Reviews (6)

Best book on interest rate models
This is the best book available on interest rate models. Very detailed. Much more focused and readable than Rebonato's book. More pragmatic and explicit than Musiela and Rutkowski. Not as theoretical as Hunt and Kennedy. James and Webber also looks very good, but I'm not that familiar with it. All other books have only bits and pieces on interest rates.

The best book I have read on the subject
With all the due respect to the other authors I would say that if one is interested in a good theoretical book whihc is also good on the implementation side then the book of Brigo and Mercurion is definetly the best book I have ever read on the subject. New stuff and nice overview: hard to beat!
In the late nineties I went through Brigo's innovative work on stochastic nonlinear filtering with differential geometry techniques. I was favorably impressed by results and style, particularly in his dissertation and in his 'geometry in present day science' very readable overview. Interesting results are found and nicely told with accurate -but not pointlessly complicated - advanced mathematics for the problems at hand, I reasoned. Read more

Subjects:  1. Business / Economics / Finance    2. Finance    3. Group Theory    4. Mathematics    5. Probability & Statistics - General    6. Science/Mathematics    7. Statistics    8. Business & Economics / Finance    9. Interest rates    10. JEL classification: G12, G13, E43    11. MSC (2000): 60H10, 60H35, 62P05, 65C05, 65C20, 90A09    12. calibration    13. pricing    14. stochastic calculus   

Reviews (19)

The way to learn algebra
Most critisism of the book are based in the fact that topic are not treated in deep, and the reason is that there is no need to do that. Lang's porpouse is to introduce the reader to HIGHER ALGEBRA, while for example Dummit & Foote just end in Category Theory or Homological Algebra. He just introduce what he consider necessary to know about groups. Of course, if your porpouse is to learn, let's say Group Cohomology, then its good for you to know as much as possible about groups, modules and stuff, but Lang's try to focus on what HE consider is important to be known.
4pro
It is one of the brilliant classics, must have for every advanced algebraist. Probably you will not find here such nouveau labyrinths of mathematical thought as in Beta Algebra by Algirdas Javtokas (which in my opinion is a revolutionary book), but it is unvaluable for seminars or supplementary material for algebra courses.

This book grows on you.
When I examined this book as an undergraduate I did not like it; often this is a sign that a book is poorly written, but in this case I just needed more background.Now I see this text as a gold-mine: clearly written, provocative, and rich in examples.
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Subjects:  1. Algebra    2. Algebra - General    3. Algebra - Linear    4. General    5. Group Theory    6. Mathematics    7. Science/Mathematics    8. Algebra Textbook    9. Mathematics / Algebra / General    10. Textbook   

Reviews (9)

classical
very well written text about the algebra of standard model,
A good *first* start
This book is good for what it is, namely, something to get your feet wet.When learning the basics of particle physics, e.g. as an undergrad or a beginning experimentalist, this is the quickest way to get a feel for the standard model gauge group. What do you need more?
I'd say that, at least, the Georgi's book is too underestimated here. Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Group Theory    4. Lie Groups    5. Lie algebras    6. Nuclear Physics    7. Particle Physics    8. Particles (Nuclear physics)    9. Physics    10. S-matrix theory    11. Science    12. Science/Mathematics    13. Solid State Physics    14. Algebra    15. Mathematics for scientists & engineers    16. Particle & high-energy physics   

Subjects:  1. Geometry - General    2. Group Theory    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. C*-algebras    7. K-theory    8. Linear algebra    9. Mathematics / Mathematical Analysis    10. non-commutative topology    11. operator algebras    12. von Neumann-algebras   

Reviews (1)

Typical Serre, concise, clean, clear.
This is a an excellent introduction to the subject.The book really breaks into 3 distinct parts.The first 5 chapters are a rapid introduction to the basics, similar to what one would get from any indroductory text.They are most notable for actually going through the details on D_n, S_n cyclic groups... The second section (chapters 6-13) gives a more graduate level presentation of the material.Starting with a discussion of group algebras, moving onto inducted representations Artin's theorem (the existence of virtual characters) The third section is Brauer Theory. The book is by Serre so it goes without saying it one of the best if not the best book on the market.His failure to deal with the additional complexities of the infinite group case (which he indicates in the title) is a small problem.He could have spent at least 1 chapter addressing how the results of the book could be extended.The index of notation is a fantastic asset for a subject where notation plays such a large role. ... Read more

