- Hardcover: 672 pages
- Publisher: Wiley; 1 edition (January 15, 1990)
- Language: Spanish
- ISBN-10: 0470002506
- ISBN-13: 978-0470002506
- Product Dimensions: 7.2 x 1.2 x 9.5 inches
- Shipping Weight: 2.9 pounds (View shipping rates and policies)
- Average Customer Review: 42 customer reviews
- Amazon Best Sellers Rank: #767,359 in Books (See Top 100 in Books)
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Texto y vida: Introduccion a la literatura espanola (Spanish Edition) (Spanish) 1st Edition
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After borrowing this book from the library, I read it cover to cover. I then bought a copy for myself to use as a reference. I learned a lot about the foundations of mathematics that I had not learned as a physics student. The book is very clearly written and actually enjoyable to read, with many examples, applications, and historical notes. The proofs were easy for me to follow.
Although the book is mainly concerned with multivariate calculus and linear algebra, it touches on many interesting and important matehmatical topics from set theory, topology, differential geometry, fractals, chaos, and analysis. It also provides an appendix that gives proofs for 25 of theorems that are considered harder to prove than is expected for a text of this level.
I also appreciated that the notation is thoroughly modern. (A glossary to the notation is given on the inside cover, with references to where in the book that you can find the full definition and explanation.) This may well be a drawback for many people, but for me it was very helpful because I now have an easier time reading papers on the more mathematical side of physics. Another modern aspect of this text is the introduction of differential forms, which are becoming essential to theoreticians in many branches of physics (quantum field theory, string theory, classical mechanics, and general relativity).
Lastly, this is a book on "pure mathematics", so if you are only interested in applied math, you will not like this book.
For me, it's been a great investment!
I purchased a used copy of the first edition nine years ago, and although I did wander through it here and there when I first got it, it has mostly been ignored along with other math books that I have kept or bought for various reasons. Only recently have I started going through it more regularly, but still rather lightly, and strictly for recreational purposes.
Some quick background for context: I have a degree in Math, so the material is quite well-known to me. It is clear from what I have been reading that this book is a unique labor of love, with more insights than I can begin to count, but, again, it was that one Theorem that closed the circle for me and told me everything I needed to know about the superior quality of this book: Theorem 1.5.10 on page 78. The Theorem actually has a title: Elegance is Not Required.
The sense of humor involved in actually expressing this as a "Theorem" made me immediately fall head-over-heels in love with this book. Even if the rest of it fails to impress – it won't, I've already looked; and it can’t, because it possesses too much élan - this "Theorem" alone was worth it. The “Theorem” says that if you ever have to make a quantity less than epsilon, it is perfectly acceptable to make the quantity less than, say 5*epsilon, or radical(epsilon^3) – as long as the expression containing epsilon goes to 0.
Anyone who has ever had a pedantic professor or grader tell you that you have to adjust your epsilons along the way in order to end up with JUST epsilon on the right of the inequality will appreciate this “Theorem”.
In any case, if you enjoy sophisticated mathematics presented in a unique, friendly, often humorous, and still fully rigorous way, then you will both enjoy, and take away much from, this book. And, by the way, the presentation of Differential Forms is wonderful. That the authors are the type of people who, in the kindest way possible, and for Mathematics’ own good, feel compelled to occasionally pull the rug out from under the feet of mathematical dogma is an extra special treat.
The spirit of the book is endearing. The mathematics is beautiful. The style is superb.