Basic Training in Mathematics: A Fitness Program for Science Students
February 24, 2011 by Actaphysica
Filed under Mathematical Physics Book Reviews
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Excellent review or introduction to math methods for physics,
This is the best book I have found for explaining the math needed by physicists and others in the hard sciences. Shankar uses a very conceptual approach to the mathematics without dwelling on proofs – leaving the reader with an understanding of the mathematics involved. He also tackles difficult ideas like: why are complex numbers necessary and where do they come from? Most books simply assume these ideas and run off into the wild blue yonder with some proofs to give a veneer of completeness, whereas Shankar tries to give a conceptual underpinning that is invaluable when he tackles advanced topics (such as contour integration). His approach throughout is conceptual and pragmatic – giving you a solid understanding for the math you will actually use. Though it is designed for undergraduates, I would also recommend it to anyone either reviewing their math or (re)learning math they should have already known. I used this book to study for the math section of my physics PhD. qualifier and I only wish that I had stumbled across it sooner – it would have made many of my physics courses a lot easier.
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Kind of a last resort,
This book tries to cover pretty much all the mathematical methods you’d need in college-level physics if you haven’t had much experience with them before. The trouble is that that is a LOT of math, and trying to cover that in a book this size is just asking for trouble.
If you don’t know any of this stuff, this book is going to kill you. It covers multivariable and vector calculus, differential equations, linear algebra, functions of a complex variable, etc. That is maybe 4-5 different math courses. The idea is that physicists don’t really need the rigor of theoretical math, they just need to learn the “tools” so they can do the practical, applied stuff.
This book is good if you already have a general idea of these concepts and just want to get the important parts.
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elegant explanations,
Mermin is perhaps best known as the co-author of ‘Solid State Physics’, a longstanding text of its subject. But his interests are diverse, and one of these is presented here. He explains the intriguing use of quantum computing. Starting with the concept of a Qbit.
The text assumes you’ve done some non-relativistic quantum mechanics. After all, the entire subject is based on quantum effects producing different results than traditional computing. You should know the bra and ket notation, that was first introduced by Dirac. This notation is amazingly concise and pervades the text. It is probably fair to say that 90% of the discussion uses this notation.
The derivations are elegant and surprisingly simple, compared to the intricacies of other applications of quantum mechanics. There is relatively little discussion of experimental methods. This is primarily a theoretical text.
One conclusion is that this field is young. No serious computations are yet capable, compared to those on computers using traditional classical physics.
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