Subjects:  1. Finite Mathematics    2. Finite groups    3. Group Theory    4. Mathematics    5. Representations of groups    6. Science/Mathematics    7. Darstellung (Math.)    8. Endliche Gruppe    9. Mathematics / Finite Mathematics    10. Mathematics / Group Theory    11. Mathematics-Group Theory   

Reviews (11)

Review nearly 40 years later
I read this book in 1965 as a freshman in Chemistry
Good Reference, Poor Textbook
This book is a double edged sword. As a reference textbook for a person who has already had a significant introduction to group theory and chemical applications of it, this book can't be beat. It provides some very detailed mathematical derivations of the theoretical formulas used within group theory which one may not find in an elementary inorganic text which skims over group theory. Additionally, Cotton covers organic, organometallic and inorganic examples which allows the reader to have a broad spectrum of systems to learn from. The blurbs about molecular vibrations and crystallography were nice too. Finally, Cotton does not lack in providing journal references to the original research that he covers in the text. Good book for its intended purpose and audience
Professor Cotton's book is a well written introduction to the theory of group representations for chemists.It is appropriate for chemical experimentalists and beginners with a more thoeretical bent.It was NOT INTENDED to be a book of algebra for mathematicians or physicists interested in Lie groups.The pure rotation group is not covered, representations of space groups are not mentioned, ray representations are not used, etc.Many of the reviewers below seem to think they will need one and only one book that deals with applications of group theory - not likely!For a beginner with a background typical of a 1st year grad student in physical or inorganic chemistry at an American university, the book is good.If the complainers below ever tried to teach a course to such students using the more rigorous books they are clamoring for, they would be hung in effigy (if they were lucky).Read more

Subjects:  1. Chemistry - Physical & Theoretical    2. Group theory    3. Molecular theory    4. Physical Chemistry    5. Science    6. Science/Mathematics    7. Chemistry    8. Groups & group theory    9. Science / Chemistry / Physical & Theoretical   

Reviews (2)

Caveat emptor!
Look at this book before you buy it.The author gets five stars; the publisher, one at most.What a shame!This is just the book for the summer before you start grad school. See Galois theory in action! But check it out of the library. It's printed on blotting paper. The illustrations are done in shades of black. If you wear glasses you will think they are dirty, but sadly, no amount of cleaning will make this book look as sharp and clear as its ideas. Of course, what you really study will be in your own handwriting, but a book this expensive should be beautiful.

Felix Klein and polynomials of the fifth degree
There are many books that discuss the fact that you cannot solve the general polynomial of the fifth degree (i.e. a quintic) using radicals.They often mention that Felix Klein showed there is a method to find the roots using rotations of the icosahedron, the regular polyhedron with 20 triangular faces.It is hard to find out exactly what this means (Klein's own book is out of print).Shurman gives all the details, and is a well written book combining group theory and geometry.Read more

Subjects:  1. Advanced    2. Algebra - Elementary    3. Curves, Quintic    4. Mathematics    5. Quintic equations    6. Science/Mathematics    7. Theory Of Equations    8. Complex analysis    9. Geometry    10. Groups & group theory    11. Linear algebra    12. Mathematics / Algebra / Elementary    13. Topology   

Subjects:  1. Algebra - General    2. Computer Science    3. Computers - General Information    4. Group Theory    5. Lie algebras    6. Lie groups    7. Mathematics    8. Science/Mathematics    9. Linear algebra    10. Mathematics / Group Theory   

Reviews (6)

A masterpiece in wavelets
This is a very well written book on the theory of wavelets and its applications. The presentation is self-contained and may serve as an introduction for someone who wants to learn about this topic. It also is an excellent book for those who have an advanced graduate degree in applied mathematics since it demonstrates how to truly understand complex concepts. This book gives a general presentation of some recent developments in wavelet theory with an emphasis on techniques that have a geometric and spectral-theoretic flavor. It can be certainly used as a textbook for graduate students as well as as a reference book for the specialists and researchers. A very nice feature of the book are the tutorials at the beginning of each chapter and some sections, which serve as summaries of main ideas and guides through the background ideas and motivation. At the end of every chapter there are plenty of excercises of various level of difficulty. Overall, this is a great book and I recommend it highly to a motivated reader.

