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The Princeton Companion to Applied Mathematics

108 points by jonnybgood 11y ago

dpflan 11y ago
This is always a good topic with numerous HN submissions and comments: Just from a search, there are some great results: 1. Mathematics for Computer Science - HN Submissions: https://news.ycombinator.com/item?id=9311752 https://news.ycombinator.com/item?id=9311752, https://news.ycombinator.com/item?id=3694448 https://news.ycombinator.com/item?id=3694448 2. How to Read Mathematics - HN Submissions: https://news.ycombinator.com/item?id=4030812 https://news.ycombinator.com/item?id=4030812, https://news.ycombinator.com/item?id=1576969 https://news.ycombinator.com/item?id=1576969 __ Here are some other excellent mathematics books: 1. Mathematics: Its Content, Methods and Meaning Containing the thoughts and direction of numerous mathematicians including Kolmogorov, this is a great survey of the field of mathematics. It touches upon Analysis, Analytic Geometry, Probability, Linear Algebra, Topology, and more. [1.] 2. Concrete Mathematics: A Foundation for Computer Science Containing the thoughts and direction of mathematician and computer scientists such as Donald Knuth, this is a great reference for computer science related mathematical concepts focusing on continuous and discrete concepts. [2.] __ [1.] http://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163 http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do... [2.] http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025 http://www.amazon.com/Concrete-Mathematics-Foundation-Comput...
- throwahdhw 11y ago
  Any HN recommendations for a good thorough book on Lambda Calculus? Preferably creative commons if such a text exists.
  - dpflan 11y ago
    Have you seen this post on StackExchange/Mathematics? This may be a good start. I can't personally recommend any. Of course, good luck learning! http://math.stackexchange.com/questions/967/learning-lambda-calculus http://math.stackexchange.com/questions/967/learning-lambda-...
deleted 11y ago
[deleted]
pavelrub 11y ago
Nice! This book is modeled after the The Princeton Companion to Mathematics [1] which is simply awesome in every sense of the word, and extremely recommended for any person who is interested in mathematics. I'm very glad to see more books being modeled after it, and I hope this trend will continue with things beyond math. My only hope is that those new books will match the quality of the original. [1] - http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809 http://www.amazon.com/Princeton-Companion-Mathematics-Timoth...
- rndn 11y ago
  Here is the Princeton Press link: http://press.princeton.edu/titles/8350.html http://press.princeton.edu/titles/8350.html
deleted 11y ago
[deleted]
eruditely 11y ago
I'll be purchasing this. I like how the other book looked and it sits proudly on my desk at my co-working spot.
- cschmidt 11y ago
  I suspect it is kind of like Knuth's TAOCP, in that it sits proudly on bookshelves more than it gets read.
  - eruditely 11y ago
    I love buying those sorts of books.
  - jey 11y ago
    The companion is fun to read, more like Wikipedia than TAOCP.
    - cschmidt 11y ago
      That's good to know. I'm more interested in topics of the new volume.
ivan_ah 11y ago
Wow this book covers a lot of topics. Given the breadth of topics, I doubt each topic is covered in much detail. Still cool though, as it would take years to learn about this stuff from different books. Speaking of math books, I wrote a math/phys text for adults called the No bullshit guide to math and physics http://noBSgui.de/to/MATHandPHYSICS/ http://noBSgui.de/to/MATHandPHYSICS/ It covers a lot of topics, starting from high school, going to first year calculus and mechanics. Worth checking out for anyone interested in the exact sciences and modelling in general.
krsree 11y ago
Perhaps some sections of interest to readers here would be (from the preface): Part VII, “Application Areas,” comprises articles on connections between applied mathematics and other disciplines, including such diverse topics as integrated circuit (chip) design, medical imaging, and the screening of luggage in airports. Application areas of Applied Math sounds funny though :)
mturmon 11y ago
The sequence of topics in the table of contents freaked me out a little: III.1 Benford’s Law 135 III.2 Bessel Functions 137 III.3 The Black–Scholes Equation 137 III.4 The Burgers Equation 138 III.5 The Cahn–Hilliard Equation 138 III.6 The Cauchy–Riemann Equations 139 III.7 The Delta Function and Generalized Functions 139 III.8 The Diffusion Equation 142 III.9 The Dirac Equation 142 III.10 Einstein’s Field Equations 144 III.11 The Euler Equations 146 III.12 The Euler–Lagrange Equations 147 III.13 The Gamma Function 148 Benford's law, and then Bessel functions, and then Black-Scholes? The reason is that some sections are in alphabetical order, encyclopedia-style. But the pace is blistering. About a half page on the Diffusion Equation.

