It's easy to find good programming e-books, but e-books about mathematics are harder to find. Does anyone know if there's a equivalent of O'reilly for math-books?
Great books about mathematics
41–50 of 61 posts
Re: Great books about mathematics
#42Another great book, starting with the basics and then exploring a wide range of mathematical subjects, is The Princeton Companion to Mathematics : http://press.princeton.edu/titles/8350.html It's fun to just flip it open and start reading.
I clicked the link expecting to see this book. It's pretty impressive (and beautifully finished besides).
Re: Great books about mathematics
#43An enjoyable fiction that may help your kids get interested in maths is The Parrot's Theorem reviewed on a maths fiction site
http://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumbe...
Re: Great books about mathematics
#44Earlier quoted context omitted.
Good points. I have already gone through several levels of engineering mathematics, so do understand differential and integral calculus well. I am assuming that is that Spivak's book is about -- please correct me if I am wrong; Amazon is not showing a preview of the book. You are right in bringing countability arguments into the picture; I understand them only to some level. I would love to read a book that gives it…
Spivak's Calculus starts with a set of 13 axioms which characterize the real numbers and then derives all the results you're familiar with in calculus. It's rigorous in the mathematical sense, so if you've never worked through a rigorous math textbook before then this might be a good start since you're familiar with the underlying material. Here are some exercises to give you a sense of the flavor. If you find these…
> Spivak's Calculus is used as a first-year calculus textbook at lots of schools
Umm... where? Not at Stanford, where we used a mainstream, much easier book. So does Princeton. Harvard is famous for having developed a "touchy-feely" calculus book.
Perhaps abroad? It is typical of calculus courses in the US that the students come with fairly weak backgrounds, and a major purpose is to expose and patch holes in the students' backgrounds in algebra and trigonometry.
Re: Great books about mathematics
#45Does someone have a recommendation for a book that get deeper into mathematics by teaching actual mathematics rather than teaching about it? Many of the books I have come across leave me with more questions than answers [1]. I am interested in pure mathematics mainly including logic, set theory, category theory, etc. [1] An excellent example not mentioned by others here is also The Road to Reality by Roger Penrose. T…
What are you looking for that isn't simply a math textbook? Honestly, that's how mathematicians learn "actual" mathematical subjects, too. If you're comfortable with calculus as a subject, for example, and want a "pure mathematics" approach, I recommend Michael Spivak's Calculus . If you've never worked through a pure math textbook from start to finish, that's a good start. There's not that much interesting in the th…
Seconding the recommendation of Spivak's Calculus. That book lit a fire in me when I was 18. Be sure to work through the exercises, that's where all the fun is.
Re: Great books about mathematics
#46It's easy to find good programming e-books, but e-books about mathematics are harder to find. Does anyone know if there's a equivalent of O'reilly for math-books?
Springer-Verlag has ebooks but they're incredibly expensive, unfortunately.
Re: Great books about mathematics
#47Does someone have a recommendation for a book that get deeper into mathematics by teaching actual mathematics rather than teaching about it? Many of the books I have come across leave me with more questions than answers [1]. I am interested in pure mathematics mainly including logic, set theory, category theory, etc. [1] An excellent example not mentioned by others here is also The Road to Reality by Roger Penrose. T…
Since you mentioned you already have a strong applied math background, try Mathematics: Form and Function by Saunders MacLane for a broad portrait of mathematics that might get you excited to read more deeply into a given subtopic. Note that while this book surveys a broad swathe of mathematics, it depends on the reader already having a pretty high level of mathematical maturity.
Other than that, if you want to go deeper into mathematics, just choose a topic and read on it. If your experience is mostly applied, consider something like topology which is often presented more formally than earlier math courses, or go back to the stuff you've already studied, but in a more pure context (for linear algebra, Axler's Linear Algebra Done Right and Halmos' Finite-Dimensional Vector Spaces; for calculus, Spivak as mentioned already and then an analysis book).
Re: Great books about mathematics
#48Another great book, starting with the basics and then exploring a wide range of mathematical subjects, is The Princeton Companion to Mathematics : http://press.princeton.edu/titles/8350.html It's fun to just flip it open and start reading.
Agreed, well worth the price. The most useful books i have are these 2 Math for Physics undergrads books that capsulize the first 2 years of calculus, linear algebra etc that all math, physics, EE students go thru
http://www.scribd.com/doc/65695685/Mary-L-Boas-Mathematical-...
(older edition of Arfken et al
http://www.scribd.com/doc/84183760/Arfken-G-B-Weber-H-J-Math...
Re: Great books about mathematics
#49May I present one of the greatest math books for general audience: Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent’ev.
http://www.amazon.com/Mathematics-Its-Content-Methods-Meanin...
Math books rarely move from the Soviet Union to west, but this did and for really good reason. Just look at the list of writers included. So far I have not seen any math books that come even close to this. Reading this book together with the The Princeton Companion to Mathematics was real treat.
Re: Great books about mathematics
#50Great list. I would also add:
What is Mathematics? http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-...