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"What is Mathematics?" by R Courant

Hey

I'm waiting for this book to arrive with the mail any day now and I just like to know you guys' opinions on it? Is it a good read? Does it contain a lot of math or is it more of a general read?

Are there any other good books which you would recommend a soon to be first year undergrad?

Cheers

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Reply 1

datr

It's a brilliant maths book and has loads of maths in it. However it is more like a textbook than a pop math book so it is quite a struggle to get through it all.

Reply 2

D.Hilbert

datr

It's a brilliant maths book and has loads of maths in it. However it is more like a textbook than a pop math book so it is quite a struggle to get through it all.

Hi, thank you. Then maybe I wont have time for another book :P But if, would you recommend any in particular?

Reply 3

s.e.r.e.n.e

Haha I actually have the book What is Mathematics 2nd edition by R Courant and updated by Ian Stewart sitting on my desk, having borrowed it from the local library a week ago...

Having flipped through it (and completed a chapter), I think that for quick refreshment of concepts needed to "survive" the 1st few mths at Imperial, a Further Mathematics book would be the best, since they concentrate more on routine drills of key techniques required in those regular exams.

But What is Mathematics, as Einstein put it, contains all the gems of all fields of mathematics. Basically it shows all the nice and important results of practically everything (eg, the Fundamental Theorem of Algebra...). Somehow it shows you how all the different "key skills" we have learnt up till now for maths fit together in a more general context.

I am only at the beginning so cannot really comment much. But from the feel of it, "What is Mathematics" to "some Further Mathematics book" is like Chicken Essence to Antibiotic. I highly suspect that regular reading of the book through the undergrad would help to improve the general maths ability of a person, which, as you know, is very important when the exam get tough...

Lastly, the book is 566 pages thick. 482 pages for the 1st edition and 60 additional pages added by Ian Stewart. Should be enough to last you until school starts so no worries. The nature of the book: very "pure maths", maths for the sake of doing maths and less on regular routine drill and problem solving.

Reply 4

D.Hilbert

Thank you spencer :biggrin:

Reply 5

mulletboyjay

where can you order the second edition from?

Reply 6

s.e.r.e.n.e

Hey don't tell me you guys actually order the book online and have it shipped to you...

I borrowed it from the local Library and I can describe the book as a timeless classic. It is going to due soon so I think I am going to send it to a local photocopy shop and have it copied.

I guess the reason why Imperial recommend us to read this book is less on the techniques but more on the style and feel of maths at university --- rigourous proves are more important than the result itself.

Like school maths, we would automatically asume the following is true:

if for continuous function f(x)

Unparseable latex formula:

\[a \le x \le b\]

and f(a) < 0 and f(b) > 0, then we would assume that there exist some value k such that f(k) =0 and a < k < b. This is only intuitive because the curve needs to cut the x-axis somewhere. But then the book go and include a "rigourous proof" for this result on page 313 and went on with one full page in small fonts for that... (pg 313 Proof of Bolzano's Theorem)

ya so that's how it feels like. the book is dotted with gems in all fields of maths... certainly a timeless classic.

Reply 7

D.Hilbert

spencer11111

Unparseable latex formula:

\[a \le x \le b\]

Yes I did

(but it only cost me about 14£) I ordered it from adlibris.com (but that's a Nordic company I think)

I've read the first 40 pages or so and it's a really good read.

Most of the proofs are easily followed, but they require some time to let them sink in, so I don't think I will have time for another book this summer :smile:

Reply 8

s.e.r.e.n.e

Rickard.N

Yes I did

Haha I am still not in the era of internet shopping yet... I only know Amazon.com or eBay.com.

"14£" <--- why do you always put the pound sign behind that number... I thought it should be £ 14... Do you have the pound sign on your keyboard? I don't.... coz using US-101 layout :s-smilie:

Reply 9

Speleo

Just ordered this for a little over £12 from amazon marketplace, thanks guys :smile:

Reply 10

D.Hilbert

spencer11111

Yeah sorry, should be "£14". We write it the other way around with the Swedish "krona", for example I bought the book for 199 kr :smile:

(not kr199)
And yeah, I have the pound sign on my Swedish keyboard, as well as "$" and "€"

And Speleo: That's some well spent £12 :smile:

Reply 11

s.e.r.e.n.e

Hi, anyone knows why m' must be introduced on the prove on p.24?

Reply 12

eponymous

is it introducted to set up a contradiction?

Reply 13

s.e.r.e.n.e

Yes the proof involves a contradiction. But why is it that the m' must be introduced in the first place? No explanation given...

Reply 14

Chewwy

spencer11111

"What is Mathematics" to "some Further Mathematics book" is like Chicken Essence to Antibiotic.

???

Reply 15

s.e.r.e.n.e

chewwy: "What is Maths" actually builds your whole Maths up, A-level Maths only aim for the narrow specifics.

Reply 16

Chewwy

i know, i just have never heard the phrase "like Chicken Essence to Antibiotic" before, nor do i understand it!

Reply 17

s.e.r.e.n.e

So do you understand it? You say you know but you say you don't understand?

Come on, your general health would improve by taking supplements like Chicken Essence. But popping antibiotic everyday is not going to get you healthier, although it does cure a myriad of illnesses. On the contrary, Chicken Essence is not going to cure you of your bad flu, but antibiotic does.

So you get it?

Reply 18

henryt

I loved this book. Sometimes a bit heavy to read, but usually fine. I especially enjoyed the chapters on Topology. Had quite a long chat in my interview about the stuff in that section with one of the tutors...