Mathematical Methods: For Students of Physics and Related Fields (Lecture Notes in Physics) Review

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Mathematical Methods: For Students of Physics and Related Fields (Lecture Notes in Physics) ReviewWhen I took undergraduate quantum mechanics 30 years ago, we learned a lot about Louis deBroglie, Max Planck, the photoelectric effect, then moved into wave functions, the Schroedinger equation, simple one-dimensional potentials and the hydrogen atom. Maybe there was a little angular momentum tossed in. It was not until graduate school that I learned much about
/X> = xi/x>
where /X> is a vector in an n-dimensional, linearly independent vector space and the xi's were its components in the basis /x>. A lot of things like representations might have made more sense. Anyway, Hassani's undergraduate text gives one an excellent view of vectors and coordinate systems. In particular, it trains one well to leap into the more abstract view of vectors one reads about in, say, R. Shankar's excellent book on quantum mechanics, and also gives one a good deal of exercise on how to translate between coordinate systems. In graduate school, I found the ability to roam between coordinate systems to be very, very handy and the laborious time spent learning it was worth it. I'm not done with this book yet. I'm now getting into his chapters on complex variables and differential equations, but Hassani's treatment of vectors and coordinate systems is very good indeed. Undergraduate physics students who plan to go on into graduate school will find time with this book well spent.Mathematical Methods: For Students of Physics and Related Fields (Lecture Notes in Physics) OverviewIntended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material.Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics.This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.

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Classical Invariant Theory (London Mathematical Society Student Texts) Review

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Classical Invariant Theory (London Mathematical Society Student Texts) ReviewExcept for some new terms ( transvectants, Hessians, Syzygies, special Euclidean groups)
and notation ( I haven't figured out exactly what he means by A^(-T) yet, inverse transpose?),
it is a well written book that revives the ancient Hilbert
invariant theory and translates that into
modern terms. I was hooked when I realized the connection to the elliptic invariant.
It has this neat section on Gordon's method of digraphs as algebraic invariants.
I really think some of this could be made where it could be taught to undergraduates without calculus.
For me the treatment of invariants tied a lot of loose ends together.Classical Invariant Theory (London Mathematical Society Student Texts) OverviewThere has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth of new applications, ranging from number theory to geometry, physics to computer vision. This book provides readers with a self-contained introduction to the classical theory as well as modern developments and applications.The text concentrates on the study of binary forms (polynomials) in characteristic zero, and uses analytical as well as algebraic tools to study and classify invariants, symmetry, equivalence and canonical forms.A variety of innovations make this text of interest even to veterans of the subject; these include the use of differential operators and the transform approach to the symbolic method, extension of results to arbitrary functions, graphical methods for computing identities and Hilbert bases, complete systems of rationally and functionally independent covariants, introduction of Lie group and Lie algebra methods, as well as a new geometrical theory of moving frames and applications. Aimed at advanced undergraduate and graduate students the book includes many exercises and historical details, complete proofs of the fundamental theorems, and a lively and provocative exposition.

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Basic Training in Mathematics: A Fitness Program for Science Students Review

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Basic Training in Mathematics: A Fitness Program for Science Students ReviewThis 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.Basic Training in Mathematics: A Fitness Program for Science Students OverviewBased on course material used by the author at Yale University,this practical text addresses the widening gap found between themathematics required for upper-level courses in the physical sciencesand the knowledge of incoming students. This superb book offersstudents an excellent opportunity to strengthen their mathematicalskills by solving various problems in differential calculus. Bycovering material in its simplest form, students can look forward to asmooth entry into any course in the physical sciences.

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