Why are textbooks in math and science so bad?

[TMFKAN64]

I don't have the patience to reply to your long post. Try to summerize your main point to something that i can easly reply to. thanking you.

I think this pretty much sums up the entire thread in a nutshell.

 

[Ki Man]

We should try stringing these posts together and then editing them in order to make a textbook out of it on how to properly make a textbook. with the lengths of the posts the way they are now, we'll be there in no time.

Just find a good one and stick to it. don't just blindly go around buying books, take a closer look before you invest so you don't end up wasting that $60

 

[Cincinnatus]

We should try stringing these posts together and then editing them in order to make a textbook out of it on how to properly make a textbook. with the lengths of the posts the way they are now, we'll be there in no time.

Or we'd have a horrible book catering to the lowest common denominator, wait, I thought we already had a thousand of them?

Really though, while I'm posting on this thread I'd like to mention some good books I discovered recently. When it comes to recommending math texts everyone seems to talk about the same ones. You know, everyone likes Spivak, Munkres, Rudin, maybe Apostol etc. These books show up in every thread about book recommendations.

I just recently discovered the "Princeton lectures in analysis" series which I haven't seen anyone mention on here before. It was written by Elias Stein and Rami Shakarchi. Stein at least, as far as I can tell, seems to be pretty well known...

The series is organized interestingly because they start with Fourier analysis (first volume) and use it as motivation to develop real and complex analysis in the later three volumes. Reading all four seems like it would give a pretty good foundation to understand a wide range of topics in analysis. Though I admit I've only read (most of) the first two volumes and nothing from the later books.

So I'm wondering if anyone else is familiar with this series? If so, did you like them? Here's a link https://www.amazon.com/dp/069111384X/?tag=pfamazon01-20

 

[mathwonk]

shakarchi and stein was the choice by the young analysts in my department for the most recent beginning grad analysis text. obvioiusly they respect stein, and presumably like the book. another recent choice by older faculty, was by wheeden and zygmund.

grad texts are an exception to the "professor hates the book" theme, since the students are strong, or expected to be, and the professor actually chooses the book. very few good undergraduate texts are being written, because people do know their audience. but lots of fine grad texts are being written because that audience is still expected to perform. still grad students also are getting more diverse in ability, or a certain lack of preparation is getting tolerated more, and grad books are hence getting more explicitly written, shall we say.

if your professor denigrates the book he is using, then you know you are in a course for less than outstanding students, where the dept forced a mediocre book on him because the students are not expected to be able to read a better one.

and you yourself also have the option of qualifying for a better course and choosing it, unless you cannot qualify, which tells you something.

 

[WolfOfTheSteps]

if your professor denigrates the book he is using, then you know you are in a course for less than outstanding students, where the dept forced a mediocre book on him because the students are not expected to be able to read a better one.

Well this is b.s.

In the math department I've noticed this to be true, but I'm an EE and I was talking about courses that absolutely every EE is required to take. There is only 1 course above freshman level which has an honors/"regular student" distinction in the EE department at my school.

And besides, one of the worst books I've ever been assigned to use was a text also used in graduate courses. If the department chose it because they thought we were "not outstanding enough" to read something better, then they were smoking crack. The book was written by a prof at the school... That's why it was chosen.

 

[hrc969]

It goes without saying that the person who bought the book should have the prerequisites courses done, but perhaps there are certain "tricks" that are not cover in the standard prerequisite courses. What happens than?

Again, sometimes the courses listed as prerequisites are not those courses such that having done those you will find everything in the class easy to do. Instead many times it is the minimum of knowledge you need to have such that you can understand most of it if you work hard enough. So yeah sometimes knowing something from a course that is not listed as a prerequisite can help, be it a trick or a standard method in a certain field.

Don t put works in my mouth. I am not saying reading a math books should be easy, but there should be a more easilar, efficient way of writing it.

Why should there be? Because YOU say so? And sometimes there is an efficient way of writing something but that way is not necessarily the one that helps you understand what's going on the best. I think that a good author will point you in the direction of the most efficient way, and will justtify why they chose a certain method. Of course probably a lot of authors don't do that.
As an example, when I was studying out of Krantz's Several Complex Variables book, he said that the best way to solve the Levi problem can be found in a book by R. Michael Range, however as it was a combination of modern techniques and classical ones it was not as instructive as the one he went on to present.

I like the advice of my english 101 professor, thy should always know one s audience.

Better yet, you should know the authors audience, that way you will know whether you are a part of it or not.

 

[WolfOfTheSteps]

Better yet, you should know the authors audience, that way you will know whether you are a part of it or not.

Most importantly, make sure the author's main audience is not his bank account.

 

[mathwonk]

indeed i was talking abut math, where you agree it is true.

but i would conjecture it is also true on EE, unless no good books exist there.

if you want to know ask your EE prof, but bear in mind what you think of as a bad book, may be subjective.

but think about the logic of your own statements. If the book has to serve all EE majors, then is it likely it is designed only for outstanding students?

