Teach Yourself to Read Advanced Math and Science Like a Foreign Language

This post is from an Amazon.com list here.

I’ve basically taught myself to ‘read’ math as a ‘foreign language,’ from calculus on forward. That’s to say, I never took a calculus course (though I did tutor HS math for years, so I had a pretty solid foundation), but now I can read almost the most advanced math books and understand what they’re saying. That’s not to say I could solve problems and get the right answers, but I can follow when others do it (and in a pinch, I could find the way to get the right answers).

This has opened up whole new fields of math and science texts that would otherwise be off-limits as ‘for specialists only.’ And it all came from the books yous see below. I’m convinced ANYONE can teach themselves to read math as a foreign language. But math is so often taught poorly. These books do it right.

I’m not saying it’s easy, learning a foreign language never is. But eventually you start to get a sense of why mathematicians and scientists make the basic moves they do, like one would get a sense of the grammar or idiomatic phrases in a foreign language, what the symbols mean, what is generally assumed as already known, and it turns out that the basics are much easier than they seem. If only someone had written ‘advanced math for the rest of us.’ Till then, these books are the best things I’ve found yet, and they’re actually pretty great.

Concepts of Modern Mathematics
1.  Concepts of Modern Mathematics by Ian Stewart
The list author says:
“Definitely start with this one, it assumes nothing more than HS math, and it has a wide range of topics in it. And its clear!”
$8.06   Used & New from: $4.65
4.7 out of 5 stars  See all reviews (18 customer reviews)
Mathematics: From the Birth of Numbers
2.  Mathematics: From the Birth of Numbers by Jan Gullberg
The list author says:
“This encyclopedic book provides a basic, understandable, and often humorous introduction to most fields in contemporary math. Written by a non-mathematician who just loves the field, it’s full of historical insights and curiosities. If you want the history too, this is the way to go. Only HS math required, a good alternative to the first on the list.”
$31.18   Used & New from: $9.32
4.7 out of 5 stars  See all reviews (74 customer reviews)
What Is Mathematics? An Elementary Approach to Ideas and Methods
3.  What Is Mathematics? An Elementary Approach to Ideas and Methods by Ian Stewart
The list author says:
“This one is a bit old, but its solid, and surprisingly clear. Good stuff, also assumes no more than HS math.”
$14.97   Used & New from: $8.97
4.8 out of 5 stars  See all reviews (37 customer reviews)
Mathematics for the Nonmathematician (Dover books explaining science)
4.  Mathematics for the Nonmathematician (Dover books explaining science) by Morris Kline
The list author says:
“A great intro, a bit long.”
$10.17   Used & New from: $0.87
4.5 out of 5 stars  See all reviews (28 customer reviews)
The Princeton Companion to Mathematics
5.  The Princeton Companion to Mathematics by Timothy Gowers
The list author says:
“This is one of the most amazing books on math ever printed. It introduces just about every branch of modern math, its history, etc. Over 1000 pages, it’s not possible to exhaust it. And its easy to read! Ok, its expensive, but this is one of those rare books that is worth every penny, and it’s hard cover and binding are built to last a lifetime. Incredible.”
$71.12   Used & New from: $49.98
4.6 out of 5 stars  See all reviews (35 customer reviews)
Unknown Quantity: A Real and Imaginary History of Algebra
6.  Unknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire
The list author says:
“This book rocks. Its a math history book that’s also a page turner, and it also explains along the way just how traditional algebra transformed into a subject that seems, on the surface, to have nothing to do with it – the algebra of groups, rings, etc. Great stuff. And its very, very readable.”
$10.77   Used & New from: $2.81
4.6 out of 5 stars  See all reviews (38 customer reviews)
Mathematics: The Loss of Certainty (Galaxy Books)
7.  Mathematics: The Loss of Certainty (Galaxy Books) by Morris Kline
The list author says:
“Another math history book, this one is great for history of analysis/calculus. If you don’t know the history of math, you can’t really tell why it developed the way it did, and how it ended up so wacky now.”
$19.95   Used & New from: $3.10
4.7 out of 5 stars  See all reviews (20 customer reviews)
Plato's Ghost: The Modernist Transformation of Mathematics
8.  Plato’s Ghost: The Modernist Transformation of Mathematics by Jeremy Gray
The list author says:
“Another math history, really well done, a bit wordy, though. Really strong on the development of non-Euclidean geometry.”
$37.32   Used & New from: $32.98
4.0 out of 5 stars  See all reviews (2 customer reviews)
Does God Play Dice? The New Mathematics of Chaos
9.  Does God Play Dice? The New Mathematics of Chaos by Ian Stewart
The list author says:
“Ian Stewart is great. Here’s two more of his books, this one focuses a bit more on the math related to chaos/complexity studies.”
$20.52   Used & New from: $12.00
4.4 out of 5 stars  See all reviews (18 customer reviews)
From Here to Infinity
10.  From Here to Infinity by Ian Stewart
The list author says:
“Another good one by Stewart. You don’t need more than a few by this guy, they repeat topics after a while.”
$14.47   Used & New from: $1.35
5.0 out of 5 stars  See all reviews (3 customer reviews)
Bourbaki: A Secret Society of Mathematicians
11.  Bourbaki: A Secret Society of Mathematicians by Maurice Mashaal
The list author says:
“A good history book on this rather odd, secret society of mathematicians who really did a ton to promote math as a ‘structuralist’ enterprise. It also does a good job of explaining some of what the ideas they were proselytizing along the way.”
