Books

[Lyssia]

What are we all reading, maths-wise?

 

Mention your second year complex analysis textbook if you really want to, but I'm interested in hearing about what people (especially postgrads, postdocs, whatever category Matt Grime falls into, and PeopleWhoOnceWereMathmosButThenTurnedTraitor - like me) are reading about maths in their spare time.

 

I'll start off with my current - Modular Forms and Fermat's Last Theorem. It's not easy by any stretch, but it's interesting.

 

What about you?

[cosine]

What are we all reading' date=' maths-wise?

 

Mention your second year complex analysis textbook if you really want to, but I'm interested in hearing about what people (especially postgrads, postdocs, whatever category Matt Grime falls into, and PeopleWhoOnceWereMathmosButThenTurnedTraitor - like me) are reading about maths in their spare time.

 

I'll start off with my current - Modular Forms and Fermat's Last Theorem. It's not easy by any stretch, but it's interesting.

 

What about you?

 

Sorry, only an undergrad, but here's some new stuff I've been reading:

 

http://www.cogsci.indiana.edu/farg/peiwang/PUBLICATION/

 

Dr Pei Wang of Indiana State University has been research NARS, Non Axiomatic Reasoning System, to work on how the human mind's logic system works. There is even an interactive program he's made using NARS.

[Lyssia]

Hm, I thought the comment about postgrads etc could possibly be misinterepreted. My bad.

 

This sounds silly but the idea of axioms existing in my reasoning is so...uh, axiomatic, that to not have them would seem quite weird. Thanks for the link, I'll bookmark it and get round to having a browse sometime. What do you make of those works?

[cosine]

Hm' date=' I thought the comment about postgrads etc could possibly be misinterepreted. My bad.

 

This sounds silly but the idea of axioms existing in my reasoning is so...uh, axiomatic, that to not have them would seem quite weird. Thanks for the link, I'll bookmark it and get round to having a browse sometime. What do you make of those works?[/quote']

 

Well Pei Wang's delved into the subject in some very interesting ways. He distinguished between Pure Axiomatic Systems, and NARS, (and there is also a Semi-Axiomatic which is more like NARS). I should probably clarify a bit though.

 

Pure Axiomatic Systems are purely deductive from the axioms. They assume full knowledge and resources for any question asked them, and if they can't answer a given question, it is the questioner's fault and not the system's.

 

NARS are more inductive, being presented with problems with which they have insufficient knowledge and resources, so they are constantly changing. One of the most important distinctions being made here is that PAS (Pure Axiomatic Systems) are purely deductive, where as NARS are not.

 

However the interesting thing about studying NARS is that if it is a system then there must be inner workings, which of course there are. Pei Wang is studying them, and has even programmed what he's found into a demo on his website. Pei Wang is continuously working on this so there is new research often on his site.

[Lyssia]

I'm reading through Introduction to Lattice Theory by Rutherford at the moment. Believe it or not I had to get some kind of background in lattices as they're used as a basis in a formal expression of semantic aspect.

 

I'm usually rather wary of mathematical texts from that period (this book's from the 1960s) but it's pleasantly surprising so far!

[rakuenso]

you read MATH books for... FUN>?

 

GASP

[Lyssia]

Yup. Is this so strange?

[cosine]

I'm reading through Introduction to Lattice Theory by Rutherford at the moment. Believe it or not I had to get some kind of background in lattices as they're used as a basis in a formal expression of semantic aspect.

 

I'm ususally rather wary of mathematical texts from that period (this book's from the 1960s) but it's pleasantly surprising so far!

 

Why worry about books from that period? I don't not much about lattices... I'm reading a book from 1969 by H.S.M. Coxeter called Introduction to Geometry, incredible reference!

[RyanJ]

you read MATH books for... FUN>?

 

GASP

 

Maths is fun! Although most people would argue with that.

