Customer Reviews

A Course in Mathematics for Students of Physics: Volume 1 (Bk. 1)

5 star:		(3)
4 star:		(3)
3 star:		(0)
2 star:		(4)
1 star:		(1)

 

 

I'm going to mention the second volume almost exclusively. This is where the action is located. It is hard to find any equivalent treatment of circuit theory using algebraic topology. You should have some mathematics background or some patience and a stack of books on algebra and algebraic topology so you can understand what these authors write so poorly. However, while the text (vol.2) loses a star for being horribly written, it gains four stars for the amazing content. If you are patient you will see a side of circuits you have never dreamt of and then you will be led into the generalized (continuous) version which is electromagnetics.

If you are looking for some really accessible and really interesting mathematics on circuits and EM buy this book (or buy it used, I bought my hardcover for 10$) You might also find it useful to consult the appendix in Frankel's Geometry of Physics for comparison.

Have fun and keep in mind that the book is written by sadists, clever and intelligent, but sadists all the way!

I can only say one good thing about this book: it steered me towards a couple of really worthwhile books. I began to read Bamberg/Sternberg about five years ago, when I was looking for a book that could explain the mathematics that physicists use. It was heavy going from the first chapter, although I am not a neophyte in mathematics. I found it slow, obscure, devoid of true proofs and explanations when I needed them most. As another reader said, the books is perfunctory while it seems it wants to aim high. I finally gave up, after the tremendously confusing chapter 5 on scalar products. But I followed a couple of their bibliographic suggestions. In particular, I read the very enjoyable and rewarding Loomis and Sternberg, "Advanced Calculus," a classic textbook, not an easy one, but one that rewards hard work. Loomis/Sternberg is a comprehensive, solid, insightful book that covers a lot of the material of Bamberg/Sternberg's first volume. I took up Bamberg/Stenberg this week again, after a hiatus of several years, having digested several books on linear algebra, topology, and functional analysis, and I still find it very difficult to read Chapter 1. The reason: nothing is fully explained or proven. Rather, the book reads like a collection of hints that barely connect and in places is painfully slow. My advice: don't try to read it unless you are forced to. For a neat, useful, modern introduction to mathematical physics, try Hassani. Or go back to that jewel, Loomis/Sternberg, if you can find it.

In short, I find this kind of a book very rare indeed.

If you are doing physics and electronics at the undergraduate level, this book will open your eyes to a whole new unified approach to several on-the-surface different topics. I wonder why many course designer's haven't looked at this book and realized how accessible it has made some of the relatively modern concepts. The authors laudably attend on each concept with a passion to make the reader confident of grasping at least a few different ways of looking at it, keeping the core well in view all the time. It is also to their credit to have kept the beauty in the ideas intact with a good balance of abstraction and concrete instances.

In particular, the authors treatment of exterior calculus is an eye opener if you are new to the topic. For a student only exposed to traditional methods, it is a revealer to see the laws of linear electrical circuits as well as Maxwell's equations of electromagnetism being expressed in precisely the same language. It is totally to the credit of the authors to have presented the concepts in such a simple to understand progression. For example, they make you see clearly why you have understood the divergence theorem or Stokes theorem of conventional vector calculus if you've grasped the essence of the calculus of functions of a single variable. Its a fantastic voyage folks, and you've got some of the best guides methinks.

All those who find physics and mathematics a drag at college should grab this book and be enlightened. I wish they fix some of the errors in the book in future editions, but the errors don't at all hinder the learning.

Ten thumbs up!

The presentation and despriptions are every good. The progression sequence of the material is right on. I am both a mathematician and a physicist in that I develop "real-world" algorithms for computer models for atmospheric, marine and alluvial environments. I use the Series (both Vol. 1&2) to tutor physics students, most of which are good at plugging into established formulas but need work at developing a formula from scratch. There is an occasional error which can usually be figured out by reading-on if you know anything about math and physics; THIS BOOK is not written for a freshman year math/physics student. My only complaint with the book is that there is no solutions for any of the exercises at the ends of the chapters. Trivial as it may sound; when a student is trying to work through the problems, sometimes they need to know if they are right to move-on. Which means they have to call me, which after a while get's to be a pain.....my suggestion for the next edition is give the solutions for at least the odds or evens to help out the teachers...In spite of this discrepancy I still use the book and recommend it.....

i could hardly believe that in the chapter on linear algebra, the authors never discuss any but 2 dimensional spaces (claiming that it is easily generalized. not so!)... and the chapter on differential forms left me scratching my head... it introduces them by a taylor expansion, and claims that they are mappings, but never explains or motivates that.

i found that this book covers its topics only perfunctorily, and aims to high, thinking that it is more mathematical than it actually is. i would recommend frankel instead (a slightly more advanced text, but much better written).

There are a number of reviews for this series, mixed good and bad, and rather than adding another, I just want to register agreement with most of the points on both sides; on the positive end, it's as far as I can tell unique in using electronic circuits as the primary motivation for the math, and provides a broad enough range of material that it should be fairly easy to pick up just these two volumes and be able to get a decent handle on the material.

On the negative side, while I haven't noticed the errors that were mentioned, the lack of solutions and occasional hand-wavery can leave one wondering -- but that's by no means a problem unique to this text. The standard point of comparison seems to be Frankel's Geometry of Physics, which is an excellent text, but I'd argue that it suffers from the same problem. This series doesn't go as deep into differential geometry as Frankel's, but offers more breadth.

This book gives a glimpse of the style the mathematics will be taught in schools say 30 years from now (despite the fact that actual results presented in it are all at least 70 years old - such is the inertia of the education). Despite the title, it should be strongly recommended to the students and teachers of pure mathematics. Reader that rated this book with one star obviously does not understand what mathematics is all about. The first chapter alone is worth more.

i could hardly believe that in the chapter on linear algebra, the authors never discuss any but 2 dimensional spaces (claiming that it is easily generalized. not so!)... and the chapter on differential forms left me scratching my head... it introduces them by a taylor expansion, and claims that they are mappings, but never explains or motivates that.

i found that this book covers its topics only perfunctorily, and aims to high, thinking that it is more mathematical than it actually is. i would recommend frankel instead (a slightly more advanced text, but much better written).

At times, the authors can be exceedingly clear, but for the most part, they get bogged down with mathmatical conundrums which rarely trouble a physicist. The text is often slow and difficult to read, and worse than that, the text is riddled with errors. This is a shame because the differential form approach to physics is so elegant and powerful. The text should not be used as an introduction to the subject. After several revisions, the authors will hopefully mold the text into something worth using.

i could hardly believe that in the chapter on linear algebra, the authors never discuss any but 2 dimensional spaces (claiming that it is easily generalized. not so!)... and the chapter on differential forms left me scratching my head... it introduces them by a taylor expansion, and claims that they are mappings, but never explains or motivates that.

i found that this book covers its topics only perfunctorily, and aims to high, thinking that it is more mathematical than it actually is. i would recommend frankel instead (a slightly more advanced text, but much better written).