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Good maths books/Textbooks

Syth · 2003-09-08 18:27:46

Here's an idea. Everyone put down good maths (as in popular science no textbooks) that you would recommend for other people to read.

08-09-2003 7:27pm

#1

Syth

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Here's an idea.
Everyone put down good maths (as in popular science no textbooks) that you would recommend for other people to read.

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#2 08-09-2003 7:32pm

Syth

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Well How to Lie with Statistics tells you how you can use statistics to say anything. Basically how you can say what is technically correct but completly misleading. If you think someone is pulling the wool over your eyes with statistics this book'll tell you how to spot them. But it's like 50 years old, so you mite have problems getting it.

Also 'Reckoning with Risk' by Gerd Gigerenzer is good. See here.

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#3 08-09-2003 7:37pm

Sir Digby Chicken Caesar

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http://www.amazon.co.uk/exec/obidos/ASIN/186046324X/qid=1063046132/sr=1-4/ref=sr_1_0_4/202-8748245-5692661

"the universal history of numbers" by Georges Ifrah. it's a pretty cool read, more of a history book than a math book, but it's pretty interesting.

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#4 08-09-2003 8:05pm

ecksor

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"Innumeracy" by John Allen Paulos is a good examination of how a poor grasp of simple mathematical ideas by the general public lead to scams and general pseudo science.

"Once upon a number", also by John Allen Paulos explains the relationship between statistics and anecdotes and shows how and why relying on just one or the other leads to false conclusions of different kinds.

(Btw, his absolute best book isn't a maths book, it's a philosophy book called "I think, therefore I laugh").

For a pop science introduction to various areas of pure mathematics then "From here to infinity" by Ian Stewart is a good read and I'd recommend it to anyone who's interested.

"The man who loved only numbers" by Paul Hoffman is an entertaining account of the life of eccentric Paul Erdos.

I also enjoyed reading "Dr. Riemann's Zeros" by Karl Sabbagh which is about the search for the solution to the Riemann hypothesis, and in particular focuses on Louis De Branges, quite an interesting character ...

Currently reading "Godel: A life of logic" which is interesting, but I like most biographys.

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#5 09-09-2003 11:19am

silverside

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'A Beautiful Mind' the biography of John Nash.

'Chaos' by James Gleick.

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#6 09-09-2003 11:39am

dod

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Euclid, The Elements, one of the most outstanding maths books in history

Archimedes, The Sand Reckoner, his proposition on how issues raised by very large numbers were dealt with in c.250 BC

Copernicus, De revolutionibus (1543)

Ptolemy, Almagest
Ptolemy, Planetary Hypotheses

and, of course

Newton, Principia

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#7 09-09-2003 11:40am

dudara

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Both of Simon Singhs books are excellent. "Fermat's Last Theorem" and "The Code Book".

Someone else also recommended "The Man Who Loved Only Numbers", a biography of Paul Erdos, which I thoroughly enjoyed.

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#8 12-09-2003 2:38am

Tree

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Originally posted by silverside

'Chaos' by James Gleick.

thats a brill book,

would also recommend ian stewarts what shape is a snowflake

The book of nothing is a good read too, by jd barrow

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#9 16-09-2003 12:52pm

smiles

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Journey through Genius: Great Theorems of Mathematics by William Dunham

<< Fio >>

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#10 14-10-2003 7:43pm

ecksor

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As opposed to the 'popular science' slant of the other thread. Basically books aimed at students or mathematicians that especially well covered a topic or illuminated a subject for you in a very nice way.

To start with, I found Introductory Mathematics: Analysis and Algebra to be a very readable (and humourous) introduction and overview of many of the basic ideas of pure mathematics and well worth reading before digging into those areas in more detail.

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#11 14-10-2003 7:55pm

dod

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A maths(ish) book that I love, great if you have any interest in econometrics itself or even a detailed interest in applied statistics. Keep it close by for regular reading! Introduction to Econometrics (Maddala). I really genuinely recommend this book for anyone with even a fleeting interest in Applied economics, statistics or Econometrics itself. Delightful stuff.

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#12 15-10-2003 5:41pm

Syth

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Flatterland by Ian Steward is very good. Humourous and explains funky maths that you mightn't learn anywhere else.

