Mathematics

[bretty]

Okay recently I've been wanting to maybe brush up on my mathematics since I've been getting into analytic philosophy as well as always having a thing for physics a la stephen hawking etc.

So can anyone recommend me some books? I was never good at math in highschool but it's moreso because I was a crappy student.

I never learned calculus and I forget alot of algebraic stuff.

Thanks in advance.

[redcannon]

i dont' know about analytic philosophy, but if you want to brush up on your physics a bit, i'd recommend getting How to Clone the Perfect Blonde. It's a humorus book that teaches everything from cloning to entwinded photons, as well as robots and the human body, space travel, black holes, and the lot.

also, in the back of the book it offers an extensive further reading section

[bretty]

I'm kind of looking for books that are good for teaching fundamental mathematics. Like Algebraic and calculus theory.

[redcannon]

they might have an idiots guide for that.

also, i'm totally in the dark about that subject. can you please fill me in on the basics?

[Janus]

Just pick up some of the textbooks that they have in the libraries and supplement it with some online resources and you should be all right.

[ComradeRed]

Go and find the Feynman series on physics, volume I. He explains basic algebra and calculus there (very well, but very fast too!).

You'll probably have to check out textbooks at the library; that's what I did. Find a local public library to start with, and read everything they have there. Then move on to a university's library.

[Rosa Lichtenstein]

Bretty, it depends on how much you already know.

If you can get hold of it, Mathematics for the Million by Lancelot Hogben is a good place to start, since it teaches you the mathematics while relating it to its discovery -- and it was written by a Marxist.

Any standard school text will give you the basics in calculus -- since I live in the UK, I cannot suggest any that might be available also in Canada.

I will give it some more thought, though.

[mikelepore]

Schaum's Outline Series. Instead of pages of discussion, they have a larger than usual number of examples, gradually increasing in complexity. The concepts sink into the reader by "osmosis."

Learning by doing, like the workers' revolution.

[JimFar]

Lancelot Hogben (http://en.wikipedia.org/wiki/Lancelot_Hogben) was quite an interesting character. He was certainly one of the great popularizers of mathematics and science (I read both his Mathematics for the Million and his Mathematics in the Making, when I was a child, and both books left a deep impression on me). He was by trade a biologist (he was one of the pioneers of mathematical biology).


In terms of his philosophical outlook, Lancelot Hogben, as I understand him, was rather inclined towards a mechanistic materialism. He attempted to synthesize Marxism with Bertrand Russell's empiricism, and he was also a Watsonian
behaviorist to boot. (See his The Nature of Living Matter).

He seemed to think that mechanism had progressive political implications, as outlined in the following quotes:

...mechanistic philosophy cannot offer to the privileged a
supernatural sanction for the things they value most. It
cannot proffer to the underprivileged the shadowy
compensation of a world into which the thought of science
is unable to penetrate.

Hogben admitted that in the nineteenth century materialism and secularism had flourished and had enjoyed support within the bourgeoisie. But in his view that was because that was a period of prosperity and expansion while "the period in which we live is one of ferment and disintegration." Therefore, the ruling class and its apologists within the scientific community had to abandon materialism along with its
benevolent liberalism in order to stabilize their social order. He cited the writings of scientists like Sir James Jeans and Sir Arthur Eddington on philosophy and religion as examples of this abandonment of a scientific materialism by ruling class apologists within the scientific community.

He was a lifelong political activist who held to a strongly socialist, antiStalinist outlook.

[Rosa Lichtenstein]

Thanks for that Jim.

Well, Hogben was like many Russian communists in the early part of the 1920's, who rejected Hegel and Dialectics. It was only when the revolutionary wave in Europe began to subside, and the revolution in China was lost, that Hegel was 're-discovered' -- later ossified in a crude form in Diamat, a al Stalin and the 'Short Course', etc..

As Lenin noted (except he did not spot that this applied to him too, post 1905), in defeat or retreat, petty-bourgeois revolutionaries turn to mysticisim -- who better than Hegel?

Of course, the Hegelians were able to brush aside these crude materialists partly because their theory was rather simple-minded, and partly because the 'god-seekers' were in the ascendancy (for the above reasons).

Looks like Hogben's theory was just as simple-minded.

[hoopla]

Maths is dull. Its just how many things you can hold in your head at once. As such its just not as involving as english etc.

IMHO

[ComradeRed]

Originally posted by [email protected] 08, 2007 12:30 pm
Maths is dull. Its just how many things you can hold in your head at once. As such its just not as involving as english etc.

IMHO
And how do you take into account, oh, everything but arithmetic? :huh:

Let's see if you're right, let's start with: discrete math. How does graph theory involve "holding" anything "in your head"? Or Boolean Algebra?

Or topology? Riemannian Geometry?

Hell, abstract algebra doesn't involve any "holding" nor does category theory.

What a surprise, your honest opinion is wrong.

[JimFar]

A good account of the lives and careers of Britains socialist scientists of the 1930s, including Lancelot Hogben, J.D. Bernal, Joseph Needham, Hyman Levy, and J.B.S. Haldane can be found in Gary Werskey's book, The Visible College.

[hoopla]

"Meow" Comrade Red...

In intelligence tests maths (I can't see this changing enough as one gets to higher levels of ability) is closly related to working memory function. As opposed to the other three varaibles of language spatial and preceptual speed. Perhps I should have added 'manipulation' :P

Beneath the hubub of your post there is very little. I don't think that introspection of when you - do Riemannian Geometry (;)), is the best way to settle this. Do you have any evidence for your claim that advanced language tasks use wm less than difficult maths problems? In my humble opinion.

[hoopla]

Nah, its not as clear cut in difficult maths, but I imagine that its still there.

[mikelepore]

Its just how many things you can hold in your head at once

You must have had the same teachers I had -- requiring memorization of the table of integrals :o)

[Qwerty Dvorak]

You must have had the same teachers I had -- requiring memorization of the table of integrals :o)
WTF, either your teacher is an idiot or youe education system is screwed up. I Ireland we're given the table of integrals, the challenge is in applying them.

Speaking from the perspective of an Irish second-level Maths student, I would have to reluctantly agree that even the higher-level mathematics course can be mastered through learning off copious amounts of information, however this would be incredibly difficult and would only get you a high C, maybe a low B grade. If you wanted the A you'd need to be apply to apply and manipulate fundamental maths. I also happen to do applied mathematics outside of school, which is much different. It's all about applying maths to practical situations. (It's one of my favourite subjects, I love the fact that actual real situations can be reduced to pure numbers and solved accordingly.) Now in this course the actual formulae you work with aren't that difficult to memorize, most of them are incredibly simple and you would know them from physics or maths anyway. However, applied maths is considered to be much more difficult than maths because applying the maths is quite hard, and you can't just learn everything off (in fact the lady who helps me out with applied maths, who is a maths teacher by profession, says she prefers the applied maths course as it 'rewards real talent').