Book Description

Multiplicity diagrams can be viewed as schemes for describing the phenomenon of "symmetry breaking" in quantum physics.The subject of this book is the multiplicity diagrams associated with the classical groups U(n), O(n), etc.It presents such topics as asymptotic distributions of multiplicities, hierarchical patterns in multiplicity diagrams, lacunae, and the multiplicity diagrams of the rank 2 and rank 3 groups. The authors take a novel approach, using the techniques of symplectic geometry.The book develops in detail some themes which were touched on in the highly successful Symplectic Techniques in Physics by V. Guillemin and S. Sternberg (CUP, 1984) , includingthe geometry of the moment map, the Duistermaat-Heckman theorem, the interplay between coadjoint orbits and representation theory,and quantization. Students and researchers in geometry and mathematical physics will find this book fascinating. ... Read more

Book Description

Reviews (2)

This book contained the stuff I wanted to know
I was interested in projecting a network onto hyperbolic space using the upper half plane projection. This book contained the equations relating to that, particularly the moebius transformation z' = (az+b) / (cz + d), and also stuff on stereographic mapping which I found useful.

I have not taken the trouble to understand much of the more in-depth parts of the book, but it is so clear and step-by-step that even though I am not a math student, I'm fairly confident that I could. The whole thing was fairly mind-opening.

Interestingly, after reading this and developing my own intuitions (eg: that flat translation, rotation and scaling are special cases of parabolic, elliptical and hyperbolic transformations with a fixed point at infinity), a re-reading discovered these conclusions in the book. So you can take the exposition and run with it. What I'd really like is to be able to get the n'th root of a transformation (to animate them). I suspect that that's in there too.

The book does not cover real-world applications (aerodynamics, electrodynamics), but that's cool. It's purely about the math.

Should be a "must read" for math students
This inexpensive book covers material not easily found elsewhere but key in understanding complex functions. The problem with complex functions is they are hard to visualize because the input is a plane and the output is another plane. The book covers Circles, Moebius transforms, and Non-Euclidean Geometry. The level is senior undergraduate, 1st year graduate. The book is easy to understand with good exercises. I really like this book. ... Read more

Book Description

Number Power Series (Revised)The first choice for those who want to develop and improve their math skills. Every Number Power book targets a particular set of math skills with straightforward explanations, easy-to-follow, step-by-step instruction, real-life examples, and extensive reinforcement exercises. Use these texts across the full scope of the basic math curriculum, from whole numbers to pre-algebra and geometry. NUMBER 4: GEOMETRY Introduces lines, angles, triangles, and other plane figures, and solid figures. ... Read more

Reviews (2)

Geometry! Clearly and Concisely Presented--Finally!
Geometry! Clearly and Concisely Presented--Finally!

I am a high school special education/alternative education teacher in Oregon, working with special needs youngsters. Contemporary's "Number Power 4:Geometry" by Bob Mitchell offers an excellent, concise presentationand review of geometry. The book is an excellent resource as a firstintroduction to students of the principles of geometry, or as a review forstudents studying for their GED, SAT or even GRE.In fact, I haverecommended this book for teachers who must take the CBEST for teacherlicensure in Oregon!

The chapters are succinct, clear, and use real lifeapplications and examples that students will find relevant and engaging.The pages in this worksheet format booklet are laid out clearly, veryclearly, and are easy for the student to negotiate. After clearlypresenting the beginning principles of geometry in short concise lessons,"Number Power 4: Geometry" gives the student plenty and frequentopportunity for them to check their understanding. This is one of thestrengths that sets "Number Power 4: Geometry" apart from othertextbooks. Here, students don't have to suffer through pages and pages ofinstruction before their comprehension is tested. Students will find thebook engaging, trust me.

I recommend "Number Power 4: Geometry"without reservation! You won't be disappointed.

-John Bain

An excellent source for instruction of fundamental geometry
This book was a life saver for me!!I used to to learn geometry to study for the GRE.It was written at a basic adult learning level, and thus there remains little need for a tutor.The chapters are clear, short, anduse real life adult examples!! A great resource!!