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#13 28-10-2003 6:23pm

charlieroot

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Vector Calculus - Marsden and Thromba.

Complex Analysis - Lang.

Primes of the form x^n+dy^n=p - Cox. (tough going but very good).

Number Fields - Daniel A Marcus (Unfortunately out of print).

Concrete Mathematics - Not sure of the author and I haven't read it but I've been told its pretty good.

Noel.

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#14 01-01-2004 6:47pm

DMT

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Originally posted by Syth
Well How to Lie with Statistics tells you how you can use statistics to say anything..... But it's like 50 years old, so you mite have problems getting it.

Can be got at Amazon.co.uk

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#15 04-01-2004 11:31pm

ecksor

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I just realised that I left out "A Mathematician's Apology", by G.H Hardy, written just before he died and after he had stopped producing original mathematical work, he defends his choice of work and explains his motivations as a mathematician. A short little book (the version I have has a foreward by C.P. Snow that's about as long as the book itself, it's 50 pages long ... )

Just finished reading "The Music of the Primes: Why an unsolved problem in mathematics matters" by Marcus du Sautoy. Obviously it covers similar things to the book I mentioned above by Sabbagh, but I found it more engrossing. He uses the analogies of musical notes of the primes and the metaphorical instruments which create them frequently as he gives a historical account of the various mathematicians who have made major contributions to the search, tries to explain those contributions, and puts them into the context of how mathematics in general was evolving as time went on. I think du Sautoy is probably the most infectiously enthusiastic writer of science matters I've come across since Feynman. I immediately signed up for a course in complex analysis

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#16 14-02-2004 9:17pm

DapperGent

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Engineering Mathematics:
http://www.amazon.com/exec/obidos/tg/detail/-/0831131527/qid=1076789101/sr=1-1/ref=sr_1_1/104-1986766-8886323?v=glance&s=books

And Advanced Engineering Mathematics
http://www.amazon.com/exec/obidos/tg/detail/-/0831131691/qid=1076789101/sr=1-2/ref=sr_1_2/104-1986766-8886323?v=glance&s=books

Both by K A Stroud. Very well written in a kind of sequenced style with each lesson building on the next, examples are episodic and you're encouraged to do plenty of scribbling yourself as you learn. It's difficult to describe just how good these books are, but it's like having an expert sitting beside you telling you to do examples and not letting you go on until your understanding of a concept or technique is complete.

Five stars, two thumbs up etc.

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#17 15-02-2004 2:24am

smiles

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For statistics & the basic probability needed to understand stats read:
John E. Freund's Mathematical Statistics by Irwin. Miller , Marylees Miller & John E. Freund

It's my one of my course text books and I can quite honestly say that it makes things very easy to understand and replicate.

General Layout: Concept explaination, Theory, Examples followed by exercises.

<< Fio >>

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#18 14-03-2004 11:08pm

davros

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Scientific American ran a column called "Mathematical Games" for 25 years until the early 1980s. They were written by Martin Gardner and are all published in book form (the list of books is here).

Martin Gardner did more to popularise the field of recreational mathematics than anyone else - there are generations of mathematicians, engineers and scientists that owe their choice of career to him. I count myself among them.

You can't go wrong with any of his books. I have collected nearly all of them myself over the last twenty years.

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#19 06-04-2004 8:41pm

vinks

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quantum computing - second edition, by mika hirvensalo. its quantum computing for dummies (~100pages) and the rest is quantum mechanics and some number theory (another 100pages or so).

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#20 15-06-2004 7:50pm

Boston

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Differential Equations & Liner Algebra by Green Berg

More to do with differential Equations and the Linear Algebra you need for them, then anything else. Requires a solid foundation in calculus though. Extremely good but maybe thats because it seems to be the same style as my lecturer.

Discrete Mathematics and its applications by kenneth H. Rosen.

Logic, advanced counting Deiscrete Probability and boolean algebra are what I use it for, but it covers other stuff as well. Really is a hellish book but it doesn't dumb anything down if you require that level.

