
An Illustrated Theory of Numbers (2017) - earthicus
http://illustratedtheoryofnumbers.com/
======
martyweissman
I hope you enjoy the book -- the AMS sale does give a great price! Part of the
reason I went with the AMS was that they're a nonprofit and their prices are
reasonable for a hardcover book printed (offset, not digital on-demand) in
color.

As the author, I'll add a few remarks and answer some questions about the
book.

1\. I made a book webpage at illustratedtheoryofnumbers.com. The errata are
there. Also you can find a series of programming tutorials, if you wish to
learn number theory with Python. I go from programming basics to primality-
testing, RSA, etc.

2\. I didn't provide solutions in the book. :( But there's always online
discussion boards. Someday I'll write many more exercises and provide some
solutions.

3\. It's been used as a textbook for undergraduate number theory, e.g. at
Rice, UC San Diego, next semester at Georgia Tech I think, etc.

4\. No full e-book version is planned. It's all very old-fashioned, but I
spent a lot of time on page layout, optimizing for print, etc.

5\. I took a stronger stance on zero being a natural number in an early draft.
Now I just try to make it clear that it's the convention I choose. If it's
good for Bourbaki, it's good for me.

Feel free to drop a note if you have more questions about the book. My email
is not hard to find.

Happy holidays! Marty Weissman

~~~
thrwthrw93223
I’m apprecticative of the amount of work and effort you put into the book.
Please consider the self-learner and those that don’t have access to
solutions, a classmate, a TA, or a professor.

I know you probably don’t want to expose solutions to the exercises so they
can be used in a classroom, but for people like me, I don’t want to create an
online discussion to every problem I attempt just to check my work.

I prefer to read textbooks that have solutions, so I can know for sure my
answers are correct.

I don’t really buy the “you know when your solutions are correct”. The
beginner can easily fool themself into thinking their solutions are correct,
when they aren’t.

Due to that, I won’t be buying your book.

~~~
martyweissman
That's cool -- you might like Underwood Dudley's book on Elementary Number
Theory. It has a similar set of topics, and I think it has more exercises and
contains some solutions. And it's inexpensive!

~~~
thrwthrw93223
Thanks! I’ll check that out.

------
earthicus
I'm submitting this beautiful book right now because the American Mathematical
Society (AMS) is having a large sale, it's 40% off until the 17th. (You have
to make an AMS account).

Table of contents (pdf):
[https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-...](https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-toc.pdf)

Sample Chapter (pdf):
[https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-...](https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-prev.pdf)

~~~
JoeDaDude
I presume you need to be a AMS member to get the discounted price? Creating an
account with the bookstore doesn't seem to get you the sale price.

~~~
dgquintas
It did for me. Just click "Register" at the top of the checkout page.

------
posterboy
> In some time past (long before 3000bce), a shepherd paired sheep and
> pebbles: as the first sheep walked by, he placed down the first pebble; the
> second sheep walked by and down went the second pebble. At the end of the
> day, the number of pebbles placed down equaled the number of sheep that
> walked past. Whether sheep and pebbles, or red dots and blue dots, equality
> of numbers is defined by pairing off.

Good one.

~~~
throwawaymath
More concisely: sets of numbers are equivalent if there exists a bijection
between them.

EDIT: Oh, the sample chapter actually mentions this exact point in a footnote.
I guess I can still be clever by saying, "Sets of numbers are equivalent if
they're isomorphic." :)

------
alok-g
Does the book discuss foundations of numbers? Peano's axioms, etc. It does not
look like from the contents or the sample chapter.

~~~
martyweissman
Nope -- I didn't take an axiomatic approach, or give a set-theoretic
construction of different sets of numbers. Instead, I take basic arithmetic
and algebra and properties of real numbers as a starting point. I do dwell on
things like division with remainder and prime decomposition.

------
KennyCason
Looks interesting. On the page I noticed a sale price of ~$41 in red text but
upon checkout it is $69. I don’t mind paying $69, but just want to confirm I’m
not missing some opening sale.

~~~
dgquintas
Create an account by clicking "Register" at the top of the checkout page. You
should then see the discounted price, at least until tomorrow (it seems the
sale runs until then).

~~~
KennyCason
Thanks!

------
thrwthrw93223
This looks great, but are solutions provided? Books like this are almost
worthless for me to self-study since I don’t have access to a classroom or
professors and no way to check my solutions.

~~~
throwawaymath
It's a nice book, but I wouldn't use it for study or as a textbook. And
solutions are not provided as far as I can tell. I'm afraid you're going to
have a difficult time finding books which contain solutions to their problems.

~~~
thrwthrw93223
Thanks. I won’t bother buying it then. Do you have any recommendations on good
math books to work through on my own that have solutions floating online, so I
can check my work? I’m looking for a theoretical math book to work through.
Primarily looking for intro to proofs or algebra related books. But anything
will do. I just want something proof-y aimed at beginners.

~~~
earthicus
Polya & Velleman are classics. They're about problem solving & proof writing
techniques, but won't teach you any abstract math. I've only ever heard good
things but i've actually never read them myself! Some other suggestions:

Niven - The Theory of Numbers. Contains hints for some of the proof based
exercises, and answers for many of the computational exercises. I used it for
my undergrad course, I remember it being reasonably beginner friendly.

Pressley - Elementary Differential Geometry. Has terse answers to _every_
exercise! The subject is a nice mixture of concrete and abstract, calculation
and proofs, and there's some interesting work using differential geometry in
CS via computational geometry. Also i think it's used in robotics and a few
other things? This book is very beginner friendly, it will get you about 1/2
way to General Relativity.

~~~
thrwthrw93223
The differential geometry book sounds awesome. Thanks!

~~~
earthicus
I should probably point out the prerequisites. You need to know basic
multivariable calculus, and basic matrix algebra.

------
bigblind
Is there a full ebook available somewhere?

------
hopler
Are there sample pages available?

~~~
earthicus
Sample Chapter (pdf):
[https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-...](https://bookstore.ams.org/mbk-105/~~FreeAttachments/mbk-105-prev.pdf)

~~~
jessaustin
_In this text, we declare: 0 is a natural number_

It's nice that they got that right, on the first page!

~~~
throwawaymath
Eh, I think it's fair to consider the natural numbers as either the non-
negative, nonzero integers or the non-negative integers. As long as an author
declared which use they intend front and center, I don't think one or the
other is more "right." Very established texts and papers alternate freely
between including and not including 0.

~~~
jessaustin
As the author says, it's a matter of taste. The author's good taste is "right"
in the same sense that e.g. 0-indexed arrays are "right": it avoids problems
that not including zero causes. How many elements are in the empty set? Why
shouldn't the natural numbers be able to answer that question?

~~~
hopler
What is 0 minus 1? Why isn't that a natural number? Why shouldn't the nth
natural number be N?

The author's own book discusses the _1st_ prime, in chapter _0_ , which begins
on page _1_. How is this natural?

 _Problem 0.4 Add the odd numbers between 1 and 30. " Why would you say 1 and
30 instead of 0 and 30, since 0 is natural?

Getting hung up on notation and arguing over conventions will hold you back
from learning math.

Offsets (0) and ordinals (1) aree both useful in arrays. The only thing
_wrong* is not saying which you mean.

[http://exple.tive.org/blarg/2013/10/22/citation-
needed/](http://exple.tive.org/blarg/2013/10/22/citation-needed/)