 

I'm currenty looking through the CRC Concise Encyclopedia Of Mathematics and thats one hell of a great book, just about everything in there!

 

Other than that I'm reading a book on the Golden Ratio and another on Pi and Irrational numbers.

 

Cheers,

 

Ryan Jones

[Lyssia]

Why worry about books from that period? I don't not much about lattices... I'm reading a book from 1969 by H.S.M. Coxeter called Introduction to Geometry[/u'], incredible reference!

 

Bitter experience, I'm afraid!

[Lyssia]

Maths is fun! Although most people would argue with that.

 

I'm currenty looking through the CRC Concise Encyclopedia Of Mathematics and thats one hell of a great book' date=' just about everything in there!

 

Other than that I'm reading a book on the Golden Ratio and another on Pi and Irrational numbers.

 

Cheers,

 

Ryan Jones[/quote']

 

Have you read The Joy of Pi?

[Dave]

I'm reading through Introduction to Lattice Theory by Rutherford at the moment. Believe it or not I had to get some kind of background in lattices as they're used as a basis in a formal expression of semantic aspect.

 

I'm usually rather wary of mathematical texts from that period (this book's from the 1960s) but it's pleasantly surprising so far!

 

I've read that book. It's really rather good, and for those that haven't touched Lattice Theory it's ideal for starters

[Lyssia]

I've read that book. It's really rather good, and for those that haven't touched Lattice Theory it's ideal for starters

 

Weren't you the person who recommended it to me in the first place?

 

I like how thick it is - about half an inch. A nice, non-intimidating thickness for a maths text like this from the 1960s!

[Dave]

Weren't you the person who recommended it to me in the first place?

 

I like how thick it is - about half an inch. A nice' date=' non-intimidating thickness for a maths text like this from the 1960s![/quote']

 

Oh yes - now I remember you asking me

 

Yes, it's a nice thickness. I've found that a lot of the older-style books are just absolutely beasting, and far too hard for a meagre undergraduate for myself to understand. Although I did pick up quite a good one on Measure Theory the other day, but I can't remember its name.

 

Currently reading "Algebraic Number Theory and Fermat's Last Theorem" by Stewart and Tall. Can't be bothered googling, but for those with some experience with ring theory and some basic algebra, it's quite an interesting insite into the problem. Also contains a lot of historical motiviation, which I find to be essential for a good maths book.

[Lyssia]

Currently reading "Algebraic Number Theory and Fermat's Last Theorem" by Stewart and Tall. Can't be bothered googling, but for those with some experience with ring theory and some basic algebra, it's quite an interesting insite into the problem. Also contains a lot of historical motiviation, which I find to be essential for a good maths book.

 

Ooh I have that book! It doesn't mollycoddle you at all, but given that it's a great intro into ANT, I think. Its predecessor ("Algebraic Number Theory"; it was first published well before Wiles' proof) was the starting point for my reading on the topic; it was a favourite of my supervisor but with good reason, I think.

 

The measure theory book I had was Lebesgue Integration and Measure. I have emotional scars from that course so I probably can't be unbiased about the book. Anyone else read it?

[RyanJ]

Have you read The Joy of Pi[/url']?

 

Not yet, it is any good? if its good I'll buy a copy have a read!

 

Cheers,

 

Ryan Jones

[Lyssia]

I don't think there's anything in it that you wouldn't find in any other "reacreational" book about pi, but I haven't read that many so I can't make a good comparison. Having said that, I do like the way it's all presented. It's probably not worth the hardback price so if you want to ask for it for Christmas or something, the paperback is better in terms of the money.

 

Ooooh, I could start off on a rant about the price of maths books here, but I won't.

[matt grime]

Harris's Principles of Algebraic Geometry is on my shellf begging my indulgence again, Cox's Primes of the form x^2+ny^2 for recreational purposes, Mumford's Red Book. Generally I don't read books much these days: I tend to read papers and use books for reference purposes. However I'm trying to get into a new area of research so there are a few of books lying around.

