
Great Math Books as Recommended by Our Readers - acangiano
http://math-blog.com/2011/02/10/great-math-books/
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krambs
To this day I still pull out Apostol's Calculus textbooks. If you're looking
to learn calculus really well, or just brush up, these are the ones.
[http://www.amazon.com/Calculus-Vol-One-Variable-
Introduction...](http://www.amazon.com/Calculus-Vol-One-Variable-Introduction-
Algebra/dp/0471000051)

~~~
gaurav_v
I would _strongly_ suggest Jerry Shurman's Calculus and Multivariable Calculus
texts, which are available for free on his website: people.reed.edu/~jerry/

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shadowpwner
This is pretty cool. Are there answers for the exercises?

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gaurav_v
He posts answers to the exercises on his website as the course progresses each
year. This year there are no answers because he's not teaching the course;
he's on sabbatical.

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psykotic
What a conspicuous absence of Russian books! To mention only a tiny handful:

\- Mathematics: Its Contents, Methods and Meaning by Kolmogorov, Alexandrov,
et al

\- Shafarevich's Basic Notions of Algebra

\- Arnold's Mathematical Methods of Classical Mechanics

Another favorite (though German, not Russian) is Brieskorn and Knörrer's Plane
Algebraic Curves.

~~~
acangiano
Thank you for your feedback, psykotic. In our defense, the submission form was
open to everyone. We simply published the entries we received. We may do a
follow up post that incorporates other suggestions, if we receive enough of
them.

~~~
psykotic
Oh, it wasn't a complaint so much as an expression of genuine surprise that
these wonderful books aren't more widely known.

~~~
acangiano
We can make them a bit more popular. ;-) Would you be interested in guest
blogging an entry about foreign or specifically Russian math books?

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moultano
My current favorite, Information Theory Inference and Learning Algorithms,
available online for free. :)
<http://www.inference.phy.cam.ac.uk/mackay/itila/>

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ot
I appreciate the effort to put together the list but the site looks very
spammy to me.

All the book links are affiliate links to Amazon. There are two adsense blocks
one of which is right under the title (and is quite annoying). Most comments
about the books don't explain _why_ the book is good, and don't give much more
information than what I can find in Amazon reviews.

EDIT: I wrote "site" but I actually meant "post", sorry about the confusion.

~~~
timwiseman
Yes, this particular post could seem spammy, but I have been reading this blog
for quite a while and generally find the content to be relevant and
interesting.

Even with this particular post, I personally have no problem with affiliate
links and this list is an interesting compilation which the readers of the
blog helped to create.

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jblow
Sadly the list is missing my favorite math book, "Linear Algebra Done Right"
by Sheldon Axler. It's an absolute must if you are learning linear algebra and
want a deep understanding of it.

Rather than make you grind through mechanical operations on matrices, as most
books do, this book takes a coordinate-free algebraic approach and does an
amazing number of things with it, cutting directly to the chief insights.
There are ninja proofs in this book, 4 lines long, showing some deep and
useful thing about linear algebra that other books would spend pages proving
in a very verbose and uninsightful way.

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acangiano
LADR is in fact in the hall of fame: <http://math-blog.com/mathematics-books/>

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grn
My favourites would be:

\- anything written by Serre,

\- Shafarevich's _Basic Algebraic Geometry_ ,

\- Silverman's _The Artihmetic of Elliptic Curves_ ,

\- Milne's notes (available at <http://jmilne.org>).

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gaurav_v
Milne's notes are an awesome resource.

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stringbot
I would have preferred a list with more editorial input than "listed in the
order received." As a math novice, I'd be much more interested to learn what
Salman Khan's favorite math book is than Joe First-Post's.

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tjr
<http://www.math.sjsu.edu/~swann/mcsqrd.html>

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Maro
The Princeton Companion to Mathematics

[http://www.amazon.com/Princeton-Companion-Mathematics-
Timoth...](http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-
Gowers/dp/0691118809)

~~~
shou4577
I own this book, and I use it occasionally, but it really requires the right
audience.

Firstly, it has several parts. Some of these are historical, philosophical, or
otherwise interesting to a general audience, but some of them are technical (I
would put most of pages 157-729, nearly 60% of the book, in this category).

For people that are interested in mathematics, but do not have a fairly
extensive background (I would estimate 2-3 courses beyond the calculus
series), these technical sections are probably not very useful (and certainly
not entertaining).

For people (like me), who are still pursuing an education in mathematics, I
would say this book is indispensable. It gives a great overview of individual
branches of mathematics, including fairly rigorous explanations of important
results and conjectures.

The exposition portions of the book are good, but don't warrant the high price
of the book on their own. Overall, though, it is a tremendous reference.

Edit: I forgot to mention that the folks who write the articles are all
outstanding mathematicians - many of them Fields medalists or other award
winners. That makes for some very good reading.

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omaranto
I agree with everything you said and would only add that if you have studied
lots (for example, are a graduate student in mathematics), then it will
probably be frustratingly shallow on anything you know reasonably well (or not
mention it at all, if it's specialized), but it is still an amazing resource
to get started in fields of math that are not your own.

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solipsist
Any parent trying to get their children interested in math should definitely
check out Murderous Maths: <http://www.murderousmaths.co.uk/>

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niels_olson
Here's a poll the rank the submissions

<http://news.ycombinator.com/item?id=2204319>

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A_A
I'm surprised there aren't any listings for Marcus du Sautoy.

"The Num8er My5teries", "The Music of the Primes" - are delightful.

Also, "Fermat's Enigma" by Simon Singh is riveting.

My other recent favorite: "Incompleteness: The Proof and Paradox of Kurt
Gödel" by Rebecca Goldstein. A highly readable biography of Gödel

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forkandwait
Gilbert Strang, Linear Algebra and Its Application, THIRD EDITION. Very
undergrad, somewhere in between first and second semester level, and oriented
to matrices (opposite of Axler), but very readable and useful.

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contol-m
Can someone suggest a good book for learning Discrete Math? I have Rosen's
book, but I did not like it much.

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pmiller2
_Concrete Mathematics_ by Don Knuth. If you want specifically graph theory,
I'd suggest _Introduction to Graph Theory_ by Doug West.

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contol-m
I found Concrete Mathematics to be a bit dense and not very suited for self
learners like me. Also it does not cover the basics like proofs, counting etc.

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euccastro
I've read good reviews of Susana Epp's Discrete Mathematics With Applications,
and I liked what I read in a preview. It's expensive, though, so I'm waiting
for the international edition (about 1/3 the cost), which is due out next
month.

