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Discovering Discrete Dynamical Systems
 
Discovering Discrete Dynamical Systems
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-0-88385-793-9
Product Code:  CLRM/53
List Price: $59.00
MAA Member Price: $44.25
AMS Member Price: $44.25
eBook ISBN:  978-1-61444-124-3
Product Code:  CLRM/53.E
List Price: $55.00
MAA Member Price: $41.25
AMS Member Price: $41.25
Softcover ISBN:  978-0-88385-793-9
eBook: ISBN:  978-1-61444-124-3
Product Code:  CLRM/53.B
List Price: $114.00 $86.50
MAA Member Price: $85.50 $64.88
AMS Member Price: $85.50 $64.88
Discovering Discrete Dynamical Systems
Click above image for expanded view
Discovering Discrete Dynamical Systems
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-0-88385-793-9
Product Code:  CLRM/53
List Price: $59.00
MAA Member Price: $44.25
AMS Member Price: $44.25
eBook ISBN:  978-1-61444-124-3
Product Code:  CLRM/53.E
List Price: $55.00
MAA Member Price: $41.25
AMS Member Price: $41.25
Softcover ISBN:  978-0-88385-793-9
eBook ISBN:  978-1-61444-124-3
Product Code:  CLRM/53.B
List Price: $114.00 $86.50
MAA Member Price: $85.50 $64.88
AMS Member Price: $85.50 $64.88
  • Book Details
     
     
    Classroom Resource Materials
    Volume: 532017; 116 pp
    Selected as a 2018 CHOICE Outstanding Academic Title!

    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.

  • Table of Contents
     
     
    • Chapters
    • 1. Fixed Points of Dynamical Systems
    • 2. Classifying Fixed Points
    • 3. Cycles and Their Classification
    • 4. Bounded Orbits and Fractal Dimension
    • 5. Sensitive Dependence and Chaos
    • 6. Sharkovskii’s Periodic Point Theorem
    • 7. Bifurcations
    • 8. Conjugacy of Dynamical Systems
    • 9. Two-Dimensional Discrete Dynamical Systems
    • 10. Iterated Function Systems
    • 11. Dynamics in the Complex Plane
    • 12. The Julia and Mandelbrot Sets
    • 13. Symbolic Dynamical Systems
    • 14. Symbolic Dynamical Systems and Conjugacy
  • Additional Material
     
     
  • Reviews
     
     
    • This slim purple volume got this reviewer excited the minute he opened it. Johnson (Swarthmore College), Madden (California State Univ., Bakersfield), and Sahin (Wright State Univ.) have developed an innovative introduction to the analysis of discrete dynamical systems. This reviewer feels inspired to get a student or two, delve into the book in greater detail, and experience discovering the subject again.

      M.D. Sanford, CHOICE
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 532017; 116 pp
Selected as a 2018 CHOICE Outstanding Academic Title!

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.

  • Chapters
  • 1. Fixed Points of Dynamical Systems
  • 2. Classifying Fixed Points
  • 3. Cycles and Their Classification
  • 4. Bounded Orbits and Fractal Dimension
  • 5. Sensitive Dependence and Chaos
  • 6. Sharkovskii’s Periodic Point Theorem
  • 7. Bifurcations
  • 8. Conjugacy of Dynamical Systems
  • 9. Two-Dimensional Discrete Dynamical Systems
  • 10. Iterated Function Systems
  • 11. Dynamics in the Complex Plane
  • 12. The Julia and Mandelbrot Sets
  • 13. Symbolic Dynamical Systems
  • 14. Symbolic Dynamical Systems and Conjugacy
  • This slim purple volume got this reviewer excited the minute he opened it. Johnson (Swarthmore College), Madden (California State Univ., Bakersfield), and Sahin (Wright State Univ.) have developed an innovative introduction to the analysis of discrete dynamical systems. This reviewer feels inspired to get a student or two, delve into the book in greater detail, and experience discovering the subject again.

    M.D. Sanford, CHOICE
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.