What I never liked much in books that should provide knowledge.

[pier4r]

https://www.reddit.com/r/math/comments/8...s_i_guess/

I would make a quick analogy with annotated chess games. Something on the line "here there is a beautiful mate in 7, but I won't deprive you from the pleasure to find it". No, one can take time and try by himself, but the book should provide a solution at least.

Why? Because a book cannot talk or change, is fixed in time, so if one is stuck the book doesn't help and fail in its purpose.

[Maximilian Hohmann]

Hello!

I would say that anybody who can make any sense of what this book talks about will definitely derive some kind of pleasure from finding the solution himself ;-)

But you are right, for mere mortals who have to read such books because they require them for their work, "hiding" vital information is not helpful at all. And even if they were able to gain some pleasure from it they might simply not have the time to do the maths themselves.

Regards
Max

[Albert Chan]

I think the author do this on purpose.

The prove probably don't add much to the text, and may even distract what follows.

The book is not knowledge without understanding, even if it gives the prove.
To understand this stuff, you really have to do the math, maybe a few plots.

There is no shortcut.

Just an example, while learning how strtod work, I build my own strtod-fast.c

[cyrille de brébisson]

Hello,

Didn't someone become famously famous because of such a note (if I remember well, the note was along the lines of: "I have found a wonderfull proof of this, but I have not placed it there as it is a little bit too long"). I will leave it to you to try to find what I am refering to ;-)





Just pulling your chain, it is Fermat :-)

Cyrille

[grsbanks]

(07-19-2018 06:24 AM)cyrille de brébisson Wrote:  Just pulling your chain, it is Fermat :-)

As far as I know, his Last Theorem still hasn't been proven!

[Nigel (UK)]

(07-19-2018 08:01 AM)grsbanks Wrote:  

(07-19-2018 06:24 AM)cyrille de brébisson Wrote:  Just pulling your chain, it is Fermat :-)

As far as I know, his Last Theorem still hasn't been proven!

Andrew Wiles published the final version of his proof in 1995. It wouldn’t fit into a margin, though!

Nigel (UK)

[grsbanks]

(07-19-2018 09:45 AM)Nigel (UK) Wrote:  

(07-19-2018 08:01 AM)grsbanks Wrote:  As far as I know, his Last Theorem still hasn't been proven!

Andrew Wiles published the final version of his proof in 1995. It wouldn’t fit into a margin, though!

Err... Right... I'm only 23 years late to the party

It's even mentioned in the article that I linked to. Too much blood in the caffeine stream.

[Albert Chan]

I remember Andrew Wiles almost failed prove to Fermat Last Theorem.

What saved it were another failed prove 3 years ago.
Ideas from two failed proves led to his success.

Moral ? Think twice before throwing stuff away.

Years ago, I throw away my Casio FX602P ... still regret it to this day :-(

[Harald]

What I like best are books that show every step of a calculation in a lot of detail, and then, when it gets complicated and you could really do with some help, they simply say "as can be easily seen...".
While most of the time it might be my fault not "simply seeing" something, I do believe there are occasion where the author didn't have a clue either how to get from one statement to the next and desperately needed to somehow fill the gap.

Cheers,
Harald

[ijabbott]

(07-19-2018 11:49 AM)Albert Chan Wrote:  Moral ? Think twice before throwing stuff away.

Years ago, I throw away my Casio FX602P ... still regret it to this day :-(

Agreed. A few years ago I threw away my disfunctional FX-502P which I'd bought from new (1979-ish), and possibly the FA-1 cassette adapter (not sure if I still have that). I wish I kept it. I still have the Program Library book that came with it.

[Albert Chan]

(07-19-2018 03:59 PM)ijabbott Wrote:  

(07-19-2018 11:49 AM)Albert Chan Wrote:  Moral ? Think twice before throwing stuff away.

Years ago, I throw away my Casio FX602P ... still regret it to this day :-(

Agreed. A few years ago I threw away my disfunctional FX-502P which I'd bought from new (1979-ish), and possibly the FA-1 cassette adapter (not sure if I still have that). I wish I kept it. I still have the Program Library book that came with it.

At least your FX502P were disfunctional ...
Except for weak battery, my FX602P were still running fine.

