Subjects:  1. Algebra - Linear    2. C*-algebras    3. Congresses    4. Mathematics    5. Operator theory    6. Science/Mathematics    7. Algebra    8. Functional analysis    9. Mathematics for scientists & engineers   

Subjects:  1. Calculus    2. Complex manifolds    3. Functional Analysis    4. Geometry - Differential    5. Holomorphic functions    6. Mathematics    7. Riemannian Manifolds    8. Science/Mathematics    9. Theory Of Functions    10. Algebra    11. Complex Function Theory    12. Complex analysis    13. Mathematics / Calculus    14. Mathematics / Mathematical Analysis    15. Several Complex Variables   

Reviews (3)

Many detailed problems, but dated exposition
Be warned that this book references Hardy's "Pure Mathematics" regularly.This book is principally a collection of results in complex analysis.The upside is that there are many problems developed in detail and the author sincerely tries to motivate every topic.The downside is that the language is so dated that often topics are excessively difficult to digest.I would not recommend this as a first book in complex functions theory.It's more useful as a supplement to other more modern courses.

Theory of functions
This is an excellent book and a very good resourc

I earned my living from this book
This is a book on complex analysis, followed by some measure theory. It is the complex analysis part which is superb. Titchmarsh is one of those rare authors that manage to motivate the results, get them with rigour and clarity and, especially, select theorems so well that you always find what you need for applications. It's like the famous short table of integrals in the famous, multi-edition, "Handbook of Physics and Chemistry". It was so wisely made that it was said that when you could not find in it the integral youneeded, you probably went wrong somewhere. So is the venerable Theory of Functions. It is particularly good in asymptotic theorems like Phragmen-Lindelof's, or in the treatment of analytic continuation. But the whole book is a joy! When the Regge Pole theory appeared in particle physics, I published several papers that were not much more than transpositions of results from Titchmarsh to the language of particle physics. So I earned my living f! rom it, for some years. ... Read more

Subjects:  1. Calculus    2. Functional Analysis    3. Functions    4. Mathematics    5. Science/Mathematics    6. Calculus & mathematical analysis    7. Mathematics / Functional Analysis    8. Mathematics | Computational Mathematics   

Reviews (9)

A good guide to Riemann, the prime number theorem, and the Riemann hypothesis
Chapter 1 analyses Riemann's paper in detail. The zeta function is the product over all primes of 1/(1-1/p^s). Taking the logarithm, one obtains an expression involving the density of primes. So to say something about the density of primes one must say something about the log of the zeta function. Riemann does this by allowing the variable s of the zeta function to be complex, which enables him to prove the functional equation of the zeta function and the product representation of the xi function defined through it. From here he can derive an expression for log zeta, thus yielding an expression for prime density. Since it comes from log zeta, this expression depends on the poles of log zeta, i.e. the zeros of the zeta function. Riemann feels that all nontrivial zeros have real part 1/2, but this doesn't really matter right now since the term in the prime density expression depending on the zeros is "periodic" in any case and Riemann thus discards it without much harm when he derives his expression for the number of primes less than x. Hadamard and von Mangoldt later gave more rigourous proofs of the product formula for the xi function (chapter 2) and Riemann's prime density expression (chapter 3). As indicated by Riemann, further progress depends on an understanding of the zeros of the zeta function. Indeed, in this way Hadamard proved the prime number theorem (chapter 4), i.e. that the prime counting function is asymptotically equal to the logarithmic integral, and also in this way de la Vallee Poussin derived a bound for the error in this approximation (chapter 5). The Riemann hypothesis would imply a better bound. Chapters 6,7,8,9,11 deal with the pitiful progress towards the Riemann hypothesis, including computational aspects. Chapter 10 tries to hot up the Fourier analysis used in the classical works by putting it in terms of self-adjoint operators and so on. Chapter 12 "Miscellany" includes a proof of the prime number theorem that "is 'elementary' in the technical sense", but, as Edwards admits, it is neither straightforward, nor natural, nor insightful.

Riemann's Zeta Function
A vey good synthesis of the state of the art at graduare level.