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#21 04-09-2004 9:09pm

mrhappy42

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DapperGent wrote:

Engineering Mathematics:
http://www.amazon.com/exec/obidos/tg/detail/-/0831131527/qid=1076789101/sr=1-1/ref=sr_1_1/104-1986766-8886323?v=glance&s=books

And Advanced Engineering Mathematics
http://www.amazon.com/exec/obidos/tg/detail/-/0831131691/qid=1076789101/sr=1-2/ref=sr_1_2/104-1986766-8886323?v=glance&s=books

Both by K A Stroud. Very well written in a kind of sequenced style with each lesson building on the next, examples are episodic and you're encouraged to do plenty of scribbling yourself as you learn. It's difficult to describe just how good these books are, but it's like having an expert sitting beside you telling you to do examples and not letting you go on until your understanding of a concept or technique is complete.

Five stars, two thumbs up etc.

without these books I would not have passed some courses...I still have t 0-333-62022-4 next to my bed 14 years later. Buy them read them use them.

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#22 22-01-2005 10:44am

bcKay

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Anyone recommend a good 'do it yourself' tensor calculus text? I 'did it myself' once about 5 years ago for a class and now regret not keeping it up since I can barely remember how to do the cross product never mind remember what the Reimann tensor is all about :S

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#23 23-01-2005 5:07pm

vinks

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bcKay wrote:

Anyone recommend a good 'do it yourself' tensor calculus text? I 'did it myself' once about 5 years ago for a class and now regret not keeping it up since I can barely remember how to do the cross product never mind remember what the Reimann tensor is all about :S

mathematical methods for physicists - arken and weber, might be handy for what you want to do, but i cant remember if it covers too much on the basics for what you want to learn to do what you are at.

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#24 31-08-2005 9:59pm

tchelyzt

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Let's start with two novels:
A most beautiful novel about the search for mathematical truth (in a world undermined by Godel's proof) is Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis and who could fail to enjoy Robert Coover's Universal Baseball Association, Inc., J. Henry Waugh, Prop about a sad little accountant who gives his evenings over to simulating baseball games with pen and paper. Maybe not maths, but only to be appreciated by the number-lover.

The next two recommendations, closer to real maths, and marred a little but not too much by rather flowery language, are:
A Tour of the Calculus and The Advent of the Algorithm both by David Berlinski. Mathematical culture and history!

Imagining Numbers by Barry Mazur explains root -1 to anybody in a charming and poetic way.

Surreal Numbers by Donald E. Knuth is interesting for the way it walks through the invention of a number system, in this case John Conway's surreals, using the classic device of the dialogue. The conversation can be occasionally cringeworthy, but this short book provides hours of intellectual stimulation.

However, if I could take only one book to the proverbial desert island, it would have to be:
Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter

We can argue over whether it's a maths book - it defies classification - but I can't imagine a mathematician who wouldn't adore it.

______________________________________
I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and the Abyss. I saw ... a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable, but it was after dinner and I let it go.
- Sir Winston Churchill -

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#25 19-09-2005 10:15pm

mindurownbusnes

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http://www.crcpress.com/shopping_cart/categories/categories_products.asp?parent_id=469&so=1

I have bought books off this site and I have found it very interesting. Permutations and combinations is a subject I am researching at the moment on population studies and Im looking for any advice on a good book? Maybe Im coming across as vague but I am studying chances in a population and permutations is being used in a research group with myself. Any body have any suggestions?

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#26 23-12-2005 9:58pm

Sir Digby Chicken Caesar

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i'm reading 'the story of numbers: how mathematics has shaped civilisation' by John Mcleish atm. It's pretty interesting, there's one or two chapters devoted to each civilisation (each one the book covers anyway, I'm sure there's plenty that's left out.. it's a pretty small book) and how they developed their number systems and how math/numerology grew in their culture.

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#27 19-02-2006 3:34am

pisslips

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ecksor wrote:

I think du Sautoy is probably the most infectiously enthusiastic writer of science matters I've come across since Feynman. I immediately signed up for a course in complex analysis

I'm just a virgin in the maths world.Doin all the usual first year stuff(linear algebra, calculus, number theory). Gettin pretty bored, lookin for a book to re-ignite my interest, something that might give me a broader understanding (interest) of the subject.

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#28 09-04-2006 4:14pm

Dr. Octagon

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"Number-The Language of Science" by Tobias Dantzig is very good.

It gives a historical perspective of mathematical techniques and their origins.

