Book Description
This self-teaching volume provides extremely readable coverage of the principles of finite mathematics and their applications in business, social science, and the life sciences. Topics are presented in a straight-forward, interesting manner (with topics from elementary mathematics reviewed as the need for them arises), and an abundance of worked examples with computational details, practice problems, exercises, chapter self-assessment tests, and reviews of fundamental concepts allow readers to work through the material confidently at their own pace. Contains many examples similar to those found on CPA, GMAT, and GRE Economics exams. Features optional, explicitly detailed use of graphing calculators, electronic spreadsheets, and mathematical software, wherever relevant. Linear Equations and Straight Lines. Matrices. Linear Programming, A Geometric Approach. The Simplex Method. Sets and Counting. Probability. Probability and Statistics. Markov Processes. The Theory of Games. The Mathematics of Finance. Difference Equations and Mathematical Models. Logic. Graphs. For anyone who needs to get up to speed with the applications of mathematics in business, social sciences, or life sciences.
Customer Reviews:
Better than the one I use, but not by enough to change.......2005-10-20
I recently evaluated this book as a possible textbook for the finite mathematics class that I teach. A great deal of space is devoted to the use of technology using a TI-83 graphing calculator and Microsoft Excel spreadsheets. Images of the calculator and computer screens are used to demonstrate the solutions. While I don't use either technology in my class, the presence of the technology solutions had no affect on my opinion of the book.
I would have little difficulty using the book and my students would have no difficulty reading it. The explanations are easy to follow and at a level suitable for the background we require of our students. There are a large number of exercises and the coverage is ordinary. By ordinary, I mean that the covered topics are the standard ones in a college level course in finite mathematics and the order of presentation is a natural one.
In the end, I chose to stick with the book that I have been using. As a general rule, I change books only when I find one that is significantly better and in this case I did not. This book is a good one and even slightly better than the one I am currently using. I just don't believe that the difference is enough to justify the change.
Great Choice.......2005-09-20
I was very satisfied with my results and the sender got my book sent to me extremely quick.
I'm glad I'm the teacher and not the student!!!.......2005-02-10
Wow. This book is bad. I have to use this book -- chosen by the department -- for a class I'm teaching. The fact that the book is a bad choice for this class is not the fault of the book -- I was given the text with instructions to teach chapters 1 - 4, 10, and 11, and then to use extra material for topics not covered in the book -- clearly, this text does not fit the class, and either the course should be redesigned, or a different text should be chosen.
Anyway, a first glance was enough to see how miserably this book is organized. The first chapter covers:
1.1 Coordinate Systems and Graphs
1.2 Linear Inequalities
1.3 The Intersection Point of a Pair of Lines
1.4 The Slope of a Straight Line
1.5 The Method of Least Squares
So, section 1.2 is dependent on 1.3 which is dependent on 1.4 -- isn't the order a bit backwards? And then in 1.5, you're on to a topic which is a huge leap in difficulty from learning how to plot a point on Cartesian coordinates from 1.1. Unbelievable.
This type of interdependence carries on through all of the sections of the book that I've looked at (admittedly not all). It seems that one must already know the material from further ahead in the book in order to use the book to learn the material in the given chapter.
I believe that by this Eighth Edition of the book, the authors should be removed from it -- it should be given to students using this text without already knowing it all, and let those students revise and edit the continuity of the material.
Matrix notation is introduced, virtually without explanation of either how to use it or why. Examples are given that attempt to show how to perform some operations on a TI-83 (or similar) calculator, but these efforts fail miserably.
Frankly, I'm having a hard time even figuring out what it is that this book is trying to teach -- and I already understand the material! If, however, the goal of the book is to confuse students such that they should hate and fear all math courses, then the authors have achieved their goals.
Book Description
Oriented matroids are a very natural mathematical concept which presents itself in many different guises, and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the first comprehensive and accessible account of the subject. This book is intended for a diverse audience: graduate students who wish to learn the subject from scratch, researchers in the various fields of application who want to concentrate on certain aspects of the theory, specialists who need a thorough reference work, and others at points in between. A list of exercises and open problems ends each chapter, and the work is rounded off by an up-to-date and exhaustive reference list.
