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Kind vs. Tough physics/math textbooks.

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Jolb
#1
Dec14-11, 04:06 PM
P: 419
I think textbooks in physics and math can generally be put into two categories: "Kind" and "Tough".

Kind textbooks are ones in which the author seems to care about explaining the subject matter so that it can be easily understood. Worked-out examples and numerous practice problems of varying difficulty can be found in this kind of textbook. Sometimes authors include a "roadmap" of which chapters provide needed background for the following chapters and which chapters are tangential, and occasionally the author will give a "difficulty" rating to sections and problems. Their drawback is that they're usually not as advanced, not as rigorous, and may seem heuristic.

Good examples:
Griffiths' Introduction to Quantum Mechanics (and his intro to EM)
Boas' Mathematical Methods in the Physical Sciences


Tough textbooks are ones in which the author cares most about creating an absolutely correct and incontrovertible tome, usually as concisely as possible. They usually serve as reference books for experts rather than learning tools for students (but often the "tough" professors force students to learn from them). They typically have very few or no worked-out examples. No roadmap or difficulty ratings are given. The advantage is that they usually contain the most formally correct logic/mathematics and don't rely on any heuristic intuitions.

Good examples:
Fetter and Walecka's Theoretical Mechanics of Particles and Continua
Rudin's Principles of Mathematical Analysis



I invite everyone to discuss which textbooks are Kind and which textbooks are Tough.


Also, I would like to know if anyone can tell me which are the Kind and Tough textbooks (beginning/intermediate graduate or advanced undergraduate level) for:

(physics)
fluid mechanics
general relativity
quantum field theory

and

(math)
PDEs
tensor math/differential geometry/Riemannian geometry
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ecneicS
#2
Dec14-11, 04:46 PM
P: 64
What it really comes down is money. A first year calculus textbook will have lots of worked examples, diagrams, and graphs along with the text because Calculus I is a gateway class into a bunch of fields so lots of people take it, and so it receives more funding because it has more potential to make money.
Jolb
#3
Dec14-11, 05:17 PM
P: 419
Quote Quote by ecneicS View Post
What it really comes down is money. A first year calculus textbook will have lots of worked examples, diagrams, and graphs along with the text because Calculus I is a gateway class into a bunch of fields so lots of people take it, and so it receives more funding because it has more potential to make money.
I disagree. Some textbooks are intentionally free of diagrams and graphs. I think Rudin's Principles of Mathematical Analysis is the perfect example. The whole idea of analysis is to prove formally the ideas of limits and the other elements of calculus. Its point is to get rid of the intuitionist approaches they teach you in intro calculus and get rid of the "proof by picture" that intro calculus is extremely guilty of.

[This mirrors the history of math--Newton and Leibniz didn't rigorously prove the different calculus rules, and they hardly even had an idea of what a limit was. They used intuition and "proof by picture"--and the math was ambiguous and relatively weak. Cauchy and the others were the heroes because they put it on a firm basis by proving everything formally.]

I think the sole reason most pictures are in textbooks is to give you an intuition without actually having to work through the proofs. Anyone who's proved Fubini's theorem knows what a pain in the butt it is to show that you're [formally] allowed to swap ∫∫ dx dy into ∫∫ dy dx, but they teach it to you in Calculus 3 through a proof by picture. But the proof by picture isn't formally correct, and including any picture with Fubini's theorem wouldn't help at all to prove it formally. In fact it would probably lead you into the Calculus mindset of thinking there's just some magical reason the intuition is formally correct.

deluks917
#4
Dec14-11, 08:31 PM
P: 367
Kind vs. Tough physics/math textbooks.

Tough (but Recommended):
Serge Lang - real and functional analysis
Narasimhan - Complex analysis in One Variable
Jacobson - Algebra 1
Jacobson - Algebra 2

Sort of Kind:
Artin - Algebra
Evans - Partial differential Equations
Guckenheimer and Holmes - Nonlinear oscilations and stuff

Kind:
Mendelson Topology
Dummit and foote - Abstract Akgebra
Galian - Abstract Algebra
Strogatz - nonlinear dynamics
Sankaku
#5
Dec15-11, 01:11 AM
P: 717
Quote Quote by deluks917 View Post
Tough (but Recommended):
...
Jacobson - Algebra 1
That is the problem with this kind of assessment. It depends on what level you are at when you read the book. For an upper-level textbook in Algebra, Jacobson is much 'kinder' than Lang or Hungerford (under the OP's criteria).