Distinguished link between math and computer science
This is an important mathematical reference written in excellent style.Wavelets have found applications in many areas of engineering and CS.The authors provide a detailed, rich and entertaining tour through this relatively young but important field for both math and CS/Eng.Connections are, e.g., made between advanced CS virtual-reality applications such as audio-systems processing, future applications such as quantum computing, and advanced math in functional analysis and operator theory.

A fresh look at wavelets
The Book by Bratteli and Jorgensen is a superb book on wavelet's theory. It is very well written and has new and a fresh point of view on the subject. Although there are several good books on wavelets, the book by Bratteli and Jorgensen covers an important niche that has not been covered before. In particularRead more

Subjects:  1. Applied    2. Functional Analysis    3. Geometry - Algebraic    4. Harmonic Analysis    5. Homotopy Theory    6. Mathematical Analysis    7. Mathematics    8. Science/Mathematics    9. Spectral theory (Mathematics)    10. Topology - General    11. Wavelets (Mathematics)    12. Applied mathematics    13. Approximation Theory    14. CS/Numerical Mathematics    15. Calculus & mathematical analysis    16. Communications Theory    17. Harmonic Analysis/Applications    18. Mathematics / Group Theory    19. Mathematics / Mathematical Analysis    20. Mathematics-Applied    21. Signal Processing   

Reviews (3)

Very nice
An excellent book.The approach, working toward the general theory via examples, has some great pedagogical virtues but also drawbacks.It also means the book has drawbacks as a reference, as important general theorems can be hard to locate (often they are in an appendix, but relevant definitions or lemmas are in several places in the text). Despite the example-oriented style, the level of mathematical sophistication assumed is reasonably high (so some physicists, for example, may find some of the explanations require boning up on certain ideas found more in pure mathematics than physics).However, many things are given very nice explanations that are lacking in some dryer texts (e.g. Varadarajan, or even Humphreys).Particularly nice is the discussion of relations between the representation theory of finite groups and Lie groups.Many mathematicians might find this book an enjoyable read to see connections made and examples worked out at a high level of sophistication, after learning the general theory.Some may also find it useful primarily as a repository of worked-out examples. I found Humphreys book "Introduction to Lie algebras and representation theory (Springer GTM series) to be an essential companion for getting the general theory with full proofs in a somewhat more logical order, if somewhat terse and a tad dry;Knapp's book "Lie groups beyond an introduction" could also serve this purpose, perhaps even somewhat better.If teaching a course, I would probably use this as supplemental reading rather than a primary text (though it could also turn out that gradually-generalizing-from-examples approach works better in a course than for self-teaching).It has been a useful book for me to own, and I recommend it, with the caution that you will probably want to supplement it with a book like Knapp's.(If you want to use only one book, and are reasonably mathematically sophisticated and already know basically what Lie groups and algebras are, use Knapp's.) I am a math-oriented physicist, who recently learned much of this material, using this and other books, in order to use it in my research.

A beautiful exposition
This is an absolutely delightful introduction to the theory of Lie groupsand their representations.The style is informal but informative, withsome of the important proofs hidden in the appendex or even omitted (i.e.existance of the finite dimensional representations for all lie algebras). However, this is a fully rigorous text, and all the important theorems arestated, and most are proved.Mathematicians should suppliment this bookwith Humphries standard text on Lie algebras.However, this book providesmotivation and intuitive insight that Humphries is missing.Additionalenjoyment may be derived from the sampling of other unusual topics, such asSchur functors and applications to algebraic geometry.Of course, thesecan also be omitted as the reader desires.Read a lecture every few nightsbefore bedtime, and soon Lie theory will seem beautiful and almostintuitive.