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Convex Bodies: The Brunn-Minkowski Theory (Encyclopedia of Mathematics and its Applications)
Rolf Schneider
Manufacturer: Cambridge University Press
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Numerical Recipes 3rd Edition: The Art of Scientific Computing
ASIN: 0521352207 |
Book Description
At the heart of this monograph is the Brunn-Minkowski theory. It can be used to great effect in studying such ideas as volume and surface area and the generalizations of these. In particular the notions of mixed volume and mixed area arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered in detail. The author presents a comprehensive introduction to convex bodies and gives full proofs for some deeper theorems that have never previously been brought together. Many hints and pointers to connections with other fields are given, and an exhaustive reference list is included.
Book Description
Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to senior undergraduate or beginning graduate students. Assuming only a modest background in elementary number theory, groups, and fields, Elliptic Curves: Number Theory and Cryptography introduces both the cryptographic and number theoretic sides of elliptic curves, interweaving the theory of elliptic curves with their applications. The author introduces elliptic curves over finite fields early in the treatment, leading readers directly to the intriguing cryptographic applications, but the book is structured so that readers can explore the number theoretic aspects independently if desired. By side-stepping algebraic geometry in favor an approach based on basic formulas, this book clearly demonstrates how elliptic curves are used and opens the doors to higher-level studies. Elliptic Curves offers a solid introduction to the mathematics and applications of elliptic curves that well prepares its readers to tackle more advanced problems in cryptography and number theory.
Customer Reviews:
Washington Elliptic Curves.......2007-01-12
I bought this book as a follow-up to working my way through "Introduction to Cryptography with Coding Theory" (by the same author together Wade Trappe) (which I strongly recommend as well). I was not disappointed - Washington covers a difficult but important topic in a masterly fashion which should be accessible to anyone with a serious interest in elliptic curve cryptography. It successfully follows a middle road between the standard, but rather abstract texts on number theory and those which give details of algorithms but few proofs. There are ample examples and enjoyable exercises. Strongly recommended.
Solid intermediate introduction to elliptic curves.......2006-06-12
I compare this book to Rational Points on Elliptic Curves (RP) by Tate and Silverman, and The Arithmetic of Ellipitic Curves (AEC) by Silverman.
RP is definitely for junior and senior undergraduates interested in elliptic curves. With modest knowledge of real and complex analysis (calculus and some complex calculus), RP introduces the concept of elliptic curves and presents many interesting results. Unfortunately, a lot of hand waving goes on, i.e., many results are merely stated, instead of proved.
AEC is definitely for graduate students who have all ready taken the graduate algebra and geometry sequences. A lot of high powered mathematics is used in this text to get at the heart of elliptic curves.
Washington's book falls right in between these two books. He assumes knowledge of some analysis and algebra (particulary abelian groups), then develops much of what else is needed. Some hand waving exists (mainly for some of the high powered projective geometry needed to fully understand the geometry of elliptic curves) in this book, but this does not detract from the understanding of the additive group on elliptic curves, the primary focus of the book.
For those with a basic handle on real analysis and group theory, this book can easily be used for self-teaching.
A clear, concise introduction to elliptic curves.......2006-02-20
I used this book as my main resource when writing my undergraduate dissertation on elliptic curve group structure. Although once I wanted to have a more in-depth look into any particular subject I had to chase up the references, this book made an excellent starting point. This book is a solid, clear introduction to the subject, which can be easily understood even by maths undergrads in the later years of their study (though if you're not a mathematician you may find it hard going!!) I found it be the clearest textbook on elliptic curves I came across, especially as it doesn't assume any background knowledge of algebraic geometry.
It might be a good book for a mathematic student but not a good one for an engineering student........2005-09-06
It might be a good book for a mathematic student but not a good one for an engineering student. There are too many mathematic jargons with very limited explanations. Many notations just take for granted that the readers have already known them. It is very hard for people who have limited math background. Moreover, there are so many editorial errors in the current version. I would suggest that the author put a mathematical symbol/sign index at the end of the book and make it easier for the readers to look for their meanings.
Excellent.......2003-07-19
Anyone who writes a book on elliptic curves will never do a bad job, for these objects are so beautiful that it would be a sacrilege to do otherwise. Those who study elliptic curves fall under their spell, not only because of their beauty, but also because of their many applications: the spinning top in mechanics, cryptography, exactly solved models in statistical mechanics, precession of the Mercury perihelion in general relativity, the proof of Fermat's Last (Wiles) Theorem, control theory, and string theory, to name a few. This book is an excellent treatment of ECs and would be good for a graduate student starting out in the field. The author gives many concrete examples of the main theorems, and helpful exercises are found at the end of each chapter.
