What are some recommended mathematics books for a semi-popular level?

[cragwolf]

I've been looking for good mathematical books to read, semi-popular level books which aren't afraid to use mathematical equations, and which might even double as a good book for a mathematics undergraduate to read as a kind of supplement to standard textbooks. Just some examples of what I have in mind:

Infinity and the Mind by Rudy Rucker (but a little too mystical for my tastes)

Proofs from the Book by Martin Aigner and Günter M. Ziegler (a bit too much for my mediocre mind, but some of it got through)

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter (a classic, but not just about maths)

Gamma: Exploring Euler's Constant by Julian Havil (really enjoyed this one)

 

[phoenixthoth]

fermat's last enigma is good. i forget the author...

 

[matt grime]

A Very SHort Introduction to Mathematics, Tim Gowers

The Joy of Counting, Tom Korner

The Music of the Primes, Marcus De Sautoy

Fourier Analysis on Finite Abelian Groups, Audrey Terras

Arfken's Mathematical Physics book, can't recall the name.

Representations of Groups, James and Lieback

Chaos, by James Gleick if it's still around.

They're a mixture of styles, levels and intents. Every mathematician ought to own at least one of them, except the Gleick one, which was fashionable about 8 years ago.

 

[karanrustagi]

Hi There,

I don't know if you've ever heard of Vedic Maths. It's a fantastic book by this Indian author... can't get the name... but just look for vedic math book... he's the guy who developed this concept and wrote the book... it teaches you to do a whole lot of problems mentally... like 97 times 98... or 1/29... trust me its worth it... look for vedic maths on the internet to get a sample of what the book contains...

 

[recon]

Hello.

I was wondering where I may be able to find an online copy of Godel, Escher and Bach as I just CANNOT find it in any bookshop I've been to. Sadly, my father doesn't let me buy books online so I can't get it from Amazon or Barnes & Noble.

 

[matt grime]

Originally posted by karanrustagi
Hi There,

I don't know if you've ever heard of Vedic Maths. It's a fantastic book by this Indian author... can't get the name... but just look for vedic math book... he's the guy who developed this concept and wrote the book... it teaches you to do a whole lot of problems mentally... like 97 times 98... or 1/29... trust me its worth it... look for vedic maths on the internet to get a sample of what the book contains...

the ability to do mental arithmetic is not a useful attribute for a mathematician, except when trying to figure out what her expenses claim is for dinner.

I don't think this book is remotely applicable to the learning of higher mathematics, merely arithmetic. A lot of people don't realize they are different things. Of course I could be stigmatizing it unfairly, but seeing as you sell it on the principle of being able to mutliply two not particulary interesting numbers together, I'll presume that's all it does.

It so happens that many mathematicians are good at sums, but I can think of a few who can't balance a check book, to borrow someone else's phrase.

 

[phoenixthoth]

agreed, but can you say you really understand math if you don't understand numbers?

 

[karanrustagi]

Originally posted by phoenixthoth
agreed, but can you say you really understand math if you don't understand numbers?

Perfect! I totally agree this book doesn't teach you math at all... but it teaches u the art of manipulation... just how you can see calculations differently... i found that impressive... Also it doens't just serve multiplication, division, etc of particular nos., specially division applies to all nos... just that it'd be slightly harder than the easiest method specified...
the reason y this book shud be of particular to indians is in India like most eastern countries, students are not allowed to use calculators at all...
You'll have to agree with me when i say manipulating nos and expressions is an art that you need every time, every where in math...
there is a big debate on the actual utility of this book and the derivation of these results from Vedas (which even i don't think is true... )

 

[phoenixthoth]

indeed. so why not delve into the art of manipulation?

 

[karanrustagi]

i would... i learned a lot from the book... i used it to learn manipulation... it dint speed up my calculations too much coz i still prefer using the calculator (thanx to the north american system)...
I like manipulation now... i used to hate it in the 8th grade but then i developed it in 10th grade and i like it a lot now (even tho I'm not a master)...

 

[phoenixthoth]

i think every mathematician learns how to manipulate in their own way. matt didn't learn it with numbers and he doesn't have to. most mathematicians push around abstract objects; that's what they're good at. playing chess won't teach you how to fight a real battle and learning numbers won't teach you how to push around abstract ideas. but the essence of manipulation is the same in all forms. debate. warfare. interpersonal manipulation. manipulation of inner chi. manipulation of "the system". the spirit of manipulation is the same in all forms. either way you pick up that spirit it makes no difference. once you learn it, you can manipulate anything that can be manipulated.