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#29 13-05-2006 10:12pm

Michael Collins

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DapperGent wrote:

Engineering Mathematics:
http://www.amazon.com/exec/obidos/tg/detail/-/0831131527/qid=1076789101/sr=1-1/ref=sr_1_1/104-1986766-8886323?v=glance&s=books

And Advanced Engineering Mathematics
http://www.amazon.com/exec/obidos/tg/detail/-/0831131691/qid=1076789101/sr=1-2/ref=sr_1_2/104-1986766-8886323?v=glance&s=books

Yes really excellent books, very suited to engineers who want to be able to solve the problems without theory overload (however shortsighted that may be!). The complex variable stuff is particularly good in the Advanced version, as it's quite hard to get access to good examples in that area.

I'd recommend: Advanced Engineering Mathematics (same name!) by Erwin Kreyszig, similar to Dapper's Advanced book above but quite a lot more topics and detail.

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#30 14-05-2006 1:18am

Civilian_Target

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For the maths of Quantum and Particle/Atomic/Nuclear Physics, at an undergraduate/postgraduate level, I can't recommend "Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles" by Eisberg & Resnick enough. Weighing in at at least 3kg, probably more like 5, it's not for the faint hearted, but it's thorough and easy to understand, given the subject material!

ISBN 0-471-87373-X

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#31 06-06-2006 6:02pm

Dr. Octagon

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dudara wrote:

Both of Simon Singhs books are excellent. "Fermat's Last Theorem" and "The Code Book".

Someone else also recommended "The Man Who Loved Only Numbers", a biography of Paul Erdos, which I thoroughly enjoyed.

I'm reading "The man who loved only numbers now"...it's good but the book is more of a rehash of mathematically history than the biography of Paul Erdos. The chapter on Fermat's last theorem might as well have been ripped cleanly from Simon Singhs book.

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#32 16-06-2006 1:19pm

Darren1o1

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http://www.mth.uea.ac.uk/jtm/
Is free online engineering and science book in modules, not too bad, is general and goes from the basics to laplace, fourier and ODE's.

I found Engineering Mathematics by KA shroud good for basics in engineering and the Advanced Engineering Mathematics 8th by A E. Kreyzig pretty good also.

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#33 18-06-2006 1:14am

sillysod1234

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amy good titles out there about the history of zero

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#34 11-04-2007 8:13pm

dan719

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Would definately recomend a couple already mentioned. i.e the man who loved only numbers, simon sing's two books, but also Prime Obsession, it introduces at an understandable level The Riemann Hypothesis and also acts as a biography of the man himself. Also The dictionary of weird and interesting numbers is well worth a look.(thnk Hardy's taxi 1729-smallest number that can be written as sum of cubes in two different ways)

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#35 07-08-2008 1:01am

ZorbaTehZ

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"Men of Mathematics" E.T. Bell
Historical account of the lives of many famous mathematicians for example Euler, Cauchy, Lobatchewsky, Galois, Boole etc. Apparently it is the book that inspired John Nash to study mathematics, amongst others. Although there are many inaccuracies in the recounts, it still makes for fascinating reading.

"Mathematics in Western Culture" Morris Kline
Great book that shows the connections between Mathematics and various other disciplines, music, art, life, etc. It's on GoogleBooks here.

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#36 07-08-2008 3:02pm

thebaldsoprano

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charlieroot wrote: »

Concrete Mathematics - Not sure of the author and I haven't read it but I've been told its pretty good.

It is indeed, provides a good intro to a few areas of college level maths.

One of the authors is Donald Knuth. Say no more...

And on the subject,

"The Art of Computer Programming - Donald Knuth" has lots of interesting maths in it...

Doubt there'd be many people around who can read the whole thing, but good for dipping in to.

My favorite is:

"How to Solve It - G Polya"

Looks at problem solving techniques without going into anything too heavy.

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#37 07-08-2008 3:46pm

ZorbaTehZ

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Speaking of problem solving books, I'd recommend Paul Zeitz' 'The Art of Problem Solving' and Arthur Engel's 'Problem-Solving Strategies'. Two excellent books, especially the former.

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#38 04-09-2008 12:31pm

rjt

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ZorbaTehZ wrote: »

Speaking of problem solving books, I'd recommend Paul Zeitz' 'The Art of Problem Solving' and Arthur Engel's 'Problem-Solving Strategies'. Two excellent books, especially the former.

