The Princeton Companion to Applied Mathematics
by Nicholas J. Higham, Paul Glendinning, Paul A. Martinez · first published 2015
46% recommend54% neutral
Why HN recommends it
Broad overview of the key areas of applied mathematics in one reference volume, suited to anyone seeking to get oriented in the field, including those working in mathematics and engineering.
Summarised by Claude from recommending comments
This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important questions, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other di
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
Mentions per year
What Hacker News says
Related books
2009–2025The Princeton Companion to Mathematics
Timothy Gowers
Recommended by 62 · mentioned by 8362 recommend · 83 mention62 recommend · 8362 recommend
Mathematics
A. D Aleksandrov
Recommended by 26 · mentioned by 3026 recommend · 30 mention26 recommend · 3026 recommend
2008–2025Mathematics for the Nonmathematician
Morris Kline
Recommended by 12 · mentioned by 1412 recommend · 14 mention12 recommend · 1412 recommend
2014–2026Methods of mathematics applied to calculus, probability, and statistics
Richard Hamming
Recommended by 6 · mentioned by 96 recommend · 9 mention6 recommend · 96 recommend
2009–2026Concepts of modern mathematics
Ian Stewart
Recommended by 12 · mentioned by 1212 recommend · 12 mention12 recommend · 1212 recommend
2008–2024Engineering mathematics
K. A. Stroud
Recommended by 14 · mentioned by 1514 recommend · 15 mention14 recommend · 1514 recommend
2010–2025Mathematics and its history
John C. Stillwell
Recommended by 15 · mentioned by 1715 recommend · 17 mention15 recommend · 1715 recommend
…and not specifically Bourbaki authored; * Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov, Lavrentev * The Princeton Companion to Mathematics by Timothy Gowers et al. * The Princeton Companion to Applied Mathematics by Higham et al.
on “The Secret Math Society Known as Nicolas Bourbaki” ↗…if you would like to learn about all the new-fangled mathematics your best bets are; a) The Princeton Companion to Mathematics - https://www.amazon.com/Princeton-Companion-Mathematics-Timot... b) The Princeton Companion to Applied Mathematics - https://www.amazon.com/Princeton-Companion-Applied-Mathemati... One important piece of advice that i have is to become comfortable with the Symbols, Notation and Formalism used in Mathematics. Most…
on “Ask HN: Best way to relearn basic math?” ↗…but you might find the following useful; * For an introduction (and a reference) to various areas of Modern Mathematics that one didn't even know existed, The Princeton Companion to Mathematics and The Princeton Companion to Applied Mathematics are a must. * All the Math You Missed: (But Need to Know for Graduate School) by Thomas Garrity - A survey and a good adjunct to a textbook. * Mathematics: Its Content, Methods and Meaning by Kolmogorov…
on “A Gentle Introduction to the Art of Mathematics” ↗…which can give you the overall sweep of Mathematics. However, you might find the following (though not textbooks per se) useful. 1) The Princeton Companion to Mathematics by Timothy Gowers et al. and The Princeton Companion to Applied Mathematics by Nicholas Higham et al. - The closest you have to a Modern Encyclopedia of Mathematics. You get unmatched breadth after which you can move on to dedicated books as needed. Well worth the money. 2)…
on “Basic Math Textbook: The Napkin Project” ↗…about trying not to think about climate change and whether it's possible to be bored by the end of the world. Lots of good info (including a visit to a climate deniers conference), bit long winded. "The Princeton Companion to Applied Mathematics". If I read only 10% still worth it. Lots of things to dip into. "The Astronomer and the Witch" Kepler fights to save his mother from persecution.
on “Ask HN: Books you read in 2015?” ↗Thanks for the link. The author is an editor of the Princeton Companion to Applied Mathematics, which also contains very high quality writing and a book I recommend to anyone interested in mathematics and engineering. I agree that this is a flawed article: the ads are irritating, the grammar is…
on “Important Algorithms That Helped Define Math, Computing, Physics” ↗…analysis, information theory … well, I could keep going, but I think you’d greatly benefit from checking out a great book which gives a pretty good overview on the key areas in applied mathematics: The Princeton Companion to Applied Mathematics. The above are just my own guesses, and it’s highly dependent on which problem you’re looking to solve.
on “Math is an insurance policy” ↗Definitely! I have both the Princeton Companion to Mathematics and Princeton Companion to Applied Mathematics and both are well worth the money. One of the difficulties in studying the breadth of mathematics is that the huge amount of jargon/notation of the different branches/models/tools all seem complex/unrelated…
on “The Hacker News Top books of 2023” ↗For mathematics, there are the Princeton Companion to Mathematics and the Princeton Companion to Applied Mathematics.
on “Making Software” ↗…courses. Many come from quite non-traditional backgrounds, and a non-negligible fraction of them end up doing interesting research. 3. "The Princeton Companion to Mathematics" and/or its sister "The Princeton Companion to Applied Mathematics" - these books do a fantastic job of giving a bird's eye view of the essential unity of mathematics, and can be excellent starting points for diving into a topic suited to one's interests. Lastly, mathematicians…
on “Ask HN: Who hires mathematicians?” ↗…more formal approach appears in handbooks.[3][4] [1] Gowers et al., The Princeton Companion to Mathematics. https://press.princeton.edu/books/hardcover/9780691118802/th... [2] Higham and Dennis, The Princeton Companion to Applied Mathematics. https://press.princeton.edu/books/hardcover/9780691150390/th... [3] Zwillinger, CRC Standard Mathematical Tables and Formulae. https://www.crcpress.com/CRC-Standard-Mathematical-Tables-an... [4] Bronshtein,…
on “Ask HN: Are there books for mathematics like Feynman's lectures on physics?” ↗…among mathematicians. The application I am somewhat familiar with is "brute forcing" proofs of inequalities, which can get very annoying, even for apparently easy stuff like 2 variable ones. Indeed, "The Princeton Companion to Applied Mathematics" edited by N. Higham et al has an entire article on this (in section II.20). In particular, the article has a reference to a library called filib++ (http://www2.math.uni-wuppertal.de/~xsc/software/filib.html). I…
on “How many floating-point numbers are in the interval [0,1]?” ↗Worth noting for the interested reader that's disappointed upon reading your comment that there's also a Princeton Companion to Applied Mathematics (ISBN-13: 978-0691150390, ISBN-10: 0691150397).
on “The Princeton Companion to Mathematics [pdf]” ↗…Mathematics (2008) edited by Timothy Gowers. This is a massive book that covers just about everything, up to and including some of the latest problems in mathematics. It's 1000 dense pages. (There's also the Princeton Companion to Applied Mathematics edited by Nicholas Higham.) - The CRC Encyclopedia of Mathematics (1999) by Eric Weisstein. This is an anti-digitization of the Wolfram MathWorld into book form. Expansive, and also famous for some of…
on “An Infinitely Large Napkin [pdf] (2019)” ↗…multiplication/division, exponents/logarithms; and then again with {NumPy, SymPy, Lean Mathlib} - Growth curve fitting; data modeling with linear and better models - "Principia" work-along notebooks - "Princeton Companion to [Applied] Mathematics" work-along notebooks - Khan Academy work-along notebooks
on “The World Excel Championship is being broadcast on ESPN” ↗