
How To Read Mathematics - Tycho
http://web.stonehill.edu/compsci/History_Math/math-read.htm
======
petercooper
If you like this, you might enjoy this delightfully funny, yet effective,
introduction to calculus book from 1914:
<http://www.gutenberg.org/files/33283/33283-pdf.pdf>

It starts by ranting about uppity mathematicians and academics while showing
how simply you can get your head around basic calculus.

~~~
RiderOfGiraffes
This is one of my all time favorite technical books - I've been searching for
a dead-tree copy on and off for years. You've reminded me that times have
changed, the technology has improved, and I should search again.

Thank you.

ADDED IN EDIT: A quick search shows that the updated version is co-authored by
one of my personal heroes - Martin Gardner. Now I'll need to get two copies.

~~~
steve19
You can't have been looking very hard ;)

[http://www.amazon.com/Calculus-Made-Easy-Silvanus-
Thompson/d...](http://www.amazon.com/Calculus-Made-Easy-Silvanus-
Thompson/dp/1409724670/ref=sr_1_1?ie=UTF8&s=books&qid=1281003280&sr=8-1)

~~~
RiderOfGiraffes
Most of the time I spent looking was before Amazon existed, but thanks for
making me feel old. 8-(

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d0m
I must confess that I always read mathematics like a novel skipping over the
theorem proofs. I was mostly reading example and quick summary of the theorem.

IMHO, proofs as their names imply, are mostly used to prove correctness with
the most rigorousness as possible.

In this perspective, I don't mind trading trust (of the manual/person/web
site) for rigorousness. I can get the big picture by reading the summary and,
usually, a couple of _well chosen_ examples help me understanding it in depth.

Sadly, it is now a burden for me to read any deep mathematical books. For
instance, the dragon book was really annoying to read since it was more
written in a formal tone instead of a example/quick explanation.

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api
Anyone know of a good book on mathematics _as a language_? What I mean is a
book that spends most of its time simply introducing the notation and the
concepts that it refers to rather than dealing excessively with the mechanics
of doing math.

IMHO math as a language should be taught first.

~~~
timwiseman
I do not know if it is exactly what you want, but Chapter Zero (
[http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-
Math...](http://www.amazon.com/Chapter-Zero-Fundamental-Abstract-
Mathematics/dp/0201437244/ref=sr_1_1?ie=UTF8&s=books&qid=1281034245&sr=8-1)
)comes close. It talks about a lot of the foundational mathematics that and
symbolism that is often never taught to non-math majors, but it does so in an
easily understood way.

Proofs and Refutations by Lakatos also touches on this topic, though it is not
the primary or sole discussion there.

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bialecki
"The best way to understand what you are reading is to make the idea your own.
This means following the idea back to its origin, and rediscovering it for
yourself."

While this is probably true everywhere, it's especially true in any hard
science.

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alok-g
>> "Reading Mathematics is not at all a linear experience ...Understanding the
text requires cross references, scanning, pausing and revisiting"

The key problem I face is when cross-references go outside of the current
article, since almost certainly then those cited articles would cite some more
themselves and you can never get to the bottom of it. Even worse is when the
author references something from outside without stating it, an example of
which could be using some variable without defining it.

Stephen Hawking believes what Euclid did in culminating mathematical knowledge
(into self-contained 13 volumes) is something that is needed again but has
never been done in the modern times. His "God Created The Integers" I suppose
is a small attempt in that direction.

I would have imagined Eric Wittgenstein's mathematics online encyclopedia
(<http://mathworld.wolfram.com/>) could be such a book. But it has too much
backward and "forward" cross-referencing.

I am currently reading Bertrand Russell's Principia Mathematica in my free
time.

~~~
oostevo
_The Princeton Companion to Mathematics_ is the closest thing to what you're
looking for that I know of.

I have a copy, and it's wonderful for looking up common topics in mathematics.
The problem is that math is so enormous as a field that you'd essentially have
to print and bind every journal article ever written to truly encompass all of
the current mathematical knowledge.

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kevinskii
Thanks for the link to the great article. This sentence in particular caught
my attention:

“[The phrase] 'It follows easily that...' does not mean if you can’t see this
at once, you’re a dope, neither does it mean this shouldn’t take more than two
minutes, but a person who doesn’t know the lingo might interpret the phrase in
the wrong way, and feel frustrated."

I encounter this phrase frequently and it always leaves me feeling like a
dope. :)

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pfedor
Regarding "Reading Mathematics is not a linear experience": You have to say,
compared with what. I remember that compared with theoretical physics,
mathematics seemed emphatically like a linear experience. A friend of mine
tried once to express in gestures the difference between learning mathematics
and learning physics. He said: "Mathematics is like this:" Then he opened a
book, moved his finger slowly along the first line on the page, left to right,
humming like a computer that's processing something. Once he got to the end of
the line, he tapped the middle of the line and said "Beep beep", then he moved
to the second line, moved his finger from left to right humming, tapped in the
middle and said "Beep beep" and so on. The he said: "Physics is like this:"
And moved the finger along the first line, then the second line, etc., and
only after he got to the bottom of the page he tapped the center of the whole
page and said "Beep beep". I remember there was a bunch of us there and we all
agreed that he was onto something.

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RiderOfGiraffes
This has gone straight into my "Great Articles" collection. Thank you.

If anyone is interested in helping me debug and test the site I'm working on (
_ad hoc_ ) to collect, browse and retrieve great articles, email me and I'll
send you an access code.

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mavelikara
One of the authors - Shai Simonson - taught at ArsDigita program. He is a
great teacher.

~~~
Tycho
I submitted this article after watching his Theory of Computation lecture
course on YouTube. It's an introduction to finite state machines, grammars,
Turing machines and other related theoretical ideas. I'm writing a program for
a problem traditionally tackled by Natural Language Processing and after
stumbling through a bunch of academic papers about parse trees and context
free grammars, it was obvious I'd need to take the plunge and learn this stuff
from the beginning. Anyway it's a good course, tough going but he's a
sympathetic teacher. I recommend the videos (search Youtube for Pumping Lemma
and that should get you lecture 3, then browse the 'More From' list).

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nhnifong
Great article, but the "imaginary reader" at the end is very condescending and
stubborn. A purely curious imaginary reader would have served the purpose
better.

