Recommend math books for a language geek

[Piggy]

I strongly suggest you narrow your focus a bit and decide what you hope to get out of your efforts

My initial focus is understanding the very basics of mathematical logic, and learning enough of the terminology and fundamentals of applicable math to begin to read more physics and astronomy outside the popular press.

I recommend taking a class rather than starting on your own with books.

I don't see that happening. After 13 years of university education, the thought of sitting in a classroom again really turns my stomach.

Given all that ... if you have an interest in mathematical logic, and in recursion (mathematical, musical, or artisitic) reading 'Godel, Escher, Bach' is a wonderful experience.

I've had several recos for that book, and it might be a good segue into the field.

Thanks for the info.

 

[Almo]

But if you're looking for a good read on the subject of math and everyday life, try John Allen Paulos' "Innumeracy: Mathematical Illiteracy and it's Consequences". It's a fun, quick read.

That guy has illiteracy issues of his own.

 

[rocketdodger]

The size and depth of mathematical knowledge is staggering and far beyond any one individual's grasp in a single lifetime of intense study.

I disagree. Becoming an expert in all fields is certainly beyond an individual's grasp, but having a working knowledge of all the main fields is definitely possible.


Personally I am inclined to side with drkitten. Calculus, linear algebra, and diffeq were easy for me when I took them but I didn't really grokk the material.

I started really understanding mathematics two years ago when I took a discrete mathematics course, and since then I have been progressing much deeper than I ever had before. I have begun to go back and re-learn calc and I find that I am grokking it now that I have the discrete base to build from.

It has also helped immensely that I am a programmer and have been able to actually watch math work before my very eyes. It is one thing to write down on paper, but to see numbers change in real time in front of you... you really appreciate how magnificent mathematics is when that happens.

 

[Piggy]

Becoming an expert in all fields is certainly beyond an individual's grasp, but having a working knowledge of all the main fields is definitely possible.

And as for me, I may not even need "all the main fields" -- probably not, I'd assume, but that's a "known unknown" for me right now.

In any case, I'm not daunted by diving into fields that are impossible to master. If I were, I wouldn't have studied English. The "what there is to know" in that field is so vast it'll give you vertigo.

It has also helped immensely that I am a programmer and have been able to actually watch math work before my very eyes. It is one thing to write down on paper, but to see numbers change in real time in front of you... you really appreciate how magnificent mathematics is when that happens.

I've done some intro-level programming, and enjoyed it. The elegance and practicality was refreshing after so many years of lit. Of course, it had much sharper frustrations -- either the code compiled or it didn't, either it ran or it didn't, either it gave you the result you intended or it didn't. And there was no choice but to dive back in and discover exactly why. But those frustrations were, in an odd way, also refreshing after dealing with the incessant "soft" frustrations of the mole-eyed theorists (sadly, in lit, "theory" means nothing like what it means in science -- it means something more like an intentional bias).

Just this week I was again frustrated by my math-idiocy when trying to chase down a reference to a "Parrondo paradox". I eventually found a pair of articles which, taken together (one provided a visual example of the flash ratchet referred to in the other), made it click. But understanding the math terms would have shortened my search considerably.

 

[1984]

Try Math Through the Ages: A Gentle History for Teachers and Others by WP Berlinghoff and FQ Gouvea.

Don't know if it's exactly what you're after. The hardback has exercises after each topic; don't know about the paperback. If you overview the history of math, you may get some idea of which aspect of math interests you most - and make inroads from there using the exercises. Famous names are covered, stuff like who came up with the concept of zero as a number, fractals, fermat's last theorem, pi, plus something about mathematics as used in astronomy, etc, etc.

 

[Piggy]

If you overview the history of math, you may get some idea of which aspect of math interests you most

Thanks. I'll look into it. There are some topics I prefer to approach from a historical perspective (e.g. religion) and others that I find more benefit from tackling the history later on once I have a grasp of the basics of the current state of the art. I think math might fall into the latter category for me, given what I want to do with it, but I'll check this out whether for now or later.

 

[Stir]

I disagree. Becoming an expert in all fields is certainly beyond an individual's grasp, but having a working knowledge of all the main fields is definitely possible.
...
It has also helped immensely that I am a programmer and have been able to actually watch math work before my very eyes. It is one thing to write down on paper, but to see numbers change in real time in front of you... you really appreciate how magnificent mathematics is when that happens.

I suppose it depends on how you define "working knowledge" and "main fields", but I'll stick by my original statement. The huge majority of mathematics is not accessible by watching how numbers change on a computer screen ... and some math elitists consider calculus, differential equations, etc to be mere tools (although very important ones) for use by engineers, more like arithmetic than 'real' math.

 

[rocketdodger]

and some math elitists consider calculus, differential equations, etc to be mere tools (although very important ones) for use by engineers, more like arithmetic than 'real' math.

That is funny because I consider arithmetic and number theory to be the "real" math heheh.

 

[jj]

I think you found this in the thread I started when I couldn't find this one, but I'll put it here, too.

"Mathematics - From the Birth of Numbers" by Jan Gullberg, ISBN 0-393-04002-X

It's a history, but enough of a history to very nearly teach math, and it's very handy for passing along the basic concepts.

 

[jj]

That is funny because I consider arithmetic and number theory to be the "real" math heheh.

Was that a conjecture? Perhaps a big erdos of math would contain some of each, say how elliptic functions read on Fermat's Last (not by him) Theorem?

 

[69dodge]

I've done some intro-level programming, and enjoyed it. The elegance and practicality was refreshing after so many years of lit. Of course, it had much sharper frustrations -- either the code compiled or it didn't, either it ran or it didn't, either it gave you the result you intended or it didn't. And there was no choice but to dive back in and discover exactly why. But those frustrations were, in an odd way, also refreshing after dealing with the incessant "soft" frustrations of the mole-eyed theorists (sadly, in lit, "theory" means nothing like what it means in science -- it means something more like an intentional bias).

It doesn't frustrate only the "soft" guys; it frustrates mathematicians too. I love the quote from Knuth: "Beware of bugs in the above code; I have only proved it correct, not tried it."