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Discovering discrete dynamical systems

Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-disco...

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Detalles Bibliográficos
Autores principales: Johnson, Aimee, Madden, Kathleen, Şahin, Ayşe
Lenguaje:eng
Publicado: American Mathematical Society 2017
Materias:
Acceso en línea:http://cds.cern.ch/record/2639505
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author Johnson, Aimee
Madden, Kathleen
Şahin, Ayşe
author_facet Johnson, Aimee
Madden, Kathleen
Şahin, Ayşe
author_sort Johnson, Aimee
collection CERN
description Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.
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spelling cern-26395052021-04-21T18:42:18Zhttp://cds.cern.ch/record/2639505engJohnson, AimeeMadden, KathleenŞahin, AyşeDiscovering discrete dynamical systemsGeneral Theoretical PhysicsDiscovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.American Mathematical Societyoai:cds.cern.ch:26395052017
spellingShingle General Theoretical Physics
Johnson, Aimee
Madden, Kathleen
Şahin, Ayşe
Discovering discrete dynamical systems
title Discovering discrete dynamical systems
title_full Discovering discrete dynamical systems
title_fullStr Discovering discrete dynamical systems
title_full_unstemmed Discovering discrete dynamical systems
title_short Discovering discrete dynamical systems
title_sort discovering discrete dynamical systems
topic General Theoretical Physics
url http://cds.cern.ch/record/2639505
work_keys_str_mv AT johnsonaimee discoveringdiscretedynamicalsystems
AT maddenkathleen discoveringdiscretedynamicalsystems
AT sahinayse discoveringdiscretedynamicalsystems