Mathematics Texts for Relativists

[Livingston]

Hello everyone!

I am currently finishing up my Applied Math/Physics Joint Honors degree and I'm moving on to a M.Sc. in mathematics focusing in relativity (University of New Brunswick does relativity research through the mathematics department).

I am looking to focus as a mathematical relativist and doing my masters in the math department gives me the chance to make up for my lack of pure mathematics courses since I didn't have the time in my undergrad to do anything other than applied math and physics.

If it helps; I have taken courses in analysis, complex analysis, linear algebra, discrete math, and differential geometry.

Would anyone be able to recommend any texts in:

Set Theory
Group Theory
Abstract Algebra
General/Point-Set/Differential Topology
Euclidean/Non-Euclidean Geometry
Noncommutative Geometry

I also missed the chance to do a Statistical Mechanics course as well as advanced Quantum Mechanics courses. If anyone could recommend texts in these areas too that would be great.

Also, please recommend any subject areas that I might have missed that would be useful for a mathematical relativist too.


Thanks!

 

[hitmeoff]

So you have not taken any abstract algebra?

I personally like Fraleigh's Intro to Abstract Algebra. It's probably the clearest, easiest to understand text on abstract algebra. The text kind of falls off when you get to Galois Theory, but that's ok since you probably will never use Galois Theory. The sections on Group theory and Ring and Field Theory are very clear and excellent. The treatment is at the undergrad level, but if you've never see abstract algebra, it might not be a bad place to start some summer reading.

I am also becoming a HUGE FAN of Dummit and Foote. Some schools use it as an undergrad text because it is very clear and does have a lot of examples and its is very well written. But it is also equally apt at treating the subject at a graduate level because it contains much much more than Fraleigh.

I think either of these are good choices to study up Abstract Algebra/Group Theory.

For topology, I have two ideas. Gamelin's Introduction to Topology is a good GRAD level book. We used as an undergrad book, but essentially only covered 1/4 of the book in a 10 week session. Its dense, it lacks examples and generally assumes you are a slick student. Having said that, its not a horrible book. If you have your analysis skills down, then this book is VERY VERY approachable, and its cheap.

Mendelson's Intro to Topology book is an undergrad level book, but its much more wordy, explanatory than Gamelin's. I used it to supplement the Gamelin book because it was cheap and well written. It still lacks examples, it lacks solutions to problems, etc.

I know Munkrees is the standard undergrad topology book, but I have not seen it. I am sure it is better than Gamelin and Mendelson, but probably much more expensive. It might be worth checking out, again...I know you are about to be a grad student, but maybe reading an undergrad level book on topology over the summer will prep you for grad work in topology.

 

[bcrowell]

Coxeter, Introduction to Geometry (a book for upper-division math majors)

 

[Livingston]

Thanks for the recommendations so far. I recognize most of those books from what other people have mentioned/what is used in the undergrad courses at MUN. I was also thinking about Functional Analysis and Exterior Calculus if anyone can think of a good text for these subjects.

 

[robphy]

http://www.ocf.berkeley.edu/~abhishek/chicmath.htm

http://www.ocf.berkeley.edu/~abhishek/chicphys.htm

 

[George Jones]

I was also thinking about Functional Analysis

Introductory Functional Analysis by Kreyszig is very readable.

https://www.amazon.com/dp/0471504599/?tag=pfamazon01-20

 

[Livingston]

Okay it looks like I'm going to go with:

Introduction to Geometry, Coxeter
Introductory Functional Analysis, Kreyszig
Topology, Munkrees
Abstract Algebra, Dummit and Foote

Anyone know any good Stat Mech texts or Quantum Mechanics/Quantum Field Theory? I've been told Ryder is a good QFT text.

 

[jasonRF]

I really like "fundamentals of statistical and thermal physics" by Reif, although it is somewhat old-fashioned. You can download a free copy of Sethna's statistical mechanics book for free from his website at cornell.edu. It isn't traditional, but is interesting and free! "An introduction to thermal physics" by schroeder is also a fun book; it is easier going than Reif but more modern.

Good luck,

jason

 

[Livingston]

Thanks for the reply!

I was looking at getting Pathria.

Shroeder is the required text for the Thermodynamics course required at MUN which was a pain because I really hated how little discussion or derivation was actually in each chapter. I mean, less than 100 pages for an entire section on Statistical Mechanics seems a little off.

I'm still not sure about a QFT text though. I might just wait and see what UNB uses for their graduate QFT course instead.