call for guinea pigs
As I've mentioned recently, I'm trying to write an undergraduate abstract algebra textbook that's readable by humans,1 because I think that somebody should.
Well, that's perhaps a little unfair. There are many completely unreadable textbooks on abstract algebra, so many of which unaccountably think it's ok to start with "Definition 1.1: a group is a set G equipped with an associative binary operation ∗ …" without first explaining either what a binary operation is or why anyone in their right mind might care, and which then carry on in that vein with almost no illustrative examples, motivation or mention of applications. But there are also quite a few which make a reasonable effort to explain either group theory or ring theory in an accessible manner, include plenty of examples, provide a bit of historical and biographical background about the key people and topics, and so on. Unfortunately, most such books either focus only on group theory and leave rings and fields out, or (more rarely) focus on ring theory and introduce groups as a bit of an afterthought.
There are also a couple of really good, readable and comprehensive books that I know of. One is A First Course in Abstract Algebra by John Fraleigh, which I bought a copy of twenty years ago in my second year at York, and which I found to be life-savingly clear. The other is Contemporary Abstract Algebra by Joseph Gallian, which also covers everything that turns up in a typical undergraduate algebra course, and does it well. Unfortunately, the current edition of Fraleigh is about £50 (nearly £80 in hardback) and Gallian is nearly £60 (or nearly £150 in hardback), so they're both beyond a typical student budget. (Presumably there's some compelling business case that these prices are optimal from a sales point of view, but I can't remotely imagine how.)
Meanwhile, the core second year Algebra II module here has been taught in alternate years recently by a very tall, high-powered Russian algebraist. He's a very clever guy, and tends to go quite fast and cram a lot of extra, advanced stuff into the course. So his lectures are brilliant if you're in the top 10% or so of the year, but are a bit less fun (sometimes confidence-damagingly so) for the other three hundred students taking the course that year, many of whom entirely turn their backs on algebra (an important area of mathematics) as a result. Over the last few years a number of my undergraduate tutees have said "I'm not really following the lectures - can you recommend a good book that might help?" and I've not really had anything helpful to tell them other than "See if you can find a cheap second-hand copy of an earlier edition of Fraleigh" or "Run to the library and grab one of the four available copies of Gallian before anybody else does".
So I thought I'd have a go at writing a textbook that was readable and comprehensive, and then see if I could persuade someone to publish it at a reasonable price (ideally, somewhere in the £20-£30 range).
About three chapters in, I serendipitously found myself in contact with a commissioning editor at a notable university press, mentioned I was trying to write a textbook and asked him if he'd be willing to have a look at what I'd got so far and let me know if he thought it was any good. Yes, sure, he said - send me your current draft and I'll take a look at it. So I did, and he liked it and encouraged me to send in a proper book proposal when I felt ready to do so - which I did a little bit later. In particular, he said that affordability is a key consideration for him, and all the books he's commissioned recently have been in the £25ish range. I've been thinking carefully about the layout, and have stolen some ideas (wide margins, sidenotes rather than footnotes) from Edward Tufte's book The Visual Display of Quantitative Information as well as a few other books: in particular Introducing Einstein's Relativity by Ray d'Inverno, which does really well at explaining really complicated stuff like tensor calculus and advanced cosmology in a very friendly way. (I mentioned this to the editor and he said "I was the commissioning editor for that when I first started working here - I'm glad you liked it".)
So at the moment we're waiting to hear back from the reviewers, who have been a bit slow, but he says he's "very keen on the book" and is pushing the reviewers to get back to him with detailed (and positive) comments. All very exciting.
Anyway, so I'm getting to the point where I could do with some test readers. I'm going to enlist the help of some of my first- and second-year undergraduate tutees (who are, after all, the target audience), but if any of the rest of you would be interested then I'd be very grateful for any constructive comments you might have.
Poll Call for Guinea Pigs
(Note added in proof: for "GCSE" read "up to and including GCSE/O-Level or equivalent" and for "A-Level" read "A-Level, AS, Scottish Higher or equivalent".)