Brilliantly Clear
An excellent companion for anybody learning lie algebras or representation theory. Also good for physics folk needing to pick up more than the basics of lie algebras; a nice followup to a "lie algebras in physics"book (and there are many of those.)Read more

Subjects:  1. Algebra - Linear    2. Calculus    3. Group Theory    4. Lie algebras    5. Lie groups    6. Mathematics    7. Representation Of Groups    8. Representations of algebras    9. Representations of groups    10. Science/Mathematics    11. Functional analysis    12. Groups & group theory    13. Mathematics / Algebra / Linear    14. Mathematics / Group Theory    15. Mathematics-Calculus   

Subjects:  1. Algebra - Linear    2. Diophantine approximation    3. General    4. Linear Algebra    5. Linear algebraic groups    6. Mathematics    7. Number Theory    8. Science/Mathematics    9. Theory Of Numbers    10. Exponential Functions    11. Groups & group theory    12. Mathematics / Number Theory    13. Measures of Independence    14. Simultaneous Diophantine Approximation    15. Trancendental Numbers   

Reviews (2)

An excellent treatment of the subject written in "mathematics."
I find Professor Gilmore's book a top-flight exposition of a "not so easy" subject.As a mathematician, I am very comfortable with the degree of mathematical rigor.It is not sloppy.I hope physicists won't be put off by the fact that this book is written in "mathematics."We are in a time when the distinction between pure mathematics and theoretical physics is rapidly blurring, if not already extinct.The physicist must become accustomed to the protocal of pure mathematics, as the mathematician must understand the needs of theoretical physics and be motivated by them.Many will disagree.
Excellent introduction to the field for physicists
Perhaps the best feature of this book is that it aims to convey the theory of Lie algebras and Lie groups to physicists. In doing so, the author is careful to give a very simplistic approach so that one not familiar withthe subject can understand it. Not to say that the book is elementary,since it builds rapidly into the far more interesting aspects of LieGroups. A very good read. ... Read more

Subjects:  1. Algebra - Linear    2. Group Theory    3. Lie algebras    4. Lie groups    5. Mathematics    6. Science/Mathematics    7. Mathematics / Group Theory   

Reviews (1)

clear coverage for practicing biostatisticians
Advances in the theory of repeated significance testing in the 1980s and 1990s has made sequential methods practical by identifying stopping rules for data collected sequentially but in groups. This material is now used to plan interim analyses and both safety and efficacy group sequential trials for clinical trials. This text provides for the first time thorough coverage of these advances with suitable references to the literature.Read more

Subjects:  1. Biostatistics    2. Clinical trials    3. Decision Theory    4. Medical    5. Medical / Nursing    6. Pharmaceutical Chemistry    7. Pharmacology    8. Pharmacy    9. Probability & Statistics - General    10. Science/Mathematics    11. Statistical methods    12. Statistics    13. methods    14. Applied mathematics    15. Groups & group theory    16. Mathematics / Statistics    17. Medical laboratory testing & techniques    18. Probability & statistics   

Reviews (4)

Good book but many errors
This is a good book, well-organized and contains many useful materials. However I do not recommend it as an independent study textbook (which is what I did). There are many errors, most of them are typographical but some of them are wrong numbers which are very difficult to correct, especially in the exercises given. And the exercises are very important -- the following discussions and proofs depend on some of them. Springer published a "corrected second printing" in 1999 but obviously they didn't do a good job (I purchased the new one and I got the old one in the library).

Fun but not easy
I am not sure I would take this specific book to a desert island but I would highly recommend it to anyone who is in possession of patience, self-motivation and willingness to spend time working through both the problems and any gaps that may occur within the proofs.This book can be used both by Graduate students or as a topics/independent study course for well prepared and motivated undergraduates. Solid, but occasionally frustrating
I used this book as a means of writing my senior thesis on the clasification of the projective unimodular groups and the Mathieu groups as being simple. Most of the proofs were well constructed and easy to follow.What this books lacks is a proof reading. Several of the proofs make nosense in the form in which they are written. Also, his notation at timesbecomes cluttered and not easy to follow. One can imagine how difficultnotation can be in general, but when it is full of typographical errors, itcan be almost impossible to wade through without the help of someone whoknows the material. This book is certainly not a waste of time to read andis very good as a reference for theorems concerning finite groups, howeverdo not put all your eggs in one basket and base your education on this onebook. ... Read more

Subjects:  1. Group Theory    2. Mathematics    3. Science/Mathematics    4. Theory Of Groups    5. Mathematics / Group Theory   