I.e. then either all your EE majors are assumed outstanding, or else the failure rate should be rather high.

Which goal does your school seem to have in view?And if a book is chosen because it was written by a prof at the school, and the current prof disparages it, doesn't that say it was forced on him for reasons other than its high quality?

Oh I see, you are trying to hold onto the idea that it is not the quality of the students that motivated the choice. your idea is tht th students are wonderful, but the bad book is forced on them by a politically powerful prof wanting to make money from it.

If that is true, it seems to me grounds for a serious complaint against the department. But I have never encountered this situation in my life in academia, in over 40 years. In all that time I have been in situations only twice where books by local authors were chosen, but the argument was justifiable on merit, and the choice was not made by the authors.

really i think my quote from vivekananda applies here again.

 

[hrc969]

I don't have the patience to reply to your long post. Try to summerize your main point to something that i can easly reply to. thanking you.

Well, that would go against what I have been trying to get you to do, which is to support your assertions.

If I tell you something I would like you to read an example to give you an idea of why I said what I said.

I guess one of the main points is that just because you think a book is bad doesn't mean it is. Some people might find that book good for exactly the same reason that you find it bad.

Another point is the one about having the adequate prerequisites and listed prerequisites are not always everything you need to find the class easy.
Again I don't just want to tell you that and try to have you believe it. I gave you examples which you can go on and verify since you are at the same school as I am.

Also you don't have to reply. I just hope you have the patience to read what I posted and keep it in mind. Oh, and the tentative schedule for next year has been posted and the math department website so if you need help planning for next year feel free to PM me.

 

[hrc969]

I just recently discovered the "Princeton lectures in analysis" series which I haven't seen anyone mention on here before. It was written by Elias Stein and Rami Shakarchi. Stein at least, as far as I can tell, seems to be pretty well known...

The series is organized interestingly because they start with Fourier analysis (first volume) and use it as motivation to develop real and complex analysis in the later three volumes. Reading all four seems like it would give a pretty good foundation to understand a wide range of topics in analysis. Though I admit I've only read (most of) the first two volumes and nothing from the later books.

So I'm wondering if anyone else is familiar with this series? If so, did you like them? Here's a link https://www.amazon.com/dp/069111384X/?tag=pfamazon01-20

I am familiar with that series. The Fourier analysis one is used in a Fourier Analysis course which I was taking last year (but dropped because I was taking the graduate level complex analysis and I had to work harder than I was used to). Also I am auditing the course this year and we are using the same book. The complex analysis book was one of the recommended ones for the graduate level complex analysis (along with Ahlfors) and is the textbook that is being followed this quarter. The Real Analysis book was the assigned one for the Real Analysis graduate series (along with Folland) and though I did not take the class this year I was planning to so I went through the first chapter of that one. My opinion is that they are great books. The exercises are great if you are at the appropriate level. In particular for me it turned out that I could do a lot of the problems and enjoyed them for the Fourier and Complex analysis books. However, I was not as familiar with the Real analysis (measure theory) material so I found most of the exercises for that book very hard for me and took me a lot longer to do than for the other two books. But anyways the material is great. The measure theory is what I had to struggle the most with since it was completely new material, but I liked it. I really have no complaints about it (or any of the books).

 

[hrc969]

Well this is b.s.

In the math department I've noticed this to be true, but I'm an EE and I was talking about courses that absolutely every EE is required to take. There is only 1 course above freshman level which has an honors/"regular student" distinction in the EE department at my school.

And besides, one of the worst books I've ever been assigned to use was a text also used in graduate courses. If the department chose it because they thought we were "not outstanding enough" to read something better, then they were smoking crack. The book was written by a prof at the school... That's why it was chosen.

If everyone has to take those courses then it is even more likely that a better (but harder) book will not be chosen. At my math department most of the "regular" courses used the same book assigned by some committee or some group prefessors (probably full and maybe associate professors).

Mathwonk could you tell us how books get chosen for the upper division courses at your school.

Now, whether a professor at the school wrote a book and the subject has very little to do with it if the professor teaching the class has enough authority. I am taking a Riemannian Geometry course right now (and took the first part of it last quarter). One of the professors at our school has a Riemannian Geometry book, and the professor for our class did not choose that book even though he has before, because he did not want to take the approach taken in that book. Instead he choose a different book for us to reference that had the approach that he wanted to take.

I have also had a professor who was teaching an honors class and did not get to pick a book he liked for the course. The reason was that he was a lecturer (not even an assistant professor, not that that would have helped). Instead he got forced into using the book that the previous class (taught by an associate professor).

As Matt Grime has said before when a class is offered by several professors in the same term more likely than not, all the classes will use the same book, which has to be chosen by the department in some way. So in those cases whether a professor is a full professor or an assistant does not matter. Maybe that is the case with you EE classes which eveyone must take.

