If mathematics is the queen of all sciences, as it is often called, then physics is undeniably its younger sister. Given the strong link between the two subjects, I decided to share a brief list of some of the best mathematical physics textbooks. In this list we will focus on textbooks that offer a wide selection of topics rather than going in depth in one specific topic. The list is mostly based on my personal preference, advice by lecturers and the online reviews. Short reviews as well as Amazon links are added for convenience.
Know any other great mathematical physics textbooks? Please share in the comments.
One of the classic basic mathematical physics books. This 1359 page tome offers an in depth analysis of all the basic topics as well as over 800 exercises. In particular, the book starts off with basic algebra and calculus, as well as a great introduction to series and complex functions. More advanced and specialized topics, such as quantum operators, probability theory and statistics are covered as well. The book offers a great introduction and a reference guide for later undergrad years. The only con of this book in my eyes is the annoying student solution manual that has to be bought separately. Selling the solution manuals separately, unfortunately, seems to be a vice shared by many of similar textbooks.
This course on mathematical physics by Szekeres has a reputation of being a quick, yet an in-depth overview of the core concepts of mathematical physics. One obvious advantage is the “tiny” size of the book — being more than twice as short as the book in the previous entry, A Course of Modern Mathematical covers roughly the same material.
Here we have another classic textbook. Written by Mary L. Boas back in 1966, the 3d edition of the book still dominates the shelves and happens to be one of the popular reference guides to both math and physics undergrads. The topics covered include basic algebra, calculus, complex analysis, series, differential equations, statistics and probability theory, tensors and a few others. In addition, the book contains problems after each section with answers to selected problems given at the end.
Another popular textbook often used as a reference source in many mathematical physics courses. Even though the book is widely used among undergrads, the reviews range from awful to absolutely recommended. Common complaints of the book focus on the lack of solutions to the exercises and the lack of depth in certain chapters. On the positive note, the book is often regarded as one of the best sources for refreshing your mathematical physics knowledge.
This entry has a reputation for being an easily accessible, clear and no-nonsense guide to mathematical techniques for physicists and engineers. The topic selection is a bit smaller than in the previous entries, but all the crucial topics are still there. In addition to the problems at the end of each section, the reader is also offered a selection of self-check questions.
Here we have a free pre-publication pdf version of the great textbook by Stone and Goldbart. It is geared towards graduate students and thus covers a little more advanced topics, including complex analysis, lie groups, calculus of manifolds, geometry of fibre bundles and so on.