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Matt Westwood (Reading, UK)

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Complex Analysis: The Hitchhiker's Guide to the Plane
Complex Analysis: The Hitchhiker's Guide to the Plane
by Ian Stewart
Edition: Paperback
Price: £39.61

1 of 1 people found the following review helpful
5.0 out of 5 stars One of the better texts on the subject, 5 Jan. 2008
Although my course notes were fully comprehensive when I did this subject, they lacked that extra something that made the exposition limpid. I got this book after I'd finished the course, but I wish I'd had it at the time because I may have got a better result (i.e. a 1 rather than a 2).

Complex Analysis is when maths grows up and really starts becoming a useful tool - it underpins the whole of modern physics and more. It's also rumoured to be a difficult subject. Stewart and Tall give the lie to this by writing a text which is one of the clearest texts I've seen on *any* mathematical subject.

I agree with all the other reviewers. This book rocks.


Brief History of Infinity: The Quest to Think the Unthinkable
Brief History of Infinity: The Quest to Think the Unthinkable
by Brian Clegg
Edition: Paperback
Price: £8.99

17 of 19 people found the following review helpful
2.0 out of 5 stars There are better works around, 5 Jan. 2008
If I'd not read Rucker's work on the subject (Infinity and The Mind), I might have thought this was pretty cool. But having said that, we may be reaching saturation point on the books about mathematicians (which this seems to be) - we need more about the *maths*.

I think there's a perception that to keep it readable it needs to be dumbed down. There's a lot of that going on. It's possible to explain *everything* in simple terms if you try hard enough. Maybe Clegg hasn't tried all that hard, or maybe he's scared of alienating the casual reader. Whatever, he doesn't do much for the mathematically literate who want to get something out of this. There's not actually all that much.


Infinity and the Mind: The Science and Philosophy of the Infinite (Penguin science)
Infinity and the Mind: The Science and Philosophy of the Infinite (Penguin science)
by Rudy Rucker
Edition: Paperback

3 of 3 people found the following review helpful
5.0 out of 5 stars I almost had it then ... it's gone ... think I'll read it again, 5 Jan. 2008
There are several mindblowing things I got from this:

1. The standard way of building up a number as the set containing all the smaller numbers (first time I'd encountered this concept - I followed it up later)

2. The difference between ordinal numbers and cardinal numbers - I followed that one up too

3. Getting from one level of infinity to another is a big imaginative stretch. I think I almost caught up with the thought for a moment, but now it's gone again. I'm alright with the lower alephs, but when you get up to the inaccessibles I sort of got lost. I need to go and try again.

This is probably the most mindblowing maths book you will ever see on the popular science shelves. And I haven't actually seen it on the shelf for a good while. Do *not* lend this book to *anyone* - you won't get it back for *years*.


The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (amsns AMS non-series title)
The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (amsns AMS non-series title)
by Colin Conrad Adams
Edition: Paperback
Price: £29.95

6 of 6 people found the following review helpful
3.0 out of 5 stars Nope, sorry, found it impenetrable, 5 Jan. 2008
I think I need to go away and work at this a bit more. I've come into this from a graph theory module at undergrad level, and a certain amount of abstract algebra at (probably) masters level, but I just haven't managed to break through this yet.

The problem's either with me, or with the exposition. I'm going to have to give it another go.

All the same, it's well and entertainingly written, just that I haven't a clue what it's on about.


Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
by John Derbyshire
Edition: Paperback

8 of 9 people found the following review helpful
5.0 out of 5 stars A popularisation the focuses on the actual mathematics, 5 Jan. 2008
Most books of this kind don't bother to try to talk about the actual maths, so they waffle on about the mathematicians, which is something like watching interviews of rock stars when you want to be seeing them performing.

This book is an exception - it does its mightiest to actually explain the innards of the conjecture and goes some way towards achieving its aim.

No quibble - this is the best book on its subject that's available at the moment, unless you're going for something more technical.


A Course in Group Theory (Oxford Science Publications)
A Course in Group Theory (Oxford Science Publications)
by J. F. Humphreys
Edition: Paperback
Price: £35.99

6 of 6 people found the following review helpful
4.0 out of 5 stars A wide scope for a book of its level, 5 Jan. 2008
Although written at the level of an undergraduate mathematics student, it goes surprisingly deep.

It starts from the basic definition of a group, but doesn't hang around with all the tedious underpinning that a lot of abstract algebra books thrive on. This is good. The reader can get on with the business of what groups are all about.

Exercises are included, and for a fair number of them there are hints and sometimes full solutions. This is admirable - not enough books do this.

I have a few quibbles: its exposition is muddy in places and it is not easy to understand where a proof or train of thought is going. But there's no room to elucidate - we're off on the next level of depth.

The main thrust of this work is that of investigating the classification of groups, and there is some emphasis on identifying isomophisms.