Excellent for experts and the casual mathematician alike
I hesitate to add to the chorus of praise here for H.M. Edwards's "Riemann's Zeta Function," for what little mathematics I have is self taught. Nevertheless, after reading John Derbyshire's gripping "Prime Obsession" and following the math he used there with ease, I thought to tackle a more challenging book on the subject. A Topologist friend suggested Titchmarsh's "The Theory of the Riemann Zeta-Function," but I soon bogged down. I happily came across Edwards while browsing, and was pleased both with the low price, and the lucid contents.
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Subjects:  1. Functional Analysis    2. Functions, Zeta    3. Mathematical Analysis    4. Mathematics    5. Number theory    6. Science/Mathematics    7. Mathematics / General   

Reviews (1)

An excellent book on this topic!
This book is an expansion of the author's lecture notes "Perturbation Bounds for Matrix Eigenvalues" published in 1987.I have used both versions for my students' projects.The book under review centers aroundthe themes on matrix inequalities and perturbation of eigenvalues andeigenspaces. The first half of the book covers the "classical"material of majorisation and matrix inequalities in a very clear andreadable manner. The second half is a survey of the modern treatment ofperturbation of matrix eigenvalues and eigenspaces. It includes lots ofrecent research results by the author and others within the last ten years. This book has a large collection ofchallenging exercises.It is anexcellent text for a senior undergraduate or graduate course on matrixanalysis. ... Read more

Subjects:  1. Algebra - Linear    2. Linear Algebra    3. Mathematics    4. Matrices    5. Science/Mathematics    6. Algebra    7. Functional analysis    8. Mathematics / Mathematical Analysis    9. Mathematics / Matrices    10. Numerical analysis   

Subjects:  1. Applied    2. Mathematical Analysis    3. Mathematics    4. Science/Mathematics    5. Fourier analysis    6. Functional analysis    7. Mathematics / Mathematical Analysis   

Reviews (1)

Feintuch's Robust Control in Hilbert Space
This book and the journal papers that preceded it launched the new era of algebraic control theory which is one of the main new trends in mathematics, engineering, and physics.Control theory is just what is sounds like: control in the intuitive sense (usually of artificialsatellites, rockets, robots, but also manufacturing and chemical plants,cars, physical and biological thermoregulatory systems, etc.).The oldcontrol theory lacked simplicity, clarity, organization, and eveninspiration, and was done by long calculations with little algebraictime-saving or space-saving.Bruce Francis, whom the author cites and withwhom the author collaborated earlier, began the search for time- andspace-saving methods, although his own monograph makes difficult reading. Feintuch's book is crystal clear, organized, and time- and space-saving. He even isolates for us his main methods: not H-infinity but nest algebrasand their operator theory framework which lead to a theory of uniformoptimal control and robustness for time-varying linear systems, Arveson'sdistance formula based on operator matrices in algebra, internal stabilityrepresenting a linear system as the range of 2x1 operator matrices withcausal entries and stabilization corresponds to left causal invertibility,the gap metric, factorizations including inner-outer, spectral, coprime. Block matrices turn out to be very important.Feintuch's theory is mostlyin Hilbert space rather than Banach space, although he introduces Banachalgebras and does some work in Banach space.Hilbert space has been foundto be defective in quantum theory by A. Bohm and was "repaired"by him by adding Hilbert and Banach lattices and rigged Hilbert spaces, butit is becoming obvious that a new direction is needed both in quantumtheory and control theory: Banach spaces.My own work is in this latterarea.I could have used Feintuch's insights when I worked in satellitesfor the U.S. Defense Department.The reader unfamiliar with themathematics can hire a consultant or tutor to translate things intoapproximate English, an endeavor well worth the time and effort. ... Read more

Subjects:  1. Advanced    2. Applied    3. Calculus    4. Control Theory    5. Hilbert space    6. Mathematics    7. Science/Mathematics    8. Theory Of Operators    9. Applied mathematics    10. Automatic control engineering    11. Functional analysis    12. Mathematics / Linear Programming   

Reviews (7)

.. and try to read everything else JvN wrote, too!
von Neumann's account of why he uses the mathematics he does and his critique of the Dirac formalism is worth the price of admission. Those who deride him for avoiding the delta formalism seem to have been seduced by its meretricious computational facility. von Neumann anticipated - actually began in this book and his work on continuous geometry - the modern approach via non-commutative geometry to physics (see Alain Connes),and M-theory.