 

[karanrustagi]

so u say that the book is useless and doesn't teach any manipulation... and that manipulation can't be learned thro such books? its gained tho the process of learning math as such?

 

[phoenixthoth]

is that for me or matt?

i didn't mean that at all. i meant that any way to learn manipulation is great, whether it be numbers or abstract ideas or martial arts.

 

[karanrustagi]

tat was for matt... i totally agree with pheonix when he/she says "i meant that any way to learn manipulation is great, whether it be numbers or abstract ideas or martial arts"

 

[himanshu121]

I totally disagree with all the things that have been cropped up concerning vedic mathematics.

It teaches u higher mathematics as well.

All the Higher Science are encoded in the form of mantras. There is no meaning to reading vedic mathematics if u don't know how to decode the matras and how to get knowledge out of it.There are instances that Calculus was used in Vedic period which was way before Newton found it.

The manipulation part Karan is dealing with is just the basic concept which have been i believe decoded by the Indian authors.

 

[cragwolf]

Originally posted by recon
I was wondering where I may be able to find an online copy of Godel, Escher and Bach as I just CANNOT find it in any bookshop I've been to. Sadly, my father doesn't let me buy books online so I can't get it from Amazon or Barnes & Noble.

recon, I will send you my copy of Godel, Escher, Bach. I'll need a mailing address, though. You can send me a private message with this info. If you're worried about sending a mail address online, you can use a post office address, or you can let your father know that I am willing to send you this book. I have no need for this book anymore, so giving it away is the logical thing to do.

 

[matt grime]

Why does the word vedic always start debate?

The initial request was for books that help you understand the mathematics taught at university, that, if you will, complement and explain how to think about the issues raised in such a course.

The reason offered to read the vedic book was because it would let you mutliply 97 an 98 in your head, and work out 1/29.

That isn't mathematics, take it from a mathematician.

The ability to do mental arithmetic is very useful, understanding how the tricks work is also useful, anything that gets students thinking must be good (I always recommend cryptic crosswords), but these aren't the things that the original request addressed.

I too went too went to a university where calculators wre banned in mathematics, but there were never any questions that required a calculator, and nor should there be in a mathematics degree, because it's mathematics, not arithmetic. If I ask you to work out the remanider of division by 37 of 36! you shouldn't need a caculator. Not because you're vedically informed and can do it in your head, but because you've learned about Fermat's Little Theorem.

"So u say that the book is useless and doesn't teach any manipulation... and that manipulation can't be learned thro such books? its gained tho the process of learning math as such?"

I said no such thing. If you read what I wrote you will see that in fact I said that it appears it does teach the manipulation of numbers, and if that's all it does it's useless for understanding the material in a course on category theory say.

And if that is a standard of the ability to write in English that is learned through reading such books then I could make more comments.

 

[karanrustagi]

Originally posted by matt grime
Why does the word vedic always start debate?

Y is this matt dude so infuriated by anythign vedic...? have u had terrible experiences with indians b4 or something?
ok... i agree this link was meant for books that help you understand math and not teach arithmetic... SO ? that doesn't really mean you can't have posts that guide people to such books as vedic math! All those people who've seen this book in my study have loved it and these are people from the math faculty of university of waterloo (canada)...
what kind of close minded mathematician are btw? the kind that thinks his own way of looking at things is the only way and little flexibility (ie. talking of arithmetic books in a thread meant for math concepts) is not even remotely acceptable?
Dude... u got to a learn to take things cool!

 

[matt grime]

Why do you think I dislike Vedic maths? Which part of what I've written implies I think it's a bad thing? In fact didn't I say that anything that gets students thinking is good and that I encourage my students to do cryptic crosswords?

I do get massively p*****d off by being misrepresented by people, especially those who can't use exclamation marks or question marks, and think that u is an acceptable variant of you except when texting.

I do not think it is very important as *mathematics* from what you say about it. Please, if you are going to reply, do not call me dude. A nod in the direction of grammar would be nice, but not important.

Generally, it seems that its supporters think it has applications everywhere and they have often hijacked threads. That is why I state it always seems to trigger a debate.

Now, you ought to read my posts and see if you can find in them any statements that actually support you opinion on my view of Vedic maths.