The author begins the book with two neat problems that motivate well the subject of elliptic curves: the pyramid of cannonballs and the right triangle problem, i.e. which integers can occur as areas of right triangles with integer sides? He then immediately begins the elementary theory of ECs in chapter 2. The treatment is pretty standard, although he proves Pascal's and Pappus's theorems using the associativity of the group operation on ECs, which is not usually done in books on ECs. Also somewhat non-standard this early in the game is the discussion of reduction of ECs modulo various primes, and the subsequent definitions of additive, split multiplicative, and non-split multiplicative reduction.
The study of torsion points is done in chapter 3 with the Weil pairing on the n-torsion of an EC taking center stage. A fairly short chapter, the author delays the proof of the properties of the Weil pairing until chapter 11, where it is done with divisors.
Chapter 4 deals with elliptic curves over finite fields, and is one of the most important in the book from the standpoint of cryptographic applications of ECs. Hasse's theorem, giving the bounds for the group of points on an EC over a finite field, is proven in detail. The Frobenius endomorphism is introduced, and a proof of Schoof's algorithm for computing the number of points on ECs over a finite field is given a detailed treatment. There are many symbolic computational software packages in both the open and commerical realm which will do the counting straightforwardly, and anyone interested in cryptography will need to be familiar with some of these. Supersingular curves in characteristic p are introduced, and the author gives a good discussion of the reason why they are named as such.
The discrete logarithm problem, a topic also very important for cryptographic applications, is discussed in chapter 5. The chapter beings with the index calculus, and, recognizing that it does not apply to general groups, the Pohlig-Hellman, baby step-giant step method, and Pollards rho and lambda methods are discussed in details. The author then shows that for supersingular and "anomalous" curves, that the discrete logarithm problem can be reduced to an easier discrete logarithm problem. Along the way, two important concepts are introduced: the p-adic valuation, and the Tate-Lichtenbaum pairing, the latter of which is related to the Weil pairing, but applies to situations where the Weil pairing does not.
Elliptic curve cryptography is then discussed in chapter 6, and the treatment is fairly thorough. The author shows to what extent the Decision Diffie-Hellman problem can be solved using the Weil pairing. He also shows how to represent a message on an elliptic curve, satisfying early on any reader's curiosity on just how this is done. The El Gamal and ECDSA are compared in terms of their computational efficiency. An EC generalization of RSA is also discussed in some detail, along with a cryptosystem based on the Weil pairing. Chapter 7 then gives other applications of ECs, such as factoring and primality testing.
Chapter 8 marks the beginning of the "heavy artillery" in the theory of ECs, for here the author begins the discussion of elliptic curves over the rational numbers, which can be viewed as an example of Diophantine geometry. The famous Mordell-Weil theorem is proved, and as a sign that one is definitely in the arena of modern mathematics, the proof is given in terms of Galois cohomology, which is an abstraction of the Fermat method of descent. The reader gets a taste of height functions, and via some good examples, gets insight into why the rank of the EC is so difficult to compute. A neat example is given of a nontrivial Shafarevich-Tate group.
I did not read the chapters 9, 10, or 11 on ECs over the complex numbers, complex multiplication, and divisors, so I will omit their review. Chapter 12 introduces the famous zeta functions, and their use in obtaining arithmetic information about an EC. Zeta functions motivate the definition of an L-function of an EC, these being tremendously important in modern developments in the theory of ECs, such as the Swinnerton-Dyer and Birch conjecture, the latter of which is motivated rather nicely in this chapter.
The last chapter of the book is an excellent introduction to the proof of Fermat's Last Theorem. Considering the level of the book, the author captures very well the essential ideas. Readers will be well prepared, after studying more algebraic number theory and the theory of Galois representations (which the author only skims in the book), to tackle the full proof if so desired.
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Introduction to Vertex Operator Superalgebras and Their Modules (Mathematics and Its Applications)
Xiaoping Xu
Manufacturer: Springer
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ASIN: 0792352424 |
Book Description
This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator superalgebras from graded associative algebras and their anti-involutions, self-dual codes and lattices.
Audience: This book is of interest to researchers and graduate students in mathematics and mathematical physics.
