5 Mathematical Methods of Physics and Group Theory in Physics v2

Mark Weitzman introduces his video series, focusing on mathematical methods of physics and group theory. He discusses core physics courses typically covered after the first year in an American college, particularly for theoretical physics majors. Courses include advanced classical physics, quantum mechanics, statistical mechanics, and computational physics. He emphasizes the importance of mathematical methods of physics in qualifying exams at institutions like Caltech. Weitzman recommends 'Mathematical Methods of Physics' by Matthews and Walker, highlighting its practical approach and suitability for advanced undergraduates and beginning graduate students.

Weitzman compares books suitable for different levels of physics students. He mentions Mary Boas' 'Mathematical Methods in the Physical Sciences' as a standard sophomore-level textbook, covering essential topics like vector calculus, differential equations, and linear algebra. He contrasts it with the more advanced Matthews and Walker book. He also discusses Riley's 'Mathematics for Physics and Engineering,' noting its extensive coverage but also its tendency to review basic topics unnecessary for physics students.

Weitzman reviews various graduate-level mathematical methods books. He highlights a Dover edition book for its rigorous approach to complex analysis and differential equations, despite lacking problems. He then mentions Arfken's comprehensive but lengthy and dry textbook, noting its evolution over editions. He praises another graduate-level book available online for free, appreciating its advanced topics like differential topology and Lie groups. Additionally, he mentions Kevin Cahill's book for its practical approach to physical mathematics, despite his personal critique of Wiley Publishing.

Weitzman discusses more specialized and rigorous books. He reviews Hassani's book, noting its heavy emphasis on definitions and theorems over practical problem-solving. He mentions courses in modern mathematical physics that delve into Hilbert space and differential geometry. He also highlights Carl Bender's lectures and book on asymptotic methods and perturbation theories. Furthermore, Weitzman examines advanced geometry and topology books relevant to quantum field theory, praising the detailed problems and discussions in Frankl's 'The Geometry of Physics'.

Weitzman transitions to discussing group theory books. He highly recommends Anthony Zee's 'Group Theory in a Nutshell for Physicists' for its comprehensive and understandable approach to discrete and Lie groups, while noting its omission of Young diagrams. He reviews Tung's book for its classical group theory coverage and problem solutions. He also mentions books by Ramond and Georgi, which provide advanced insights but may be challenging for beginners. Weitzman emphasizes the practical aspects of group theory in physics, particularly in particle physics and unification theories.

Weitzman concludes with a summary of additional group theory resources. He discusses books by Schensted, Greiner, and Ramond, noting their specific focuses and suitability for advanced students. He highlights the importance of Young diagrams and their detailed coverage in Schensted's work. Weitzman also recommends John Baez's book for its recent developments in physics and mathematical rigor. He advises caution with self-published or overly modern books and encourages starting with foundational texts before exploring more specialized literature.