That's twice now I've been completely misrepresented in this (off topic) thread. Care to make it three?

 

[phoenixthoth]

matt, i aknowledge that they are possibly misrepresenting you. i respect you as a mathematican. now read my paper, please master sir! ;P

 

[karanrustagi]

YOUR TONE IS WHAT makes me think you dislike vedic math. I have read a couple other posts and you seem like a remarkably rude personality. I pitty you students. I don't know any but one thing that I'm sure of is that teachers like make students HATE MATHS! I hated chemistry coz my chem teacher was an absolute jerk. He was money minded and thought too much of yourself. From pheonix's post, i learn that you're a remarkable mathematician. But there's so much more than knowledge that you should have.
The only reason why i could never tell my chemistry teacher all this is because he was egoistic and would love to fail me. I had no such problem with any other teacher. If i met him ever again, then i'd definitely let him know just how much all the male students hate him.
Maybe you should take a hint too and learn to be a bit more polite and understanding. It'll help u live longer.

 

[phoenixthoth]

matt is like an eastern teacher who'd hit his student with a stick to wake them up to reality. he doesn't mean any offense, i don't think.

 

[karanrustagi]

i know this sort pheonix, I've lived all my life with people like this and can handle them now. I used to be scared. Then i got disrespectful and shouted back and them. That wasn't good coz for an indian kid to be disrespectful to elders is the last thing to do. My dad is just one such teacher. I stopped learning physics and math from him just coz he never cared to understand my problem and all he did was shout and scream with a criket bat in his hand. and you know what? i never scored well. Then i stopped (completely stopped) going even around him with my books. Did what i could all by myself or friends or some nice teachers or din't do it at all. And withing 5 years, i topped my school in public exams (indian board... way harder than any board in the whole of north america). I was 5th highest in the whole country.
I know these teachers have nothing against us. They have so much knowledge. But they really have NO IDEA how to convey it. Rudeness and anger is at their nose tip. All they get out of it is ... students that HATE their subject.
Go around and ask people why they hate math, physics and chemistry. I'll bet anything that atleast 60% of these people will say "coz i hate a horrible teacher. (s)he hated me and i hated him/her.

 

[matt grime]

I certainly don't mean any offense to people who think vedic maths is important in itself. If people acutally read what is written rather than what they think is written then perhaps they'll notice that I have consistently based my opinion of the subject on the comments of the poster who only suggested it because it allows one to multiply 97 by 98 in your head. Well, I can do that without explicit recourse to vedic mathematics; it's called being numerate.

How many of my posts have you read? The ones that attempt to convey knowledge to others that want to learn?

Some people get respect that they deserve; others do not. Those who put words into my mouth and impugn my teaching skills without knowing the slightest thing about me are rapidly falling into the second of those two categories. So go back to post one by me on this subject in this thread. Do you see the phrase 'of course I could be stigmatizing this unfairly'? What do you think that means?

The vast majority of posts come across by most people in ways that aren't intended; you are the one instructing me that 'you got to a learn to take things cool', which sent a shiver down my spine, but possibly not for the reasons you intended. And yes I am rude, but only when insulted. Oh, and I never have, and never will shout at someone for not being able to do mathematics.

 

[karanrustagi]

ok Matt. That last line pretty much convinced me you're not like the teachers that I've had horrible experience with. Sorry for misunderstanding. I do read posts in a crazy hurry specially if they're long or too many. My fault. I did read that part you quoted in ur post. But just that ur tone seemed rude to me. ok...now i know u weren't being rude. SOrry again for that.
I just thought you were one of those people who have no control over themselves and would just go around ridiculing all that exists... my misunderstanding...
never meant offense.

 

[recon]

Originally posted by cragwolf
recon, I will send you my copy of Godel, Escher, Bach. I'll need a mailing address, though. You can send me a private message with this info. If you're worried about sending a mail address online, you can use a post office address, or you can let your father know that I am willing to send you this book. I have no need for this book anymore, so giving it away is the logical thing to do.

Thanks cragwolf, but I live outside the US and the postal service here isn't very reliable especially for parcels and stuff. You could definitely do something else more useful with it than having it get lost in the mail.

 

[Chrono]

Originally posted by matt grime

It so happens that many mathematicians are good at sums, but I can think of a few who can't balance a check book, to borrow someone else's phrase.

I'm a bit relieved to hear this. I guess it's not a bad thing that I can't do conversions very well.