1Most mathematics undergraduates are also humans, of course.
Well, that's perhaps a little unfair. There are many completely unreadable textbooks on abstract algebra, so many of which unaccountably think it's ok to start with "Definition 1.1: a group is a set G equipped with an associative binary operation ∗ …" without first explaining either what a binary operation is or why anyone in their right mind might care, and which then carry on in that vein with almost no illustrative examples, motivation or mention of applications. But there are also quite a few which make a reasonable effort to explain either group theory or ring theory in an accessible manner, include plenty of examples, provide a bit of historical and biographical background about the key people and topics, and so on. Unfortunately, most such books either focus only on group theory and leave rings and fields out, or (more rarely) focus on ring theory and introduce groups as a bit of an afterthought.
There are also a couple of really good, readable and comprehensive books that I know of. One is A First Course in Abstract Algebra by John Fraleigh, which I bought a copy of twenty years ago in my second year at York, and which I found to be life-savingly clear. The other is Contemporary Abstract Algebra by Joseph Gallian, which also covers everything that turns up in a typical undergraduate algebra course, and does it well. Unfortunately, the current edition of Fraleigh is about £50 (nearly £80 in hardback) and Gallian is nearly £60 (or nearly £150 in hardback), so they're both beyond a typical student budget. (Presumably there's some compelling business case that these prices are optimal from a sales point of view, but I can't remotely imagine how.)
Meanwhile, the core second year Algebra II module here has been taught in alternate years recently by a very tall, high-powered Russian algebraist. He's a very clever guy, and tends to go quite fast and cram a lot of extra, advanced stuff into the course. So his lectures are brilliant if you're in the top 10% or so of the year, but are a bit less fun (sometimes confidence-damagingly so) for the other three hundred students taking the course that year, many of whom entirely turn their backs on algebra (an important area of mathematics) as a result. Over the last few years a number of my undergraduate tutees have said "I'm not really following the lectures - can you recommend a good book that might help?" and I've not really had anything helpful to tell them other than "See if you can find a cheap second-hand copy of an earlier edition of Fraleigh" or "Run to the library and grab one of the four available copies of Gallian before anybody else does".
So I thought I'd have a go at writing a textbook that was readable and comprehensive, and then see if I could persuade someone to publish it at a reasonable price (ideally, somewhere in the £20-£30 range).
About three chapters in, I serendipitously found myself in contact with a commissioning editor at a notable university press, mentioned I was trying to write a textbook and asked him if he'd be willing to have a look at what I'd got so far and let me know if he thought it was any good. Yes, sure, he said - send me your current draft and I'll take a look at it. So I did, and he liked it and encouraged me to send in a proper book proposal when I felt ready to do so - which I did a little bit later. In particular, he said that affordability is a key consideration for him, and all the books he's commissioned recently have been in the £25ish range. I've been thinking carefully about the layout, and have stolen some ideas (wide margins, sidenotes rather than footnotes) from Edward Tufte's book The Visual Display of Quantitative Information as well as a few other books: in particular Introducing Einstein's Relativity by Ray d'Inverno, which does really well at explaining really complicated stuff like tensor calculus and advanced cosmology in a very friendly way. (I mentioned this to the editor and he said "I was the commissioning editor for that when I first started working here - I'm glad you liked it".)
So at the moment we're waiting to hear back from the reviewers, who have been a bit slow, but he says he's "very keen on the book" and is pushing the reviewers to get back to him with detailed (and positive) comments. All very exciting.
Anyway, so I'm getting to the point where I could do with some test readers. I'm going to enlist the help of some of my first- and second-year undergraduate tutees (who are, after all, the target audience), but if any of the rest of you would be interested then I'd be very grateful for any constructive comments you might have.
Poll Call for Guinea Pigs
(Note added in proof: for "GCSE" read "up to and including GCSE/O-Level or equivalent" and for "A-Level" read "A-Level, AS, Scottish Higher or equivalent".)
1Most mathematics undergraduates are also humans, of course.