Book Description
Ticciati's approach to quantum field theory falls between building a mathematical model of the subject and presenting the mathematics that physicists actually use. It begins with the need to combine special relativity and quantum mechanics and culminates in a basic understanding of the standard model of electroweak and strong interactions. The book is divided into five parts: canonical quantization of scalar fields, Weyl, Dirac and vector fields, functional integral quantization, the standard model of the electroweak and strong interactions, renormalization. This should be a useful reference for those interested in quantum theory and related areas of function theory, functional analysis, differential geometry or topological invariant theory.
Customer Reviews:
Filled with pearls for the experienced "diver".......2006-12-14
I preface my comments by stating that this book is not intended as an introduction to QFT.
The student should have a solid understanding of SR, QM, tensor analysis, group theory including Lie Groups, and Hilbert spaces.
I will not regurgitate what the book covers, one need only use the "search inside" tab to look at the contents.
Having said this, this book is an excellent and indispensible to tool to BROADEN and DEEPEN your understanding of QFT. If all you want to do is calculate scattering amplitudes and decay rates I would not recommend this book, there are plenty of better applied QFT books available for this.
This books fills in the gaps other books fail to close. There is no "hand waving" of results which was refreshing. As a consequence you begin to understanding the subtle points of QFT and why the theory is the way it is.
As mentioned in the title of the review there are plenty of "pearls". For example, there is an entire chapter on internal and external symmetries and their representations by groups of matrices ( lie groups ). There is a complete description of the importance of Lie alegbras and how the generators of the Lie Algebra create conserved currents and quantities ( operators ) which help one study the evolution of states since these quantities are conserved. By studying the structure of the lie algebra one gains importance insights into the commutative properties of the corresponding conserved current and quantity operators. There is a great section on the derivation of the S matrix and the relations between the "Schrodinger " " Heisenberg " and "Interaction" pictures of QM. We see that the evolution of the interacting state can be entirely derived from the free field hamiltonians with certain restrictions. One thing I really liked about this section is that it explains the limitations of the S matrix approach ( has to do with the assumptions of turning "on and off" interactions )which I have not come across in other standard QFT texts. This motivates the need for functional integral quantization.
Another point of contention I have had with standard presentations of QFT is that they just assume that Noether's theorem from classical field theory can be applied after the quantization process. This book explains mathematically why it can be.
Succinctly, the defects in QFT presentation in other texts is explained, which makes understanding the material more difficult. However, the payoff is that one understands the motivation behind the IDEAS of QFT.
The book is also filled with little "homework" assignments to solidfy knowledge.
The logical and organized presentation of the material made it very difficult for me to put this book down for any length of time until it was finished.
A Great Field Theory Book.......2002-08-08
Yes this book isn't perfect, but what book on physics is? That aside, there is no question this is an excellent field theory book with a rigorous approach. Physicists could learn from this style to produce better textbooks rather than following their usual mysterious approach to writing. This book is clearly laid out not only in mathematical style but also with clear and concise explanations of many physical concepts. It is in my opinion far better than Weinberg's book, written in a more readable style. It is also better than books like Peskin and Schroeder and Kaku which seem sloppily put together. Put the book together with Ryder and you will have the tools needed to get a good understanding of field theory. The title might be unfortunate, because it might keep physics professors from considering using it in their classes instead of the usual lousy standby's, which is too bad for the students.
fills a niche.......2002-01-10
This book is far from perfect, but I think it begins to fill an important niche in the world of QFT books: it presents most aspects of the theory, from basic principles to Feynman rules, gauge fields and renormalization, in a form that is unusually accessible to mathematicians. I'm coming at this from the perspective of a mathematician who has tried and failed to learn QFT from a variety of other books, and I wish I had discovered this one before even opening Weinberg or Peskin & Schroeder. Ticciati doesn't completely avoid the kind logical sleight of hand that is commonplace among physicists, but when doing manipulations whose mathematical basis is questionable, he's usually at least honest enough to point this out to the reader. I especially enjoyed the chapter on Lie algebra representation theory, which is closer to a mathematician's presentation of this subject than a physicist's, yet not without plenty of physical motivation. I'd criticize this book only for two things: (1) it's riddled with misprints (some obvious, some not) and (2) some topics are explained rather more concisely than they deserve, and not always in the most logical order; Ticciati has a tendency to use certain subtle concepts implicitly a few sections before he defines them precisely. One may hope that such errors will be corrected in a future edition.
