. 1, 279-313, (2023).
- Optimal strategies in a production-inventory control model. Authors: Nora Muler, Pablo Azcue and Esther Frostig. Methodology and Computing in Applied Probability, 25, issue 1, art. 43, (2023).
- Robust estimation in partially nonlinear models. Authors: Daniela Rodríguez and Alberto Muñoz. Statistical Methods and Applications, 32, 1407-1437, (2023).
- Robust estimators in partly linear regression models on Riemannian manifolds. Authors: Daniela Rodríguez and Guillermo Henry. Communications in Statistics: Theory and Methods, 52, issue 14, 4835-4851, (2023).
- Forecasting daily variability discharge in the fluvial system of the Paraná River. An ODPC hydrology application. Authors: Daniela Rodríguez, Manuel Benjamin and Melanie Meis. Hydrological Sciences Journal, 67, issue 14, 2121-2128, (2022).
- A statistical tool for a hydrometeorological forecast in the lower La Plata Basin. Authors: Daniela Rodríguez, Melanie Meis and M. Paula Llano. International Journal of River Basin Management, 21, issue 4, 685-696, (2022).
- Optimal Ratcheting of Dividends in a Brownian Risk Model. Authors: Nora Muler, Hansjörg Albrecher and Pablo Azcue. SIAM Journal on Financial Mathematics, 13, no. 3, 657-701, (2022).
- Level Sets Semimetrics for Probability Measures with applications in hypothesis testing. Authors: Gabriel Martos Venturini, Alberto Muñoz and Javier González. Accepted for publication in Journal of Methodology and Computing in Applied Probability, (2022).