$29.00   Used & New from: $23.33
4.0 out of 5 stars  See all reviews (3 customer reviews)
Relativity Visualized
12.  Relativity Visualized by Lewis Carroll Epstein
The list author says:
“To start learning relativity theory, this is really the only place to start. Its mostly pictures, and really well done. Gets you a real intuitive feel for things.”
Used & New from: $35.13
4.8 out of 5 stars  See all reviews (30 customer reviews)
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About Time: Einstein's Unfinished Revolution
13.  About Time: Einstein’s Unfinished Revolution by Paul Davies
The list author says:
“One of the best books on relativity and all things quantum out there. Davies is consistently readable. Sometimes he argues with himself in question and answer format, anticipating the objections of his readers. A great teacher.”
$10.09   Used & New from: $0.01
4.2 out of 5 stars  See all reviews (44 customer reviews)
A Student's Guide to Maxwell's Equations
14.  A Student’s Guide to Maxwell’s Equations by Daniel A. Fleisch
The list author says:
“If you wanna get ready to now add the math/relativity together, you’ve gotta start with Maxwell. This guide is clear as water, assumes only HS math and some basic calculus, and gets you to understanding things like Div, Curl, Grad, and how they apply to electro-mag  fields. Great prep for Einstein, its what he built on.”
$26.90   Used & New from: $20.00
4.8 out of 5 stars  See all reviews (65 customer reviews) | 1 customer discussion
The Mathematics of Relativity for the Rest of Us
15.  The Mathematics of Relativity for the Rest of Us by Dr. Louis Jagerman M.D.
The list author says:
“This is the BEST book out there on this topic. He takes you from nothing more than HS/basic calc, and gets you all the way through the math of relativity – all you need is persistence. The book is 400 pages long, but by the time your’e done, you’ll understand tensors, and how they apply to crazy stuff like the Ricci tensor. A great, great book.”
$33.50   Used & New from: $32.62
3.9 out of 5 stars  See all reviews (16 customer reviews)
The Road to Reality: A Complete Guide to the Laws of the Universe
16.  The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose
The list author says:
“This book really does try to get all the physical laws in one place, and its amazing just how good a job it does. But while its really great at explaining some things, sometimes it makes leaps, so you’ll need the other books to fill in the gaps. But its an amazing resource, reference, and has some great explanations as well, even if its hard to read cover to cover (its over 1000 pgs!).”
$15.34   Used & New from: $8.98
4.1 out of 5 stars  See all reviews (177 customer reviews) | 4 customer discussions
What Is Mathematics, Really?
17.  What Is Mathematics, Really? by Reuben Hersh
The list author says:
“A little philosophy of math to round out the list. This one’s pretty intuitive and good.”
$19.47   Used & New from: $4.50
3.9 out of 5 stars  See all reviews (10 customer reviews)
Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures (Routledge Contemporary Introductions to Philosophy)
18.  Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures (Routledge Contemporary Introductions to Philosophy) by James Robert Brown
The list author says:
“Another good philosophy of math book, this one is arranged a bit more systematically, but less intuitive than the previous one.”
$34.34   Used & New from: $20.85
3.0 out of 5 stars  See all reviews (5 customer reviews)
Ad Infinitum... The Ghost in Turing's Machine: Taking God Out of Mathematics and Putting the Body Back In. An Essay in Corporeal Semiotics
19.  Ad Infinitum… The Ghost in Turing’s Machine: Taking God Out of Mathematics and Putting the Body Back In. An Essay in Corporeal Semiotics by B. Rotman
The list author says:
“Brian Rotman is one of the best philosophers of math out there, he’s really incredible. All of his books are good, but this one seems to me to fit most directly with the stuff on this list. Again, very readable, and Rotman is also great at tying philosophy of math in with culture in the wider sense, from the rest of philosophy to painting, computation, etc.”
$23.95   Used & New from: $7.00
4.5 out of 5 stars  See all reviews (2 customer reviews)
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~ by chris on May 22, 2011.

One Response to “Teach Yourself to Read Advanced Math and Science Like a Foreign Language”

  1. Christopher, I keep picking at your site. Biting off pieces and walking away until I feel like I’m interested in digesting more. Would you be open to an off-blog conversation? I am in a masters program in Communications. Reading through “The Handbook of Communication Ethics” by Cheney, May & Munshi – just came out in 01.11. There are several chapters I have felt lost in, irritated, and directionless – because I think the gist of so many of today’s conversations are directionless, ungrounded, netherworlds of layered philosophical ramblings that have lived, died, been resurrected to only die again.

    It seems you have rotating interests in many subjects. As a disclaimer, you and I, would make exceptionally strange mental bedfellows. In terms of worldview we could not be more different – but as I read – I like your thoughts. I like the mind behind the questions. So, if you’re willing I’d like to start a discussion…in particular about gender identity and role within the conversation of feminism. Another disclaimer, I’m thoughtful, not easily swayed and certainly not anywhere as well read as you seem to be… So, if you would like to join me in a conversation – I can’t promise it will be a delightful experience – perhaps more like a wrestling match with someone who wants to learn. js

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