Skip to content
Register Sign in Wishlist
Where Do Numbers Come From?

Where Do Numbers Come From?

c.$34.99 ( )

  • Publication planned for: February 2020
  • availability: Not yet published - available from February 2020
  • format: Paperback
  • isbn: 9781108738385

c.$ 34.99 ( )
Paperback

Pre-order Add to wishlist

Other available formats:
Hardback


Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Why do we need the real numbers? How should we construct them? These questions arose in the nineteenth century, along with the ideas and techniques needed to address them. Nowadays it is commonplace for apprentice mathematicians to hear 'we shall assume the standard properties of the real numbers' as part of their training. But exactly what are those properties? And why can we assume them? This book is clearly and entertainingly written for those students, with historical asides and exercises to foster understanding. Starting with the natural (counting) numbers and then looking at the rational numbers (fractions) and negative numbers, the author builds to a careful construction of the real numbers followed by the complex numbers, leaving the reader fully equipped with all the number systems required by modern mathematical analysis. Additional chapters on polynomials and quarternions provide further context for any reader wanting to delve deeper.

    • Contains clear explanation of the various number systems used in mathematics
    • Entertaining and accessible to undergraduates
    • Solutions to all exercises are available online
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Publication planned for: February 2020
    • format: Paperback
    • isbn: 9781108738385
    • dimensions: 228 x 152 mm
    • contains: 1 b/w illus. 255 exercises
    • availability: Not yet published - available from February 2020
  • Table of Contents

    Introduction
    Part I. The Rationals:
    1. Counting sheep
    2. The strictly positive rationals
    3. The rational numbers
    Part II. The Natural Numbers:
    4. The golden key
    5. Modular arithmetic
    6. Axioms for the natural numbers
    Part III. The Real Numbers (and the Complex Numbers):
    7. What is the problem?
    8. And what is its solution?
    9. The complex numbers
    10. A plethora of polynomials
    11. Can we go further?
    Appendix A. Products of many elements
    Appendix B. nth complex roots
    Appendix C. How do quaternions represent rotations?
    Appendix D. Why are the quaternions so special?
    References
    Index.

  • Author

    T. W. Körner, University of Cambridge
    T. W. Körner is Emeritus Professor of Fourier Analysis at the University of Cambridge. His previous books include The Pleasures of Counting (Cambridge, 1996) and Fourier Analysis (Cambridge, 1988).

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×