108 points by jonnybgood 11y ago

This is always a good topic with numerous HN submissions and comments: Just from a search, there are some great results: 1. Mathematics for Computer Science - HN Submissions: https://news.ycombinator.com/item?id=9311752 https://news.ycombinator.com/item?id=9311752, https://news.ycombinator.com/item?id=3694448 https://news.ycombinator.com/item?id=3694448 2. How to Read Mathematics - HN Submissions: https://news.ycombinator.com/item?id=4030812 https://news.ycombinator.com/item?id=4030812, https://news.ycombinator.com/item?id=1576969 https://news.ycombinator.com/item?id=1576969 __ Here are some other excellent mathematics books: 1. Mathematics: Its Content, Methods and Meaning Containing the thoughts and direction of numerous mathematicians including Kolmogorov, this is a great survey of the field of mathematics. It touches upon Analysis, Analytic Geometry, Probability, Linear Algebra, Topology, and more. [1.] 2. Concrete Mathematics: A Foundation for Computer Science Containing the thoughts and direction of mathematician and computer scientists such as Donald Knuth, this is a great reference for computer science related mathematical concepts focusing on continuous and discrete concepts. [2.] __ [1.] http://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163 http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do... [2.] http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025 http://www.amazon.com/Concrete-Mathematics-Foundation-Comput...

throwahdhw 11y ago
Any HN recommendations for a good thorough book on Lambda Calculus? Preferably creative commons if such a text exists.
- dpflan 11y ago
  Have you seen this post on StackExchange/Mathematics? This may be a good start. I can't personally recommend any. Of course, good luck learning! http://math.stackexchange.com/questions/967/learning-lambda-calculus http://math.stackexchange.com/questions/967/learning-lambda-...

deleted 11y ago

[deleted]

pavelrub 11y ago

Nice! This book is modeled after the The Princeton Companion to Mathematics [1] which is simply awesome in every sense of the word, and extremely recommended for any person who is interested in mathematics. I'm very glad to see more books being modeled after it, and I hope this trend will continue with things beyond math. My only hope is that those new books will match the quality of the original. [1] - http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809 http://www.amazon.com/Princeton-Companion-Mathematics-Timoth...

rndn 11y ago
Here is the Princeton Press link: http://press.princeton.edu/titles/8350.html http://press.princeton.edu/titles/8350.html

deleted 11y ago

[deleted]

eruditely 11y ago

I'll be purchasing this. I like how the other book looked and it sits proudly on my desk at my co-working spot.

cschmidt 11y ago
I suspect it is kind of like Knuth's TAOCP, in that it sits proudly on bookshelves more than it gets read.
- eruditely 11y ago
  I love buying those sorts of books.
- jey 11y ago
  The companion is fun to read, more like Wikipedia than TAOCP.
  - cschmidt 11y ago
    That's good to know. I'm more interested in topics of the new volume.

ivan_ah 11y ago

Wow this book covers a lot of topics. Given the breadth of topics, I doubt each topic is covered in much detail. Still cool though, as it would take years to learn about this stuff from different books. Speaking of math books, I wrote a math/phys text for adults called the No bullshit guide to math and physics http://noBSgui.de/to/MATHandPHYSICS/ http://noBSgui.de/to/MATHandPHYSICS/ It covers a lot of topics, starting from high school, going to first year calculus and mechanics. Worth checking out for anyone interested in the exact sciences and modelling in general.

krsree 11y ago

Perhaps some sections of interest to readers here would be (from the preface): Part VII, “Application Areas,” comprises articles on connections between applied mathematics and other disciplines, including such diverse topics as integrated circuit (chip) design, medical imaging, and the screening of luggage in airports. Application areas of Applied Math sounds funny though :)

mturmon 11y ago

The sequence of topics in the table of contents freaked me out a little: III.1 Benford’s Law 135 III.2 Bessel Functions 137 III.3 The Black–Scholes Equation 137 III.4 The Burgers Equation 138 III.5 The Cahn–Hilliard Equation 138 III.6 The Cauchy–Riemann Equations 139 III.7 The Delta Function and Generalized Functions 139 III.8 The Diffusion Equation 142 III.9 The Dirac Equation 142 III.10 Einstein’s Field Equations 144 III.11 The Euler Equations 146 III.12 The Euler–Lagrange Equations 147 III.13 The Gamma Function 148 Benford's law, and then Bessel functions, and then Black-Scholes? The reason is that some sections are in alphabetical order, encyclopedia-style. But the pace is blistering. About a half page on the Diffusion Equation.