At the time, I thought changing batteries will loses all my programs.
To be honest, I don't know what I were thinking ...

[Gerson W. Barbosa]

(07-19-2018 12:32 AM)Albert Chan Wrote:  There is no shortcut.

And no royal road to Geometry. - Euclid

[Valentin Albillo]

.
Hi, Pier:

pier4r Wrote:I would make a quick analogy with annotated chess games. Something on the line "here there is a beautiful mate in 7, but I won't deprive you from the pleasure to find it". No, one can take time and try by himself, but the book should provide a solution at least.

Certainly, I fully agree with you. At least for chess, you don't have to waste time and effort to find that "beautiful mate in 7" in you don't want to, you simply set up the position in any free chess program and it'll instantly find the mate for you, or the main line, or whatever. But with a math or engineering book you can't do that, your only recourse is to try and find it solved in the internet, which can take time or even fail altogether.

With books, I've experienced many times exactly what you describe and, frankly, I hated it. I remember in particular Knuth's "The Art of Computer Programming" and Scheid's "Numerical Analysis". The latter in particular included lots of exercises for the reader but most of the time would only give the final numeric result and frequently not even that, so you could never be sure your answer was correct.

Regards.
V.

[brickviking]

(07-19-2018 08:41 PM)Valentin Albillo Wrote:  .

With books, I've experienced many times exactly what you describe and, frankly, I hated it. I remember in particular Knuth's "The Art of Computer Programming" and Scheid's "Numerical Analysis".

I noted that Knuth made the point that some of his exercises varied from dead simple to really really advanced post-graduate level, in fact some exercises may not have had a provable answer at that time. Thankfully he indicated the general difficulty at the time he printed the questions. Additionally if you'd been able to create a valid proof for some of those exercises, it might help gain your post-graduate degree.

(Post 259)

[Thomas Klemm]

(07-20-2018 10:53 AM)brickviking Wrote:  in fact some exercises may not have had a provable answer at that time.

I wonder if Andrew Wiles ever handed in his proof of Fermat's Last Theorem as a solution for the homework in Knuth's Art of Computer Programming.
And more important: did he receive a check of $2.56?

Cheers
Thomas

[brickviking]

That would rather depend upon whether Andrew Wiles had Dr Knuth as a professor, or had done the course which used TAOCP as a coursework. As I don't know either of these, I am unable to say. I think he stopped handing out cheques on a real bank, and so those cheques (if they still exist) are rare indeed.

And yes, I found some of the material in TAOCP difficult to understand, though this is more because I haven't been educated past the school system, I never went to university/college. I had more fun with the TeX manual.

(Post 260)

[David Hayden]

(07-18-2018 04:16 PM)pier4r Wrote:  I won't deprive you from the pleasure to find it.

I figure that usually means "I can't remember/find how to prove this, so I'll make a dismissive comment to make you feel dumb and me feel smart."

[Albert Chan]

I like the exploring part of learning, and will not peek at the answer,
unless I am really stuck.

How would you feel if the newspaper sudoku puzzle already have
the missing digits filled in ? Where is the fun in that !

[ttw]

Based on some years teaching math (and some music and chemistry) and computer science, I find such an approach unhelpful. It somewhat reminds one of the "Moore Method" of teaching (topology of course) where the teacher provides a few axioms and expects the students to come up with the theorems. I did drop a (topology of course) course because that was the method being used; I was interested in concepts of convergence, boundedness, and other such things of use to numerical analysis.

I assume that students took my courses because they wanted to learn something that the didn't already know (or that the courses were required but that wasn't my problem.) Give the beginner (or a genius who hasn't seen the material) a chance to get started. Different people have hang ups on different parts of mathematics; all of the subject should be presented at the level required.

[mcquiggi]

(07-19-2018 09:45 AM)Nigel (UK) Wrote:  

(07-19-2018 08:01 AM)grsbanks Wrote:  As far as I know, his Last Theorem still hasn't been proven!

Andrew Wiles published the final version of his proof in 1995. It wouldn’t fit into a margin, though!

Nigel (UK)

There’s a great book on how it was proved, and the extreme effort it took, including the setback that is mentioned in this thread:

“Fermat's Enigma”, by Simon Singh, ISBN 978-0-385-49362-8.

Kevin