Advanced Methods of Mathematical Physics

Rating:
Summary: Excellent reference for grads and postdocs
Review: This book sports introductions, concepts, theorems, proofs, and summaries of key mathematical areas needed for graduate level and postdoctoral mathematical physics. Those focusing on theoretical physics will especially appreciate the book; it puts all the concepts and most of the theorems you need in one handy reference. Overall, it's another, must-have expert reference from the CRC Press.

Like all mathematical physics books, it emphasizes applications and concepts at the expense of pure mathematical rigor. This means that some concepts will be explained in plain, rather than mathematical, terms and that some more advanced theorems will be asserted--with supporting logic--rather than showing full proofs or mentioning aspects applicable to areas outside of currently known physics. Most physics people will consider these omissions an advantage. If you seek a deeper, less applied, more pure mathematical approach for certain areas, the book provides numerous launching points to other texts, in the references section.

Since the book contains chapter after chapter of concise, clear, prose and equations--but no problem sets--this is a reference rather than a textbook. For physics people who quickly want to learn the math concepts needed to read a research paper, understand a theory, or conceptually approach a problem, this is one of the best references I've seen--and I've seen a lot of them.

Please note, as well, that the reference does not attempt to cover the writing of computer algorithmns to automate the methods discussed. This is another topic in itself, and is better left to other texts, such as the "Numerical methods in..." series.

Overall, I rate this reference book a conceptually clear and concise overview of advanced mathematical physics. I highly recommend it for graduate students and postdocs practicing in theoretical physics today. The book covers, lucidly and in one volume, what would otherwise require you to mine from 10+ texts in different disciplines. From those with limited time but a taste for conceptual precision, this text will save you days, weeks, years. :)