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=3694448

2. How to Read Mathematics - HN Submissions: https://news.ycombinator.com/item?id=4030812, https://news.ycombinator.com/item?id=1576969

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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.]

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[1.] http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

[2.] http://www.amazon.com/Concrete-Mathematics-Foundation-Comput...

Any HN recommendations for a good thorough book on Lambda Calculus? Preferably creative commons if such a text exists.

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-...

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-Timoth...

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

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/ 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.

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

I suspect it is kind of like Knuth's TAOCP, in that it sits proudly on bookshelves more than it gets read.

The companion is fun to read, more like Wikipedia than TAOCP.

That's good to know. I'm more interested in topics of the new volume.

I love buying those sorts of books.

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.

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 :)