Skip to main content

Mathematics: As an Infrastructure of Technology and Science

  • Chapter
  • First Online:
A Mathematical Approach to Research Problems of Science and Technology

Part of the book series: Mathematics for Industry ((MFI,volume 5))

  • 1905 Accesses

Abstract

One of the roles of mathematics is to serve as a language to describe science and technology. The terminology is often common over several branches of science and technology. In this chapter, we describe several basic notions with the emphasis on what is the point of a definition and what are key properties. The objects are taken from set theory, groups and algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. M. Alexa, D. Cohen-Or, D. Levin, As-rigid-as-possible shape interpolation, in Proceedings of ACM SIGGRAPH (2000), pp. 157–164

    Google Scholar 

  2. D.A. Cox, J. Little, D. O’Shea Ideals, Varieties, and Algorithms, An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3rd edn. (Springer, New York, 2007)

    Google Scholar 

  3. S. Kaji, S. Hirose, H. Ochiai, K. Anjyo, A Lie theoretic parameterization of affine transformation, in Mathematical Progress in Expressive Image Synthesis, MI Lecture Note, vol. 50, (Kyushu University, 2013), pp. 134–140

    Google Scholar 

  4. S. Kaji, S. Hirose, S. Sakata, Y. Mizoguchi, K. Anjyo, Mathematical analysis on affine maps for 2D shape interpolation. in Proceedings of SCA2012 (2012), pp. 71–76

    Google Scholar 

  5. M. Koecher, R. Remmert, Hamilton’s Quaternions, in Numbers, (Springer, New York, 1991)

    Google Scholar 

  6. G. Matsuda, S. Kaji, H. Ochiai, Anti-commutative dual complex numbers and 2D rigid transformation, in Mathematical Progress in Expressive Image Synthesis, MI Lecture Note, vol. 50, (Kyushu University, 2013), pp. 128–133

    Google Scholar 

  7. H. Ochiai, K. Anjyo, Mathematical Description of Motion and Deformation—From Basics to Graphics Applications—, SIGGRAPH Asia 2013 Course, http://portal.acm.org, (Revised course notes are also available at http://mcg.imi.kyushu-u.ac.jp/english/index.php ) (2013)

  8. F. Reinhardt, H. Soeder, G. Falk, in dtv-Atlas zur Mathematik, Deutscher Taschenbuch (Springer, New York, 1978)

    Google Scholar 

  9. J. Vince, in Quaternions for Computer Graphics (Springer, New York, 2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hiroyuki Ochiai .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Japan

About this chapter

Cite this chapter

Ochiai, H. (2014). Mathematics: As an Infrastructure of Technology and Science. In: Nishii, R., et al. A Mathematical Approach to Research Problems of Science and Technology. Mathematics for Industry, vol 5. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55060-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-55060-0_1

  • Published:

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-55059-4

  • Online ISBN: 978-4-431-55060-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics