How to Use The Princeton Companion to Applied Mathematics

The Princeton Companion to Applied Mathematics, discussed in these previous posts, has a wide target audience, which includes mathematicians at undergraduate level or above; students, researchers, and professionals in other subjects who use mathematics; and mathematically interested lay readers.

Here are some examples of how different people can use the book.


  • Undergraduate students can use it to get an overview of topics they are studying and to find out what areas of applied mathematics they might like to pursue at graduate level. Many of the articles have minimal pre-requisites (indeed some contain few, if any, equations). My article Color Spaces and Digital Imaging, for example, requires just knowledge of integration and basic linear algebra.
  • A teacher might find useful the articles The History of Applied Mathematics and the four-part article Teaching Applied Mathematics, as well as the various short articles on interesting problems and applications (e.g., Cloaking, Bubbles, The Flight of a Golf Ball, Robotics, Medical Imaging, Text Mining, and Voting Systems).
  • Researchers can use the book to find out about topics outside their area that they encounter in seminars but never have the time to study in the research literature.
  • Engineers can use the book to find out about some of the latest mathematical developments relevant to their interests. The articles Aircraft Noise, Inerters, and Signal Processing, and the index entries “aerodynamics”, “energy-efficient buildings”, and “finite-element methods”, are good starting points.
  • Students at all levels can learn about how to read and write mathematics, including the use of relevant computer tools, from several articles in Part VII, “Final Perspectives”.
  • Anyone can use the book for reference. Although it is not a dictionary, encyclopedia, or handbook, The Companion‘s extensive index makes it easy to locate material, including definitions, equations, functions, laws, theorems, and so on.


  • The book, produced with \LaTeX, is a great example of how to typeset mathematics, with examples of all kinds of equations, figures, and tables. For those learning \LaTeX or new to mathematical typesetting it should be a source of ideas and inspiration. The \LaTeX source code is not provided, but feel free to contact me with questions about how things were done and I will write a post that answers the most common questions.
  • The final collection of articles, by mathematicians from China, France, the UK, and the USA, gives advice on how to make the case for mathematics to politicians, and will be of interest to anyone who wishes to promote the importance of mathematics.

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