Hilbert Space Formulation of QM
The ultimate source of Hilbert Space applied to Quantum Mechanics.John von Neumann was the first to systematically formulate QM in such a powerful and elegant vector space.If this is the Bible of QM in HS, Hughes is the missioner!Get the book as well -- The Structure and Interpretation of Quantum Mechanics.

Has Strengths and Weaknesses
First the strengths:Read more

Subjects:  1. Advanced    2. Mathematics    3. Quantum Mechanics    4. Quantum Theory    5. Science    6. Science/Mathematics    7. Chemistry    8. Functional analysis    9. Mathematics / Advanced    10. Physics    11. Quantum physics (quantum mechanics)   

Reviews (2)

The Guide
Various types of non-stationarities are common in time series data from financial markets. This requires a guide for selecting among numerous tools to deal with the non-stationarity. A unified treatment of filters like this book is a great help since it provides a fast and rigorous introduction. Easy to understand!
The book is a wonderful reference in that it brings together various filtering methods. It is an excellent introduction to the topic, clearly written and easy to understand. The text does not assume a high-level math background. Further, unlike the various books which simply provide the theory but include very few or no applications at all, this book by Gencay, Selcuk, and Whitcher has many applications that help you get the right picture. ... Read more

Subjects:  1. Accounting - General    2. Business & Economics    3. Business & Economics / Econometrics    4. Business / Economics / Finance    5. Business/Economics    6. Econometrics    7. Economics    8. Economics - General    9. Finance    10. Functional Analysis    11. Harmonic Analysis    12. Mathematical Economics    13. Mathematical models    14. Wavelets (Mathematics)    15. Budgeting & financial management    16. Business & Economics / Finance   

Reviews (11)

a superb book
This is a rewrite of the great book by Courant, and it does justice to its origin.I prefer the somewhat more charming original book of Courant myself, but I have taught from this one too and learned something more.
More than an introduction
Those books (volumes 1-2) can be seen as a new edition of Courant's classical Differential and Integral Calculus, volumes 1-2 (that can still be used for general calculus courses). The first volume was written while Courant was still alive, and the second was postumous. I believe that they are the best work to start understanding analysis. Indeed, for the general scientist (as a physicist) it contains all the theory needed for any application. The book is not easy reading though. Much of the text can be understood on first reading, but there are pretty profound sections, mostly on the appendixes, that turn the book genuinely onto a book of analysis. The second volume requires some mathematical maturity, and I doubt whether it is suitable for beginners, but it is simply the best book of multivariate calculus that I know - and it is really difficult to think of a better presentation. Courant was a giant, and his concept of mathematics shines in every page of those books (although he did not see the publication of the second volume, his hand can be seen in every page). For the serious mathematician, a must-have. For the beginner, the best way to get in love. Courant and John don't lie, they give every proof and guide you most gently in this complicated garden called mathematics. I'd give it aleph stars if it was possible.

Absolutely beautiful!
I give 5 stars to this book because in contrast with the majority of the calculus textbooks it gives the reader the perfect combination between rigor and intuiton. Another thing that I also like a lot is the fact that volume 2 has solutions to almost all the excercises, which is great because some of the problems are very difficult. I really think this book is a "must have". ... Read more

Subjects:  1. Calculus    2. Functional Analysis    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Calculus & mathematical analysis    7. Fourier series    8. Mathematics / Functional Analysis    9. Real analysis    10. numerical methods   

Reviews (1)

Such a Gem!
The book contains all the significant problems for a first year calculus course. Working on these problems would dramatically help you gain perfect grades from your calculus classse. (At least that happened to me and my friends who use it.) No matter you are a math, physics, biology, or economics or even chemistry major, you would find it extremely useful. It also contains some very challenging problems up to the level of the world's most difficult undergraduate contest: The Putnam! ... Read more

