Solved problems on manifolds: A resource for physics students

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Discussion Overview

The discussion revolves around the search for resources containing solved problems on manifolds, particularly for physics students. Participants explore various books and resources, express differing opinions on the usefulness of solution manuals, and share recommendations for related topics such as electromagnetics in the context of differential forms.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Homework-related

Main Points Raised

  • Some participants inquire about specific books that provide solved problems on manifolds, emphasizing the need for resources aligned with physics exams.
  • One participant suggests that all books on manifolds can be viewed as containing problems and solutions, but others seek more structured resources.
  • Recommendations include "Analysis, Manifolds and Physics" by Choquet-Bruhat and Dewitt-Morette, and "Spivak's Differential Geometry" as potential resources.
  • There is a contention regarding the value of solution books, with some arguing they are detrimental to learning, while others find them helpful for self-study and checking work.
  • Participants mention alternative resources such as class web pages and previous exams that may contain problems and solutions.
  • Some participants express frustration with the idea of providing solutions, suggesting that students should develop problem-solving skills independently.
  • In a separate thread, participants discuss the search for introductory electromagnetics books that utilize differential forms, with suggestions for more advanced texts that cover the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the usefulness of solution books; some advocate for their use while others argue against them. The discussion on electromagnetics also reveals differing opinions on the availability of suitable introductory resources.

Contextual Notes

Participants express varying assumptions about the role of solutions in learning, with some emphasizing the importance of independent problem-solving skills. The discussion also highlights the challenge of finding resources that meet specific educational needs.

ala
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Is there some solved problem book about manifolds? (or where can I find solved problems on manifolds)
 
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every book on manifolds can be considered such. just regard all the claims and statements as problems, and the proofs as solutions.
 
I know that that theorems can be considered as hard problems... but I need some book with problems (problems that can be [and are] given on exams for physics students) and solutions.
 
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spivaks differential geometry volume one. or why not make them up yourself/ then they suit your students better.

or look in guillemin and pollack. oh you want solutions.

well i think that a bad idea. if you can't solve them yourself you should not be teaching the course, and your stdudents can't solve them either. or are you a student?

even if you are, there is a very good reason books do not have solutions in them, it is harmful to learning. i just received a new edition of edwards and penney from the publsher yesterday and a gigantic two volume book of solutions to problems, how insulting and useless. i intend to burn it lest it fall into the wrong hands.

solutions to problems are about as useful for learning as a video of someone else doing exercises. both these things are designed to make someone else rich, not to help you.
 
Apologies if this is off topic. I think solution books are very helpful. But then again, I'm self-studying. I read the problem, and try to solve it, and then use the solution to either check my solution, or give me a hint if I'm stuck. Without having a teacher to offer any guidance, I need something to give me a prod in the right direction if I can't solve it myself.

To the OP: one trick I've found is scouring the net for class web pages. They frequently have problem sets, and sometimes have solutions to those problems as well. Also, many schools post previous prelim exams sometimes with answers.
 
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i suggest you stop prowling for other peoples solutions and spend more time thinking about your own.
 
So if you have a student who can't figure out the answer to a homework question, your response is: spend more time thinking about it? You never give out solutions to your students? Or grade their work, and point out where their misunderstandings lie?
 
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as hard as it may be to beieve, yes, i did mean what i said.

in fact i am generously grading your work now. guess what your grade is so far?
 
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  • #10
It is hard to read the tone across the internet.

You seemed dismissive of leveraging any solutions. I agree that the should be the absolute last resort. But for self-learners, the feedback they provide seems indispensible. If you have any other suggestings, as always, I appreciate your input.

Back to the OP:
These aren't solutions books, but they do have some worked examples:

Bamberg,Sternberg: A course in mathematics for students of physics

Arnold: Mathematical Methods of Classical Mechanics

Lee: Introduction to Smooth Manifolds

Solutions book in GR:

Lightman: Problem book in relativity and gravitation

Other solutions books I haven't used:
There are Schaum's books in topology, and differential geometry that may be useful for you.
 
  • #11
what should we do when students ignore good advice, say, that's fine, i guess you will be ok, or just ask more bluntly when they anticipate getting a clue?

we are not geting paid here so our advice has a tendency to be honest.it is sort of like the ethical dilemma one faces when asked to tell someone where to get cigarettes. should you tell them, or say honestly, do you realize those are bad for you?
 
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  • #12
ala said:
Is there some solved problem book about manifolds? (or where can I find solved problems on manifolds)

This book -Introduction to Tensor Calculus and Continuum Mechanics, by John H. Heinbockel is available online and for free at http://www.math.odu.edu/~jhh/counter2.html

It isn't exactly what you're looking for but perhaps it has some solved problems.

Good luck

Pete
 
  • #13
I am looking for an introductory electromagnetics book in the language of differential forms. I am not looking for a differential geometry type of book with a small section on EM but all about EM in differential forms language. Any recommendations?
 
  • #14
kengwit said:
I am looking for an introductory electromagnetics book in the language of differential forms. I am not looking for a differential geometry type of book with a small section on EM but all about EM in differential forms language. Any recommendations?

I don't think there is one at the introductory level... with exception of
http://www.ee.byu.edu/forms/

A more advanced book that has a detailed but not exclusive discussion with differential forms is
http://www.elsevier.com/wps/find/bookdescription.librarians/503573/description#description

A more theoretical monograph is https://www.amazon.com/dp/0817642226/?tag=pfamazon01-20
 
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  • #15
Bamberg,Sternberg: A course in mathematics for students of physics

This book is a very good treatment of EM using differential forms. It's not introductory, though.
 
  • #16
redrzewski said:
Bamberg,Sternberg: A course in mathematics for students of physics

This book is a very good treatment of EM using differential forms. It's not introductory, though.

I would have mentioned Bamberg&Sternberg and Burke's Applied Differential Geometry...
however, these aren't E&M books... although their sections on using differential forms in E&M are more than a few chapters...and certainly great places to read up on it.

Here's some more advanced E&M texts:
http://www.google.com/search?q="Multivectors+and+Clifford+Algebra+in+Electrodynamics"
https://www.amazon.com/dp/0471648019/?tag=pfamazon01-20

You might want to browse: http://users.tkk.fi/~ppuska/elmag_alg.html
 

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