Reviews (5)

Good book of reference
I purchased this as a book of reference.When I want to know something about Commutative Algebra (while reading Hartshorne's Algebraic Geometrry), I like a standard book of reference.But it seems a good book to learn commutative algebra aswell.

very good, but should be read slowly
Some proofs are somewhat abstract to the beginner. Although you are forced to check them on the paper, I think it is very good for the study. Also, you need a professor to instruct you, because in math, any language could only express the part of the oringins. Anyway, algebraic geometry is the course that you have to have a good professor to help you, otherwise stop study this field. In one word, it is a very very good book, so read it slowly!!!!!!

Superb
If one is interested in taking on a thorough study of algebraic geometry, this book is a perfect starting point. The writing is excellent, and the student will find many exercises that illustrate and extend the results in each chapter. Readers are expected to have an undergraduate background in algebra, and maybe some analysis and elementary notions from differential geometry. Space does not permit a thorough review here, so just a brief summary of the places where the author has done an exceptional job of explaining or motivating a particular concept: Read more

Subjects:  1. Algebra - General    2. Commutative algebra    3. Geometry - Algebraic    4. Geometry, Algebraic    5. Group Theory    6. Mathematics    7. Science/Mathematics    8. Algebraic Geometry    9. Groups & group theory    10. Mathematics / Geometry / Algebraic   

Reviews (16)

very accessible introduction to group theory and it's history
The equation that couldn't be solved is about the history of group theory. The stories of two of it's early contributors Abel and Galois is told in detail. In addition the author provides an accessible overview of group theory. The specific equation that couldn't be solved is the quintic, which cannot be factored in general. That means that while there are specific examples of polynomials with a factor of x raised to 5 or greater that can be factored there is no general formula like the quadratic eqauation that can factor all quintic or higher polynomials. Although originally used to study factoring, group theory has evolved to be about many other things including the mathematical concept of symmetry. Symmetry arises in many parts of mathematics and science so it is very imporant. I came away from this book with a knowledge of the history of group theory and a smattering of knowledge about group theory and it's applications. I highly recommend this book to those people, like me, who are interested in mathematics and would like to peek under the surface to see what it is all about.

Sinusoidal
As I was reading this book, my interest level ebbed and flowed; it was like that all the way to the end. For the most part, the book held my attention, but often I got the feeling that the author was straying from the symmetry theme a bit too much. So this is very much a book of peaks and valleys (hence the title of my review).
More of a biography
I bought this book thinking that it was going to discuss symmetry in mathematics, but it barely touched on it in any depth.It was mostly a biography of Abel and Galois; which was intriguing.On the whole, the book was worth reading, but it was not what I was expecting.They really should change the title of the book.If you are looking for any earnest discussion of symmetry, look else where. ... Read more

Subjects:  1. 1811-1832    2. Galois theory    3. Galois, Evariste,    4. Group Theory    5. History    6. History & Philosophy    7. History Of Mathematics    8. Mathematics    9. Science/Mathematics    10. Symmetric functions    11. Mathematics / General   

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Complex analysis    5. Groups & group theory    6. Mathematics / Number Theory   

Subjects:  1. Functions, Special    2. Group Theory    3. Integral transforms    4. Lie groups    5. Mathematical Analysis    6. Mathematical Physics    7. Mathematics    8. Representations of groups    9. Science/Mathematics    10. Theory Of Functions    11. Theory Of Groups    12. Functional analysis    13. Mathematics / Group Theory    14. Mathematics / Mathematical Analysis    15. Mathematics-Mathematical Analysis    16. Science-Mathematical Physics   

Subjects:  1. General    2. History & Philosophy    3. Information Theory    4. Mathematical Analysis    5. Mathematicians And Their Works    6. Mathematics    7. Science/Mathematics    8. Artificial intelligence    9. Computers / Information Theory    10. Computers-Information Theory    11. General Theory of Computing    12. Groups & group theory    13. Mathematical foundations    14. Mathematics / History    15. Medical-General   

Subjects:  1. Differential Equations - Partial Differential Equations    2. Mathematical Analysis    3. Mathematics    4. Differential equations    5. Groups & group theory    6. Mathematics / Mathematical Analysis