 

I have a few non-technical books: Tim Gowers's Very Short Introduction to Mathematics is one I often reread and should be on everyone's shelf. Plus The Man Who Loved Only Numbers, Erdos's biography.

 

Somewhere inbetween there's the Proofs from the Book book that often glance at. Less so these days since I no longer need to find interesting, relatively content free high level mathematics to talk to undergraduates about these days (no teaching for three years!)

[Lyssia]

Hey, if it no longer interests you then I'm happy to take Proofs from the Book from you on an "extended loan"!

[Dave]

I have The Joy of Pi sitting on my bookshelf. It's quite a nice little book, as you rightly said

 

What else? There's a couple of boring undergraduate analysis texts (Numbers and Functions, RP Burn - even the title sounds dull) but I do have another excellent book for any first year undergraduates called "The Foundations of Mathematics" by Stewart and Tall (again). It's quite nice for those who are just starting a degree and helped me a bit during my first term.

[Lyssia]

I have a plethora of books about infinity. Well, all right, about four or something (which I still think is a bit excessive). Later on today I'll draw up A List and you can all gawk at it.

[Lyssia]

Right, this is the infinity book I'm reading at the moment: Everything and More. The Amazon page comes with some impressive-looking reviews but the only customer review is disappointing. To be honest, I can see both points of view. The front of the book carries a one-liner: "If Terry Pratchett wrote a book about mathematics, it would look uncannily like this."

 

Which is true, in a way. Wallace's prose is easy to read, his language is about as far from stuffy as you can get (cf. footnote 29 on p. 114, which begins "Sh*t. All right. The strict truth is more complicated than that....") and sometimes it's just downright funny. It's a book that attempts to present the story of [math]\infty[/math] at least somewhat comprehensively and yet in a way that makes it accessible to those without university level maths.

 

It sounds a tall order, and it is. Does Wallace manage it? I'm only about half way through at the moment but so far, I have to say I have my doubts. The main stumbling block for me is the most obvious: there isn't a contents page. I don't know how he (or his editor) justifies it - throughout the book is referred to as "a booklet" but it's just over an inch thick: much bigger than your average "booklet" and certainly big enough to make a ToC necessary, let alone a good idea.

Other than that, the Amazon reviewer's concern about the proliferation of abbreviations is also something that bugs me. Well, it wouldn't bug me so much if all the abbreviations Wallace were actually given in the Foreword. A third and more minor annoyance is the way that everything carries a heavy US-bias. Continual references to Calc 1 don't mean much to a European who has no experience of the USA university system.

 

If you can ignore (or at least live with) those two down points, then the book's quite good style-wise. I still have doubts about the way Wallace gets through the maths - can it really be said that someone with no higher maths experience will understand it as an "armchair book"? I'll reserve judgement for when I've finished reading it. In the meantime, I'll recommend it - for mathmos, at least - simply because it's got a very blue cover, and blue is my favourite colour.

[Lyssia]

Has anyone read God created the integers? I just found it on Amazon today and wondered if there's some feedback from here*.

 

*it was a long shot, but there's no harm in trying.

[Mot]

Rereading "What is Mathematics" by Robbins and Courant.

 

Cheers

Mot

[silkworm]

I just began reading Principia Mathematica by Isaac Newton.

 

It's published under "Principia" in the On The Shoulders of Giants series, and it boasts a foreward from Steven Hawking, which I haven't read and really care less about at this point. Maybe I'll gain some interest in it later.

 

Unfortunately the book has been translated from Latin, and it took me a few hours to realize that the first paragraph was saying that density*volume=mass, because I guess mass was a new concept at the time.

 

I'm going to have to take notes on translating the translation to understand it but I'm excited to hear it from Ike himself (even if it's translated translated version).

 

Directly after this I plan on devouring anything and everything I can get my hands on written by Galileo.