Keeping it R.E.A.L.

Keeping it R.E.A.L.: Research Experiences for All Learners

Carla D. Martin
Anthony Tongen
Copyright Date: 2011
Edition: 1
Pages: 142
https://www.jstor.org/stable/10.4169/j.ctt5hh9xm
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  • Book Info
    Keeping it R.E.A.L.
    Book Description:

    Keeping it R.E.A.L.: Research Experiences for All Learners is a collection of computational classroom projects carefully designed to inspire critical thinking and mathematical inquiry. This book also contains background subject information for each project, grading rubrics, and directions for further research. Instructors can use these materials inside or outside the classroom to inspire creativity and encourage undergraduate research. R.E.A.L. projects are suitable for a wide-range of college students, from those with minimal computational exposure and precalculus background to upper-level students in a numerical analysis course. Each project is class tested, and most were presented as posters at regional conferences.

    eISBN: 978-0-88385-961-2
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Acknowledgments
    (pp. vii-x)
  3. Table of Contents
    (pp. xi-xii)
  4. 1 Introduction and Motivation
    (pp. 1-10)

    The projects presented in this book are short-term research projects that

    reinforce material covered in class;

    show real-life applications in a variety of fields;

    are research-like in that answers are not readily available, have not been thoroughly investigated, or present open-ended questions whose answers may lead students down different paths of discovery.

    A majority of these projects have been used in the sophomore-level numerical methods course taken by all mathematics, physics, and quantitative finance majors at James Madison University (JMU). Since programming is taught as part of the course, many of the projects can be executed by students with little...

  5. 2 Computer Exploration of Mathematical Concepts
    (pp. 11-52)

    Projects grouped in this chapter require only a precalculus background and a short introduction to computer programming. Many of our students had had at most three weeks of exposure to programming when the projects were assigned. The motivations behind these projects were to provide a mechanism for reinforcing programming concepts in class and to give the students an interesting way to explore mathematical concepts with their new programming skills.

    Students in this course learned Matlab [34] as their programming language. However, we have intentionally made the project assignments in this book programming-language independent, so that any language can be used...

  6. 3 Numerical Algorithms
    (pp. 53-90)

    When students see fascinating applications, they become inspired and empowered to learn more mathematics because they are able to put their mathematics background in perspective. It is especially helpful for students in other majors and those not planning on graduate school to see how valuable mathematics can be in a variety of applications. The projects in this chapter serve this purpose by exposing students to interesting applications of mathematics while being accessible to most undergraduate students in math or scientific disciplines. The prerequisite for most of the projects in this chapter is standard first-year calculus (including Taylor series). All other...

  7. 4 Advanced Numerical Analysis
    (pp. 91-122)

    The projects in this chapter were assigned in a senior-level numerical linear algebra class. These topics are more specialized than those in earlier chapters and include solving linear systems, least squares systems, and eigenvalue computation utilizing matrix factorizations such as LU, QR, and singular value decomposition (SVD).

    Every project in this chapter was worked by a single student or a group of two students. Standard linear algebra and an introductory scientific computing course served as prerequisites for this class. The projects were created to cater to these advanced students and designed to offer enough variety so that each team of...

  8. Bibliography
    (pp. 123-126)
  9. Index
    (pp. 127-128)
  10. About the Authors
    (pp. 129-129)