So, perhaps each book listed should have a description of what level it is aimed at?

In general, I think the kind/tough distinction is more between teaching books and reference books. For example, I feel Rudin's PMA is really a reference book while Bartle's ERA is a teaching textbook. If a prof assigns a reference book for a course, you better hope they are a good teacher.
Mépris
#6
Dec15-11, 10:57 PM
P: 830
Tough. Any day.
I prefer a thorough approach to my learning.

If one trips a few times, then using another book for a while to get a little more comfortable with the subject could be a sound idea.
Sankaku
#7
Dec30-11, 09:38 PM
P: 717
Sorry, I felt the random need to reawaken this thread.

Quote Quote by Mépris View Post
Tough. Any day.
I prefer a thorough approach to my learning.
Just to ask a sincere question: Why?

I can't know your motivations, but (personally) I think that many of the books idolized as "tough but good for you" are actually very poor textbooks (Rudin's PMA for one). Not that they don't have a good purpose, but being a textbook for a course might not be one of them. I am curious if you might give and example of a "tough" textbook you liked and why?

Fo me, a good example of what I am talking about is Axler's Linear Algebra Done Right. This is a book very carefully designed to teach, rather than be a reference book. It is very rigorous, but takes you carefully through the material one step at a time and (mostly) motivates all the steps. It is not very good as a first book in linear algebra and would be considered "tough" by someone at that level. However, at the right level and combined with a good prof, it makes the subject very "easy." Although it is great looking at how Axler frames his proofs, I would say it isn't really that good as a reference book. Is this book Kind? Is it Tough?

If it were up to me, I would ask:

- What level is this book really aimed at? The author saying "This book is accessible to any undergrad who knows how to add and tie their own shoes," does not count.

- Is this book a reference book or a teaching book? The author may not know the difference.

- Is this book well written for its purpose? Not just do you like it - does it work for more than 20% of the class?

In the end, though, everyone has their own learning style and you can't please a whole class. Additionally, preferences in books may change over the course of your learning. What bothers me is the simple association with Tough=Good (I am generalizing here). Without additional reasoning, it always smacked of bravado (cue the Four Yorkshiremen as mathematics students).

http://www.youtube.com/watch?v=-eDaSvRO9xA

Aye, when we were 4 years old, we had to read all of Bourbaki every morning before going to mill and working for 26 hours a day...
homeomorphic
#8
Jan2-12, 05:37 PM
P: 1,242
I don't mind books that are both kind AND tough. Like, maybe they make you work out some of the details yourself. There was a logic book I found online that was based on Moore's method, which is, in some ways, as tough as you can get. You have to work all the proofs out yourself. But, I didn't think it was that bad of a book, even though I prefer more kind books.

I mean, I am no Riemann, but I have extremely strong intuition, and even I will not be able to figure out all the intuition for myself if I read a really unintuitive book. I will just end up being mislead, and it will take me 100 times longer to learn it with less understanding.
genericusrnme
#9
Apr9-12, 08:33 AM
P: 615
Good examples:
Griffiths' Introduction to Quantum Mechanics (and his intro to EM)

wat o.O
Jorriss
#10
Apr9-12, 11:00 AM
P: 1,054
Quote Quote by genericusrnme View Post
Good examples:
Griffiths' Introduction to Quantum Mechanics (and his intro to EM)

