Why are textbooks in math and science so bad?

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  • #126
matt grime
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If it is not easy, then why the hell would they work there? :rofl:

That seems to summarize you ignorance quite succintly. I can't say I had much sympathy for your position before, but now any residues just vanished off the face of the earth. The mere fact that you state maths is hard to learn from text books (and *forces* you to have attend to lectures as if that were a burden rather than a privilege - you're at UCLA, right, so you actually get to hear Terry Tao in person) speaks volumes. Maths *is* hard to learn. Yes, some textbooks are bad, but the fact you find them difficult doesn't appear to be any metric on the book's quality.
 
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lower division books like calculus, are chosen by a committee, and a commitment is even made to use it for so many years. I am currently teaching from and complaining about a book, the nth iterate of thomas, by others including hass and maybe finney, that is just terrible. Excelent books are available but considered too hard for todays students, who are often deficient in algebra trig and geometry, plus all forms of formal reasoning.

Upper level books, meaning 4th year, grad level, math major books, or grad degree, even linear algebra and proof theory books, are usually chosen by the professor, who is allowed to choose his/her own books.

I have used my own notes at times, providing them free to the students, as I do some of them to the entire world on my website. Other professors choose to use their own books, but these in my opinion are among the very best books available, both pedagogically and mathematically.

In lower level courses we have been in the position of choosing books by our own faculty, which in my view were not the best books available mathematically on the subject of calculus. But these books are among the very best available for the average audience now taking calculus and were written by our professors with that fact in mind.

These professors do profit from these sales, and deserve to do so. We are free to drop these books at any time, and recently did so in favor of the thomas hass finney book, which unfortunately is greatly inferior to the book by our own former professors.

In graduate level courses the books available are mostly excellent, written by profesionals for people wishing to become professionals. Still they are often too hard for students to read, and hence a new generation of easier books even at the graduate level has become common, e.g. dummit and foote in grad algebra. this is a good book but not an excellent book.

the book by lang used to be standard for grad algebra and that by hungerford was considered second tier. now lang is considered much too hard, the book by hungerford is even considered hard, and that of dummit foote is the default choice many places.

you notice there is a steady tendency downwards, even at the grad level. so this year i found myself criticizing the DF book that I had chosen for the grad algebra course, at the request of some of the students who said they liked it.

At the grad level, for a person like myelf who has a phD but is not a specialist in algebra, to write an algebra book, is considered odd. Even in algebraic geometry which is my speciality, we prefer to sue books not just by algebraic geometers, but by world famous figures at or near the fields medal status, such as those by Mumford, Hartshorne, Shafarevich,...


My notes in most cases consist of the result of reading and teachiong from books by better authors and filling in gaps which I or my students have found troubling, or adding material or expanding where it seems helpful. Some books, even by top authors have errors which it is fun to find and correct.

So my notes contain as much help as I am able to give, and may be easier to read than standard books, but the danger for the student in choosing a book by someone not of top stature is that the insight only a master can give is lost. An author cannot give what he does not have, and only the best see deepest.

since my own research is in riemann surfaces and their jacobians and moduli, theta divisors and their singularities, and torelli theorems, it is only in these areas that i feel qualified to comment knowledgeably. and yet ironically, it was only recently that i learned to appreciate the work of my friend George Kempf on the topic of riemann singularities theorems, done over 30 years ago!

indeed some of my writings on the topic must have puzzled some people, for their naivete, these past three decades. on the other hand i have been part of some research in areas of this question where kempfs ideas did not apply, so there is a good side to trying your best, even in ignorance. I.e. it is possible for someone more knowledgable to write a more complete book, and yet for someone else less so to do some new research in that very subject. i.e. knowing and doing are different, so there is hope for all of us.
I am taking the honors undergrad algebra course at my school right now and the professor doesn't follow any book, he just "gives" us his notes. (However for him giving us his notes means we go to class and copy them from the board.) He does however assing a book for the class a a reference which we may or may not buy. This year he choose Dummit and Foote for (almost) the same reason that you did. Two years ago when he taught the class some of the students found the DF book and they said they liked it. Actually this professor used to recommend Michael Artin's book but I guess this was too hard for most people and hence they ended up looking in other books.

