
A Computational Introduction to Number Theory and Algebra - luu
http://www.shoup.net/ntb/
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mrcactu5
Algebraic Number Theory: A Computational Approach
[http://wstein.org/books/ant/ant.pdf](http://wstein.org/books/ant/ant.pdf)

A Course in Computational Algebraic Number Theory
[http://bit.ly/1heah8l](http://bit.ly/1heah8l)

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williamstein
Author of "Algebraic Number Theory: A Computational Approach" here, in case
anybody has any questions. Here's the history of that book. I first taught an
_undergraduate_ class at Harvard in maybe 2002 and went over the first 20
pages of Swinnerton-Dyer's brief course on algebraic number theory book --
expanding it into course-length notes. I taught the course next to grad
students at UC San Diego, and added more content inspired by the excellent
"Algebraic Number Theory" by Cassels-Frohlich. Then I taught it again twice at
Univ of Washington, adding more modern computational content, and resulting in
a rough draft of this book. Finally, Travis Scholl (a UW grad student) and I
spent the last year polishing it and making it look a bit nicer. The book is
under contract to be published by the American Mathematical Society soon.

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pm90
Thanks for putting this out there for free! I think its an amazing thing to
do, especially for the more academic books. Anecdotally, my friend, who is now
a mathematics grad student in University of Western Ontario, learned
mathematics entirely from ebooks and the low price editions that you find in
India.

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visarga
Not saying the book isn't good, but I have a general observation to make. Such
books would be better if they provided a sequence of carefully difficulty-
graded exercises that would build on towards practical mastery. Instead, there
is a flood of theorems with a spattering of exercises. With two exercises one
can't feel confident about learning a theorem or other deep complex math
concept.

It's one thing to read a theorem, another to be confident to apply it. When I
was learning math in university, it was the same. Theorems, axioms and
definitions by the truckload, but exercises - nada. In reality it all comes
down to applying math.

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Ebbit
What background of mathematics does this book assume?

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xyzzyz
From the preface:

Prerequisites. The mathematical prerequisites are minimal: no particular
mathematical concepts beyond what is taught in a typical undergraduate
calculus sequence are assumed.

The computer science prerequisites are also quite minimal: it is assumed that
the reader is proficient in programming, and has had some exposure to the
analysis of algorithms, essentially at the level of an undergraduate course on
algorithms and data structures.

Even though it is mathematically quite self contained, the text does
presuppose that the reader is comfortable with mathematical formalism and also
has some experience in reading and writing mathematical proofs. Readers may
have gained such experience in computer science courses such as algorithms,
automata or complexity theory, or some type of “discrete mathematics for
computer science students” course. They also may have gained such experience
in undergraduate mathematics courses, such as abstract or linear algebra. The
material in these mathematics courses may overlap with some of the material
presented here; however, even if the reader already has had some exposure to
this material, it nevertheless may be convenient to have all of the relevant
topics easily accessible in one place; moreover, the emphasis and perspective
here will no doubt be different from that in a traditional mathematical
presentation of these subjects

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anton-107
What would be a good textbook for Math 101, specifically to learn some
advanced mathematical formalism without actually diving in applied science
behind it?

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tomku
Keeping with the free theme, Book Of Proof by Richard Hammack is a nice
introduction to proofs and formalism. It's available free from the author as a
PDF[1], and also as a physical book on Amazon[2].

An alternative if you're willing to spend a little is How to Prove It by
Daniel J. Velleman, also available from Amazon[3] and probably many other
retailers. Both books cover roughly the same topics.

[1]:
[http://www.people.vcu.edu/~rhammack/BookOfProof/](http://www.people.vcu.edu/~rhammack/BookOfProof/)

[2]: [http://www.amazon.com/Book-Proof-Richard-
Hammack/dp/09894721...](http://www.amazon.com/Book-Proof-Richard-
Hammack/dp/0989472108)

[3]: [http://www.amazon.com/How-Prove-It-Structured-
Approach/dp/05...](http://www.amazon.com/How-Prove-It-Structured-
Approach/dp/0521675995)

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kasperset
[https://www.crcpress.com/Applied-Combinatorics-Second-
Editio...](https://www.crcpress.com/Applied-Combinatorics-Second-
Edition/Roberts-Tesman/9781420099829)

This is also a nice complementary book.

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Hackernaut
How relevant is this book to artificial intelligence

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jordigh
Depends what you mean by AI. Back in the day, a computer algerbra system was
considered AI, in which case, this book is very relevant. But I can't think of
another interpretation of AI that would make this book relevant.