wat o.O
Do you disagree? That book is a really easy read as far as textbooks go. It's incredible, but his exposition makes it easy to get through. Well, it has the tone of 'kind' anyhow.
mathwonk
#11
Apr9-12, 11:47 AM
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Last time I taught complex analysis, I myself had on hand about 9 or 10 textbooks at every level, (Mackey, Lang, Churchill, Cartan, Greenleaf, Hille, Knopp, ...) for my own use in preparing and teaching the course. Each book had something useful. I admit however I seldom look at Rudin for anything. Under the helpful category, I would list anything by Sterling K. Berberian.
genericusrnme
#12
Apr9-12, 05:56 PM
P: 615
Quote Quote by Jorriss View Post
Do you disagree? That book is a really easy read as far as textbooks go. It's incredible, but his exposition makes it easy to get through. Well, it has the tone of 'kind' anyhow.
The textbook just doesn't have enough rigor, a lot of questions are hand waved away and there are some minor inconsistencies throught. Imo it's a bad textbook for learning QM from, you're better off using one that does it properly (sakurai, shankar, L&L etc)
Jorriss
#13
Apr9-12, 06:19 PM
P: 1,054
Quote Quote by genericusrnme View Post
The textbook just doesn't have enough rigor, a lot of questions are hand waved away and there are some minor inconsistencies throught. Imo it's a bad textbook for learning QM from, you're better off using one that does it properly (sakurai, shankar, L&L etc)
oh, woops! I didn't read that, I thought it was his electrodynamics book being mentioned; which is much better. Yeah, his quantum book is not very good. Quantum is weird, so I think he tries to ease students into it by being ultralaid back but it doesn't work.
Jolb
#14
Apr10-12, 10:59 PM
P: 419
Quote Quote by genericusrnme View Post
The textbook just doesn't have enough rigor, a lot of questions are hand waved away and there are some minor inconsistencies throught. Imo it's a bad textbook for learning QM from, you're better off using one that does it properly (sakurai, shankar, L&L etc)
Landau and Lifschitz as an intro textbook? Are you crazy? That's probably the most comprehensive QM textbook of all time, and it was written for graduate students preparing for the "Theoretical Minimum Exam" (which I believe under 100 people ever passed). "Not a word of Landau; not a thought of Lifschitz."

Griffiths QM is a great book. It really helps you to understand the subject, despite it being not entirely rigorous and toning down some of the mathematics. I think the entire idea of the book is to get you to actually DO quantum mechanics without being too bogged down in technicalities, which I think is a great way to introduce QM. Also, Griffiths discusses some really important philosophical implications of QM in the last chapter of the book, which most textbooks, Shankar for example, completely avoid. So for a person who never plans on doing Quantum again, it really encapsulates the whole subject.
Sduibek
#15
Jul24-12, 12:12 PM
P: 8
Do any "kind" Trigonometry books exist? I am aiming to further myself in programming (though not necessarily a CS degree) and while I love programming I haven't found a book that says "this is why trig is fun and awesome, here's the concepts in a logical, intelligent, absorbable fashion instead of two pages of explanation following 1000 exercises to work through". I am currently in Trig but want to have a firm grasp on it beyond the classroom, especially because I'll be going into Calculus in a few quarters.

Thank you
homeomorphic
#16
Jul24-12, 12:52 PM
P: 1,242
Do any "kind" Trigonometry books exist? I am aiming to further myself in programming (though not necessarily a CS degree) and while I love programming I haven't found a book that says "this is why trig is fun and awesome, here's the concepts in a logical, intelligent, absorbable fashion instead of two pages of explanation following 1000 exercises to work through". I am currently in Trig but want to have a firm grasp on it beyond the classroom, especially because I'll be going into Calculus in a few quarters.
Trigonometry is a whole different ballgame, since it's a different level than most of what was being discussed on this thread.

What would be a kind trigonometry to me, most students at that level would probably find very unkind. I'm not very familiar with all the options out there, but trigonometry has such a wide audience, I would imagine it's been done in every style you can imagine, though I could be wrong.
Sduibek
#17
Jul24-12, 05:38 PM
P: 8
Quote Quote by homeomorphic View Post
Trigonometry is a whole different ballgame, since it's a different level than most of what was being discussed on this thread.

What would be a kind trigonometry to me, most students at that level would probably find very unkind. I'm not very familiar with all the options out there, but trigonometry has such a wide audience, I would imagine it's been done in every style you can imagine, though I could be wrong.
I ended up getting 10 well-rated Trig books today. At least one of them is bound to be helpful :D


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