Seconded. And Knuth's books too.

"Calculus" by Michael Spivak is excellent. Also, "Galois Theory" by Ian Stewart (which has some great historical stuff in it).

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#39 02-12-2008 5:40pm

p to the e

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The Road to Reality by Roger Penrose is a very good book. this is the mathmatician that inspired Stephen Hawking. He describes the use of numbers in applications like Thermodynamics to String Theory and it's laid out in a relatively easy fashion.

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#40 02-12-2008 6:56pm

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I know they're far more physics-y than maths-y, and that there probably is absolutely no need to even mention them, as I'm sure most people looking at this thread would have read them, or at least know of them. But the Feynman Lectures on Physics are a must.

Genius, Feynmans biography by James Gleick, is also brilliant.

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#41 30-12-2008 7:24pm

Thomas_S_Hunterson

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tchelyzt wrote: »

However, if I could take only one book to the proverbial desert island, it would have to be:
Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter

We can argue over whether it's a maths book - it defies classification - but I can't imagine a mathematician who wouldn't adore it.

Picked this up today, looking forward to it.

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#42 14-01-2009 9:26pm

timbrophy

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How are you getting on with GEB? It is one of my two favourite books of all time.

If you can get a copy of "What is the Name of this Book" by Raymond Smullyan, which is the other, you will find it also explores Godel's theorem from a different direction - Logic Puzzles. I think it is out of print but you may be able to pick up a second-hand copy somewhere.

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#43 14-01-2009 9:51pm

Thomas_S_Hunterson

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timbrophy wrote: »

How are you getting on with GEB? It is one of my two favourite books of all time.

Really enjoying it so far, it's thought provoking and mind-expanding and structured really nicely.

timbrophy wrote: »

If you can get a copy of "What is the Name of this Book" by Raymond Smullyan, which is the other, you will find it also explores Godel's theorem from a different direction - Logic Puzzles. I think it is out of print but you may be able to pick up a second-hand copy somewhere.

I must look into this, I've heard it mentioned before. Seems it's available on Amazon so I might grab it next time I place an order.

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#44 18-01-2009 12:48am

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Just finished reading the biography of Srinivasa Ramanujan, it's called The Man Who Knew Infinity. Very good book. And Ramanujan was such an amazing person - such a pity about his early death.

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#45 18-01-2009 10:57am

mrhappy42

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http://en.wikipedia.org/wiki/Ramanujan

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#46 18-01-2009 12:37pm

eZe^

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I got The Fabulous Fibonacci Numbers by Alfred S. Posamentier and Ingmar Lehmann three or so years ago and I really really enjoyed it.

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#47 09-02-2009 3:29pm

confurius

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I gonna write my maths higher in June.
looking the book Text & Test 5. Ive got text & Test 4 already but cant find the following. does anyone know?

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#48 09-02-2009 3:32pm

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confurius wrote: »

I gonna write my maths higher in June.
looking the book Text & Test 5. Ive got text & Test 4 already but cant find the following. does anyone know?

This isn't the thread for this. But, here are second hand books, or here it is new.

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#49 09-02-2009 4:24pm

confurius

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-JammyDodger- wrote: »

This isn't the thread for this. But, here are second hand books, or here it is new.

Good man:rolleyes: Thanks

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#50 04-06-2009 9:44pm

random.stranger

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Michael Collins wrote: »

Yes really excellent books, very suited to engineers who want to be able to solve the problems without theory overload (however shortsighted that may be!). The complex variable stuff is particularly good in the Advanced version, as it's quite hard to get access to good examples in that area.

I'd recommend: Advanced Engineering Mathematics (same name!) by Erwin Kreyszig, similar to Dapper's Advanced book above but quite a lot more topics and detail.

Yes, these are excellent books. I couldn't recommend them highly enough. I would NOT say that they are exclusevely for engineers either. A lot of the content of Engineering Maths (KA Stroud) is relevent to leaving certificate students. It starts off at a basic level with worked examples and builds up your understanding as you go through it. It is very easy to go through it on your own. Stroud is a genius.

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#51 20-08-2009 3:28pm

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I was a fan of Engineering Maths by K.A. Stroud - helped me in my Science Degree no end, its beige cover was creased

I liked some of the popular science books by Ian Stewart which contained many mathematical elements in them

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