I will be taking graduate algebra next year and my professor had told me to make sure to read Lang. He said that most people just read Hungerford because it is easier. What do you think of Hungerford's book? The reason I ask is that maybe I will not even get that book. If I can find everything I need in Lang or everything that Hungerford has then I'll just read Lang. Basically, does Hungerford's book have anything to offer that Lang doesn't.
 
  • #128
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I am not sure you know my criticism.
I wouln't think he does either given that you never really gave one. All you have been saying is "most books are bad". You don't really say why you think they are bad. You said Gamelin style in his complex analysis book was unacceptable but never said what that was supposed to mean. The only reasons that you have given however (though not nearly satisfactory) indicate that you find books bad because they are hard. If this is not the case then please clarify.


In my view, it is hard to learn the subject by reading the book.
You are probably right on this. This is probably why in getting our education not only are we provided with books that we should read but also with classes that we should go to and professors that we should talk to.

In my opinion, a good "a" level textbook is one that any person with "a" level prerequisite should be able to master without appeal to outside sources.
What is an A level book? What does it mean to have an A level prerequisite? If a book if not as you just decribed does it mean its a bad book?
 
  • #129
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That seems to summarize you ignorance quite succintly. I can't say I had much sympathy for your position before, but now any residues just vanished off the face of the earth. The mere fact that you state maths is hard to learn from text books (and *forces* you to have attend to lectures as if that were a burden rather than a privilege - you're at UCLA, right, so you actually get to hear Terry Tao in person) speaks volumes. Maths *is* hard to learn. Yes, some textbooks are bad, but the fact you find them difficult doesn't appear to be any metric on the book's quality.

You were saying that i misjudge the chore and burden of being a professor of math. I said if it was hard, then why would anyone be a pro of math. Now, in case you did not notices, i was being carcastic. Obvious, people like math not because it is all hard, but in addition, there are other psychological reasons that amuses them. I am not going to list them of course. prof besides doing what amuses them, they still have a obligation to teach, and transfer knowledge. They have the obligation to write, or use good textbooks to aid that transfer of knowledge process.
 
  • #130
mathwonk
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grad algebra books

for aslgebra use both hungerfoird and lang, lang for theory, hungerford for examples.

and i recommend my webnotes for both.

as a remark on books and lectures, when iw as a student no courses used books at all. beginning with freshman calculus, all my courses merely recommended books as background and gave complete lectures covwering all nbeeded materialin an independent way.

my freshman calculus class was from john tate. my sophomore several varia=bles class was fromn lynn loomis.

my algebraic top-[ology cloass was from ron stern, my one variable complex class was from bobert t seeley, and my several variables complex class was from hugo rossi.
my intro to aklgebra was from maurice auslander and my intro to alkg geom was from alan mayer. my intro to riemann surfaces was from herb clemens, and my intro to moduli and abelian varieties course was from david mumford. my course on hodge strucrtures was from phillip griffiths.

none of these coiurses u8sed books although it was expected one learned as much as possible form existing books.

we were grateful to these professors for providing us with niotes mnore up to date than current booksd, whereas many students complain that lecturers do noit follow books, but this is stupid, like asking an arftist why he does not use a paint by numbers kit.
 
  • #131
ZapperZ
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Since this thread has degenerated into an insult-throwing match, and since I simply do not have the time nor patience to weed-out various colorful posts, this thread is DONE.

I will remind EVERYONE to re-read the https://www.physicsforums.com/showthread.php?t=5374" that you have all agreed to. If you are being insulted by a member, DO NOT RETALIATE. Instead, report it. It is why the REPORT post button is there. DO NOT WAIT until things escalate like this.

Zz.
 
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