The later part of the book touches on the problem of the classification of the sporadic groups, a long-term project of modern mathematics which has only been completed a couple of decades ago. A full list of the sporadic groups is listed at the end, and the some discussion of the Mathieu groups is undertaken, which is possibly the most exciting aspect of the entire book.

Highly recommended as a companion to any undergrad course in group theory.


Elements of Abstract Algebra (Dover Books on Mathematics)
Elements of Abstract Algebra (Dover Books on Mathematics)
by Allan Clark
Edition: Paperback
Price: £7.99

1 of 1 people found the following review helpful
4.0 out of 5 stars Compact and meaty, 5 Jan. 2008
This innocuous-looking book is only tiny, but contains a thorough grounding in modern abstract algebra.

Starting from the raw basics of set theory, it covers group theory up to the Sylow theorems and some basic results about the symmetry groups; ring and field theory; Galois theory, and classical Ideal theory.

The pace is brisk, but not rushed - although the exercises tend to be difficult. Mind, the results often lead on logically to the next stage, so if you're not able to work out how to do an exercise, there may be clues later on. As with all works of this kind, doing the exercises is the only way to consolidate what's been learned. Unfortunately there are no answers given - it's sink-or-swim.

Best taken on along with another work (or two), reading them in parallel. I found that worked for me - if I didn't understand something in Clark, I'd try it from another point of view, e.g. Warner or Whitelaw, and vice versa.

No 5 stars because there is the occasional flaw in the reasoning, and it can be a bit ambiguous and confusing in places. A good book nevertheless.


Top Secret Ultra
Top Secret Ultra
by Peter Calvocoressi
Edition: Paperback

6 of 7 people found the following review helpful
3.0 out of 5 stars An interesting insight, 5 Jan. 2008
This review is from: Top Secret Ultra (Paperback)
Unfortunately you don't learn a great deal about Bletchley Park in this volume, but you do get to feel you have a nodding acquaintance with some of the key players.

By its nature a book like this (memoirs of someone working there from some thirty years on) is going to be sketchy and anecdotal, and very far from being complete, but as an interesting adjunct to all the other works which document this crucial aspect of WWII it's worthwhile.

The author's style is self-deprecatory in places, almost apologetic, but a sense of his love for the whole episode shines through.

Get this if you're a serious historian, borrow it if you're interest is merely casual, but read it anyway.


Pink Floyd Encyclopedia CD & Book
Pink Floyd Encyclopedia CD & Book

5.0 out of 5 stars About as complete as it gets, 5 Jan. 2008
What is it about the Floyd that attracts so many cataloguers, collectors and organisers?

Vernon Fitch has done a bang-up job in cataloguing practically every single person, artwork and place that Pink Floyd have ever had a connection with.

It's not (I believe) 100% complete and accurate in that not every single recording session has been catalogued in full detail (in particular, knowing the exact personnel who attended the Saucerful of Secrets sessions may be important to some, and there is a little ambiguity) but practically everything else is there.

There's even a Hawkwind CD with a cover of Interstellar Overdrive in my copy (not the first Floyd song they covered, they also did a creditable version of Cymbaline, woodjableve).

Floyd completists: get it. Others: get it anyway.


Modern Algebra (Dover Books on Mathematics)
Modern Algebra (Dover Books on Mathematics)
by Seth Warner
Edition: Paperback
Price: £22.99

2 of 2 people found the following review helpful
5.0 out of 5 stars Rigorous and complete, 4 Jan. 2008
Warner does not shy away from a rigorous justification of practically all his results. Every link (except for some straightforward results which are left to the student to finish off) is detailed in the chain of reasoning from reasonably-first principles to the establishment of the natural numbers, integers, rationals and beyond.

There is a wealth of interesting byways introduced in the copious exercises and problems, some of which are easy and some rather more difficult. The only downside is that the solutions are in general not given, although some are explored later in the text.

At the start I had difficulty with his idiosyncratic notation (e.g. using triangles for the general operation - most writers use a small circle), but if you were to try and rewrite some of this work using the more conventional notation, you would see he has amply good reasons for using the notation he does.

The book could be somewhat improved by tidying up the layout (and not least by using some means to indicate when a proof is finished), but then again this was written way back in the dim and dark 1960's before we had such delights as, for example, LaTeX.

Also, I did find one or two inaccuracies (e.g. in the proof of Theorem 19.11 it states that an isomorphism is established which is in fact a monomorphism) but I haven't found anything serious except for one or two problems which I can't solve and I'm uncertain as to whether the problem as given is correct - but that's probably just me needing to think about it a bit harder.

As has been pointed out, this is probably inappropriate as an introduction to the subject, but as a means of consolidating a course of study that has already been (perhaps shakily) accomplished, it's admirable. If you're confused, for example, by the integers' ring properties (like I was - don't ask, it's complicated, and I couldn't get anyone to understand what I was on about), then you have *definitely* come to the right book.

It's hard work, but if you really want to understand everything there is to know about abstract algebra, then this is the work to study.


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