 

[mathwonk]

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 knowledgeable 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.

 

[WolfOfTheSteps]

Oh I see, you are trying to hold onto the idea that it is not the quality of the students that motivated the choice. your idea is tht th students are wonderful, but the bad book is forced on them by a politically powerful prof wanting to make money from it.

A lot of the students are lazy... But the average math SAT at my university as a whole is above 700, and probably near 800 in the engineering department, so they aren't stupid either.

You seemed to accuse me of being in remedial classes because I couldn't make it into better classes. I was just defending myself, since this is obviously not true since, (1) the worst book I've used was a graduate text, and (2) all engineers above freshman level take similar classes.

I'm just making the point that the worst texts I've used have been texts written by profs at my university. (With the exception of math... I minor in math, and the math department is better. I 'm taking an upperlevel undergraduate course on nonlinear differential equations with a text written by a prof that is excellent.) I'm not really making an accusation, just stating the facts. And I don't think anyone is using a prof's book because of political bullying... I think things just work out that way.

 

[mathwonk]

perhaps someone outside math would be willing to rcommend a good book if you share the topic you are interested in.

and you seem to have equated "less than outstanding" with "stupid" or "remedial". I can assure you even many students with over 700 on SAT's do not do well using the most outstanding books available from profesionals, especially now that those very SAT's have been downgraded to raise the level of today's students.

Of course I am only one eprson but I myself had well over 700, under the old scale, and I had great difficulty reading Courant in my freshman year. Of the 135 other students, all presumably as well prepared as I or better, only half survived into the second semester.

My problem was not that I was unusually stupid, but that I was unused to reading difficult books, and unused to hard work in general at the level expected in honors courses in college in the 1960's.

there is a huge difference betwen being stupid and being treated with kid gloves, so that not too many will fail, and have to learn a new level of work ethic.

Again, I have said I make no claim at all about non math courses, only a conjecture. I merely challenged you to actually ask your professors how they chose the books you object to, and which ones they think are best.

I do not need to best you in an argument, I would like to help you find some answers. you are not going to find them shouting into the air here anonymously.

 

[WolfOfTheSteps]

Mathwonk,

Fair enough.

I actually spent a good bit of time reading Courant/John's Intro to Calculus and Analysis when I was taking calculus (the class text was Hughes-Hallet, which I actually thought was pretty good... just not very rigorous). While I remember spending days on a single page of Courant, I enjoyed it more than any science/math book I've ever encountered.

I don't mean to whine. I guess I'm somewhat frustrated that I'm studying EE when I prefer math. In a math course I'd go and happily buy books, with almost no regard for price. But in EE it's harder to motivate myself, and it's also harder to fork over the money, so I get really annoyed when the profs assign bad books. I was just venting my frustration. :)

 

[mathwonk]

well i understand. but ill bet there are really smart guys in the EE section who will tell you what books they like. they really like meeting smart motivated students. the classroom environment is hard to get acquainted sometimes, but they are people and appreciate students who want to get the best training. give it a whirl.

and thanks for your patience with me. courant and john is just superb by the way, as you know. read as much as you have time for in that. and maybe try afterwards methods of mathematical physics, by courant and hilbert. i have never read it but i bet it is great.

 

[Werg22]

and thanks for your patience with me. courant and john is just superb by the way, as you know. read as much as you have time for in that.

I second that! Though Courant is sometimes hard to follow, especially for the unexperienced mathematicians, as the arguments he provides are very minimalistic: a very large portion of reading his books is about trying to understand those arguments rather than what they stand for!

 

[kant]

The only words I put in your mouth were the ones you wrote: that research is easy, that professors have lots of free time (and presumably that writing maths is easy), thus they should find it easy to write lots of maths for you to understand easily.

If it is not easy, then why the hell would they work there?

There certainly do exist poor textbooks, but none of the criticisms you've levelled have displayed any sign that you appreciate what a good textbook is or what it should intend to do. You criticisms seem more like bleating about how hard you find them to understand for the wrong reasons.

I am not sure you know my criticism.

I can certainly cite several texts that are badly written (very poor language, riddled with mistakes) but your reasons seem far more pedestrian: assumes that the reader ought to work harder, for example, or 'means one ought to go to the lectures'. Well, you're bloody well supposed to go to the lectures; the books are there for a reference

In my view, it is hard to learn the subject by reading the book. 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.

 

[kant]

I think this pretty much sums up the entire thread in a nutshell.

Do you mean " i don t know what the hell is your problem"?

 

[TMFKAN64]

Do you mean " i don t know what the hell is your problem"?

No, rather the contrary. I know *exactly* what your problem is...

 

[matt grime]

If it is not easy, then why the hell would they work there?

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 textbooks (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.

 

[hrc969]

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 knowledgeable 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.

 

[hrc969]

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?

 

[kant]

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 textbooks (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.

 

[mathwonk]

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.

 

[ZapperZ]

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.