Mathematics for Physics: An Illustrated Handbook 1st Edition by Adam Marsh (PDF)

Description

This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.Contents: Mathematical Structures Abstract Algebra Vector Algebras Topological Spaces Algebraic Topology Manifolds Lie Groups Clifford Groups Riemannian Manifolds Fiber Bundles Categories and Functors Readership: Students in mathematics and physics who want to explore a level deeper into actual mathematical content.

User’s Reviews

Editorial Reviews: From the Back Cover This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints, some of which would seem to be novel to the literature. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Fine math physics text

⭐This book has more common to a novel than a math book.

⭐This book is a godsend to anyone setting out to learn the advanced mathematics required for theoretical physics. E.g. Lie groups and Lie algebras, algebraic topology, calculus on manifolds, fiber bundles, connections, gauge theory. All the good stuff is here, and it is presented more clearly than I’ve seen it presented anywhere else.Let’s face it: the language of theoretical physics is subtle and often complex, even when the underlying concepts are rather simple. There is tons of machinery, often used differently from author to author, and it can be very difficult to see how it all comes together into a workable and useful description of the world around us – which is why we’re into this, after all!If you’re lucky enough to have a quality teacher to clarify confusions over notations, nomenclature, concepts, relationships, etc. that is one thing. To venture into this realm without such a guide is not for the faint of heart, to say the least.That is where this book really shines, I think. I would rate it a must-have for anyone who has studied these subjects out of a few texts and still struggles to ‘put it all together’. But it really helps for those who are trying to find their own way.The organization, clarity, and sheer pedagogical effectiveness of the exposition here – in terms of imparting felt understanding – is hardly paralleled in my extensive self-study of this material. The only thing that comes close are Dr Frederic Schuller’s lecture videos on General Relativity and the series on The Geometrical Anatomy of Theoretical Physics (both HIGHLY recommended and both available for free on Youtube).As fantastic as it is, this book should be used to complement one’s study of theoretical physics, not as a centerpiece. This is because it actually doesn’t contain much actual PHYSICS at all. Marsh does not often specify which parts of the mathematical machinery map onto which elements of the physical systems we want to discuss. However, once you read through this book thoroughly a couple times, you will be fluent enough in the mathematical language that it will no longer distract you from the physics being presented, using that language, in texts that do focus on the physics.I could go on and on about the virtues of this book and the joy it has given my little brain. If you’re struggling at all to learn theoretical physics, buy it, read it, read it again. The Kindle edition is one of the best buys out there for about $20.

⭐Fantastic illustrations!

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