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A Study of Braids (Mathematics and Its Applications)
Kunio Murasugi , and
B. Kurpita
Manufacturer: Springer
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ASIN: 0792357671 |
Book Description
This book provides a comprehensive exposition of the theory of braids, beginning with the basic mathematical definitions and structures. Among the many topics explained in detail are: the braid group for various surfaces; the solution of the word problem for the braid group; braids in the context of knots and links (Alexander's theorem); Markov's theorem and its use in obtaining braid invariants; the connection between the Platonic solids (regular polyhedra) and braids; the use of braids in the solution of algebraic equations. Dirac's problem and special types of braids termed Mexican plaits are also discussed.
Audience: Since the book relies on concepts and techniques from algebra and topology, the authors also provide a couple of appendices that cover the necessary material from these two branches of mathematics. Hence, the book is accessible not only to mathematicians but also to anybody who might have an interest in the theory of braids. In particular, as more and more applications of braid theory are found outside the realm of mathematics, this book is ideal for any physicist, chemist or biologist who would like to understand the mathematics of braids.
With its use of numerous figures to explain clearly the mathematics, and exercises to solidify the understanding, this book may also be used as a textbook for a course on knots and braids, or as a supplementary textbook for a course on topology or algebra.
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Orthonormal Systems and Banach Space Geometry (Encyclopedia of Mathematics and its Applications)
A. Pietsch , and
J. Wenzel
Manufacturer: Cambridge University Press
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ASIN: 0521624622 |
Book Description
Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra.
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Geometry, Topology and Quantization (Mathematics and Its Applications)
P. Bandyopadhyay
Manufacturer: Springer
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ASIN: 0792343050 |
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This monograph deals with the geometrical and topological aspects associated with the quantization procedure, and it is shown how these features are manifested in anomaly and Berry Phase. This book is unique in its emphasis on the topological aspects of a fermion which arise as a consequence of the quantization procedure. Also, an overview of quantization procedures is presented, tracing the equivalence of these methods by noting that the gauge field plays a significant role in all these procedures, as it contains the ingredients of topological features.
Audience: This book will be of value to research workers and specialists in mathematical physics, quantum mechanics, quantum field theory, particle physics and differential geometry.
Book Description
While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: · Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory · Thorough revisions of all remaining chapters · Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software · Two indices: An Index of Defined Terms and an Index of Cited Authors · Greatly expanded bibliographies
Customer Reviews:
Very comprehensive overview of computational geometry.......2001-03-26
This book, written by many well-known experts in the field, is a fine compendium of articles on the most active areas of computational geometry. Each article is supplemented with a glossary of terms needed for understanding the relevant concepts and frequently contains a list of open problems. An overview of the convex hull of a collection of random points in Euclidean n-space is given in one of the articles on discrete aspects of stochastic geometry, where also a very interesting discussion of generalizations of the Buffon needle problem is given.
There are a few articles overviewing Voronoi diagrams, such as the one on Voronoi diagrams and triangulations. The applications of Voronoi diagrams are many, and include tumour cell diagnosis, biometry, galaxy distributions, and pattern recognition. This article is a little short considering the importance of the subject.
The article on shortest paths and networks is somewhat disappointing since there is no in-depth discussion on network routing algorithms.
The article on computational topology highlights some of the results in this very important area. Many problems in topology have been tackled recently using computers, particularly the work of the mathematician A.T. Fomenko. Computational topology is a relatively young field, having been in existence only since the early 1990's. The applications are enormous, ranging from meshing, morphing, feature extraction, data compression, and in many scientific areas such as computational medicine, chemistry, and astrophysics. It can also be used in computer security via graphical passwords. It is an immense help in visualizing complicated topological objects, such as Lens spaces, horned spheres, and thickened knots. The article does not touch on the use of Mayer-Vietoris sequences to design efficient divide-and-conquer schemes for computing the homology of higher-dimensional complexes. The interplay between topology and finding better algorithms in computational geometry is one that will flourish no doubt in years to come.
The last section of the book covers applications with the most interesting article being the one on sphere packing and coding theory. The algorithms in sphere packing have direct applicability to error correctiong codes over the field GF(q). The author of this article does touch briefly on general algebraic-geometric codes, which is good considering their importance in applications.
The last article appropriately discusses available software for computational geometry. Although the list of Web sites is quite extensive, there are many more available since this book was first printed.
A very fine addition to the literature on computational geometry and should be on everyone's shelf who is interested in this important area.
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