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I am currently studying geometry and topology (with applications in physics) from the books T. Frankel “The Geometry of Physics” and M. Nakahara “Geometry, topology and physics” Both these books work pretty fast up to a sophisticated level, and I am lacking in practice. I can easily read the beginning chapters, but then when these concepts and tools are applied in later chapters – I see that I lack familiarity with the details, calculations and intuition with these objects. So I was wondering if someone would be kind enough to recommend a good source of EXERCISES WITH SOLUTIONS in these fields, aimed at physicists. I am not completely without mathematical competency, so the occasional pure-proof derivations and proof-exercises wouldn’t hurt either. The exercises in these books are quite awful and useless, and lack solutions. SOME examples are worked through in the text, but many of the more basic things (like giving concrete examples of vector fields, pull-backs and diffeomorphisms etc) are ignored. Although I am in general very appreciative of these books, I would like to complement with something that has 1) more exercises 2) easier exercises, of “drill” type and 3) covers many topics.

Many thanks my fellow physicists 😀

Answers and Replies

MathematicalPhysicist

I am not sure if I know similar textbooks like Nakhara with solutions to its exercises. But if you want textbooks with solutions in the sepcific topics of differential geometry, GR and QFT, there are textbooks like Maggoire’s QFT and some professor from Oxford Springer edition GR (both have solutions and hints to problems in them), and for differential geometry there’s the textbook by O’neal (not sure about my spelling).

Most advanced textbooks such as Nakhara’s don’t include solutions and rarely even hints, it’s really rare to find advanced textbook which include solutions.

I suggest “Classical Mathematical Physics” by Walter Thirring.
amazon/dp/0387406158/?tag=pfamazon01-20 The book is dense but makes up with the rigor by providing lots of diagrams and examples. It contains problems and solutions to all the problems. Pretty amazing book if you ask me. ^^ You can also try the latter part of “Mathematical Physics: A Modern Introduction to its Foundations” by Sadri Hassani. I’m specifically talking about parts 7 and 8 (“Groups and Manifolds” and “Lie Groups and Their Applications” respectively). The book is laden with end-of-chapter problems that are less sophisticated than Nakahara’s.

amazon/dp/0387985794/?tag=pfamazon01-20

Goodluck! =)

Last edited by a moderator: Apr 25, 2017

Wow, thank you so much! It is true that most books at the level of Nakahara don’t have many problems, exercises let alone solutions. What I was hoping on was that somewhere on the internet there would be a good source from some professors course, some researcher’s note or some PDF, or past exam papers with solutions.

Again, thanks a lot!

Hi, Could you help me with the Geometry ,”the same book” in case you have found useful Pdf’s or may be yours notes.I have started the Geometry this year and it seems exactly as you said. Thanks in advance

Sara

My solutions to Nakahara’s Geometry, Topology, and Physics has found a permanent and updated home on github! Go here:

mathphysics/LaTeX_and_pdfs/Nakahara_GTP-solutions.tex

The Google Drive links below will not be up-to-date; go to the github repository mathphysics for the latest version.

From the beginning of năm nay, I decided to cease all explicit crowdfunding for any of my materials on physics, math. I failed to raise any funds from previous crowdfunding efforts. I decided that if I was going to live in abundance, I must lose a scarcity attitude. I am committed to keeping all of my material open-sourced. I give all my stuff for không lấy phí.

In the beginning of 2017, I received a very generous donation from a reader from Norway who found these notes useful, through PayPal. If you find these notes useful, feel không lấy phí to donate directly and easily through PayPal, which won’t go through a 3rd. party such as indiegogo, kickstarter, patreon.

Otherwise, under the open-source MIT license, feel không lấy phí to copy, edit, paste, make your own versions, share, use as you wish.

Previously…

Read Nakahara’s Geometry, Topology, and Physics, Ch. 9, 10, if you’re interested further on Principle G-Bundles and the Dirac magnetic monopole. Also read if you’re interested in what my previous diagrams, drawings, and posts are all about.

Here are my notes and solutions to the book:

drive.google/file/d/0B1H1Ygkr4EWJU05JUjdmdk5LS0E/edit?usp=sharing
drive.google/file/d/0B1H1Ygkr4EWJbklkQWFGQTBVdmM/edit?usp=sharing

I’d like to share these notes and solutions for others who are studying and trying to get handle on the material.

If you’re coming across some kind of pitfall or you don’t understand something, maybe my notes could help out in terms of pointing the right direction.

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This is a solution manual written by somebody else, not the author of the book. (with tex/pdf)
more details here: github/ernestyalumni/mathphysics/tree/master/LaTeX_and_pdfs

• Series: Graduate student series in physics

• Pages: 50

• Language: English

• Topic: 132

• Org File Size: 489,483

• Extension: rar

• Tags:
  Solutions nakahara Topology geometriy physics

• Toc: contains solutions to all problems in the book.

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