Subjects:  1. Calculus    2. Functional Analysis    3. Mathematical Analysis    4. Mathematics    5. Problems, exercises, etc    6. Science/Mathematics    7. Calculus & mathematical analysis    8. Differentialrechnung /Aufgabensammlung    9. Integralrechnung /Aufgabensammlung    10. Mathematics / Calculus    11. Mathematics / Mathematical Analysis    12. Mathematics-Functional Analysis    13. Mathematics-Mathematical Analysis   

Subjects:  1. Calculus    2. Holomorphic functions    3. Mathematical Analysis    4. Mathematics    5. Operator theory    6. Probability & Statistics - General    7. Science/Mathematics    8. Theory Of Functions    9. Functional analysis    10. Geometry    11. Mathematics / Differential Equations   

Subjects:  1. Functional Analysis    2. General    3. Mathematical Analysis    4. Mathematical Physics    5. Mathematics    6. Nonlinear functional analysis    7. Science/Mathematics    8. Theoretical methods   

Subjects:  1. Algebraic Fields    2. Arithmetic functions    3. Drinfeld modules    4. Functional Analysis    5. Group Theory    6. Mathematics    7. Science/Mathematics    8. Algebraic number theory    9. Differential equations    10. Geometry    11. Mathematics / Number Theory    12. Topology   

Reviews (1)

Excellent supplment to Brown and Churchill
I used this book for two Graduate semesters of Complex Analysis. The course text was Brown and Churchill which I often found lacking in detail. This book might not be consider by some as a Graduate level text however I found it to be an excellent supplemental text to fill in the gaps and improve my understanding of the material. ... Read more

Subjects:  1. Calculus    2. Functional Analysis    3. Functions Of Complex Variables    4. Mathematical Analysis    5. Mathematics    6. Science/Mathematics    7. Complex analysis   

Reviews (3)

An excellent overview
The field of statistical learning theory has not only seen considerable advances in the last fifteen years, it has also found many applications, some of these appearing in commercial packages. It is now classified as a subfield of artificial intelligence, and as such gives an alternative, and frequently more general viewpoint on such topics as pattern recognition, regression estimation, and signal processing. The author of this book is one of the originators of statistical learning theory, and has written a book that will give the mathematically sophisticated reader a rigorous account of the subject. Most of the main results are proven in detail, but the author does find time to include insightful discussion on the origins and intuition behind the concepts involved in statistical learning theory.
new approach to inference based on VC dimension
Vapnik and Chernovenkis extended the Glivenko-Cantelli Theorem in their work on classification and statistical learning.Vapnik in recent texts has described a form of nonparametric statistical inference based on approximating functions and the Vapnik-Chernovenkis dimension. Rich & Valuable
This book aims at rigorours and deep treatment of statisticallearning and is divided into three parts :Read more

Subjects:  1. Artificial Intelligence - General    2. Computational learning theory    3. Computers - General Information    4. Functional Analysis    5. Mathematical Analysis    6. Mathematics    7. Probability & Statistics - General    8. Science/Mathematics    9. Machine learning    10. Mathematics / Statistics   

Subjects:  1. Applied    2. Functional Analysis    3. Geometry - Algebraic    4. Homology Theory    5. K-theory    6. Mathematics    7. Science/Mathematics    8. Topology - General    9. Algebraic topology    10. Calculus & mathematical analysis    11. Geometry    12. Mathematics / Functional Analysis    13. Mathematics | Pure Mathematics   

Subjects:  1. Applied    2. Asymptotic expansions    3. Calculus    4. Functional Analysis    5. General    6. Mathematical Statistics    7. Mathematics    8. Mellin transform    9. Probability & Statistics - General    10. Science/Mathematics    11. Theory Of Functions    12. Applied mathematics    13. Calculus & mathematical analysis    14. Mathematics / Geometry / General   

Subjects:  1. Geometry - Algebraic    2. Mathematics    3. Science/Mathematics    4. Algebraic geometry    5. Functional analysis    6. Mathematics / Geometry / Algebraic    7. Mathematics | Pure Mathematics   

Subjects:  1. Applied    2. Engineering - General    3. Functional Analysis    4. Mathematics    5. Science/Mathematics    6. Technology & Industrial Arts    7. Electrical engineering    8. Operational research    9. Science / Dynamics