Chris P. Abilene, TX ... Read more

Book Description

The focus of this book is geometric properties of general sets and measures in Euclidean spaces. Applications of this theory include fractal-type objects, such as strange attractors for dynamical systems, and those fractals used as models in the sciences. The author provides a firm and unified foundation for the subject and develops all the main tools used in its study, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Besicovitch-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of Euclidean space possessing many of the properties of smooth surfaces. ... Read more

Book Description

A basic problem in computer vision is to understand the structure of a real world scene. This book covers relevant geometric principles and how to represent objects algebraically so they can be computed and applied. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. Richard Hartley and Andrew Zisserman provide comprehensive background material and explain how to apply the methods and implement the algorithms.First Edition HB (2000): 0-521-62304-9 ... Read more

Reviews (3)

Comment on the first edition
The first edition of this book could have been much better written. It took up a lot of topics, but treated each in a summary fashion. In fairness, though, I must say that this may be as good as any other book with its aim and scope, and better than some. Any writer on computer vision faces the problem of guessing who the reader is likely to be and what the reader's background is. Also, each of the various topics really merits a sizable book. In particular, the mathematics needs a truly mathematical treatment in a separate book. I have not seen this second edition, but there was room for improvement over the first edition.

very informative, fairly easy to read
The book succeeds in introducing you to the world of multiple view geometry. Specially the math and geometry concepts associated with it. In my research, I had to work on stereo images and this book provided very good information about it. The algorithms are presented very clearly and have been easy to implement (at least in Matlab).

It's a good reference book to have.

A must for readers in computer vision
It is the best book in this area that I have seen up to now. It is well-organized and all the notations and words are friendly to beginners and even experts in this field. Included materials are really tracing the latest advanced techniques. Actually, it is great that there are a lot of exercises at the ends of each chapters but there is no sufficient solutions or detail explanations to each questions. ... Read more

Book Description

Whereas Sacred Geometry introduced readers to two-dimensional forms, Platonic & Archimedean Solids presents the world of three dimensions, which was understood as early as neolithic time. Daud Sutton elegantly explores the eighteen forms-from the cube to the octahedron and icosidodecahedron-that are the universal building blocks of three-dimensional space, and shows the fascinating relationships between them. For anyone interested in design, architecture, and mathematics, this will be a delight. Wooden Books

Small Books, Big Ideas Historically, in all known cultures on Earth, wise men and women studied the four great unchanging liberal arts -numbers, music, geometry and cosmology-and used them to inform the practical and decorative arts like medicine, pottery, agriculture and building. At one time, the metaphysical fields of the liberal arts were considered utterly universal, even placed above physics and religion. Today no one knows them.

Walker & Company is proud to launch Wooden Books, a collectable series of concise books offering simple introductions to timeless sciences and vanishing arts.

Attractively simple in their appearance yet extremely informative in content, these unusual books are the perfect gift solution for all ages and occasions. The expanding title range is highly collectable and ensures continuing interest. In addition, the books are non-gloss and non-color, appealing to a greener book-buying public. Wooden Books are ideally suited to non-book outlets.

Wooden Books are designed as timeless. Much of the information contained in them will be as true in five hundred years time as it was five hundred years ago. These books are designed as gifts, lovely to own. They are beautifully made, case-bound, printed using ultra-fine plates on the highest quality recycled laid paper, finished with thick recycled endpapers and sewn in sections. There are fine, hand drawn illustrations on every page.

The fast-moving world of Wooden Books brings you a selection of fascinating titles. All hardcover, 64 pages, 100% recycled paper at $10.00 each. ... Read more

Book Description

This book consists of essays that stand on their own but are also loosely connected. Part I documents how numbers and geometry arise in several cultural contexts and in nature: the ancient musical scale, proportion in architecture, ancient geometry, megalithic stone circles, the hidden pavements of the Laurentian library, the shapes of the Hebrew letters, and the shapes of biological forms. The focus is on how certain numbers, such as the golden and silver means, present themselves within these systems. Part II shows how many of the same numbers and number sequences are related to the modern mathematical study of numbers, dynamical systems, chaos, and fractals. ... Read more

Book Description

This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory.The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged.Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. ... Read more

Book Description

Reviews (6)

A good start
Historically, combinatorial topology was a precursor to what is now the field of algebraic topology, and this book gives an elementary introduction to the subject, directed towards the beginning student of topology or geometry. Due to its importance in applications, the physicist reader who is intending eventually to specialize in elementary particle physics will gain much in the perusal of this book.

Combinatorial topology can be viewed first as an attempt to study the properties of polyhedra and how they fit together to form more complicated objects. Conversely, one can view it as a way of studying complicated objects by breaking them up into elementary polyhedral pieces. The author takes the former view in this book, and he restricts his attention to the study of objects that are built up from polygons, with the proviso that vertices are joined to vertices and (whole) edges are joined to (whole) edges.

He begins the book with a consideration of the Euler formula, and as one example considers the Euler number of the Platonic solids, resulting in a Diophantine equation. This equation only has five solutions, the Platonic solids. The author then motivates the concept of a homeomorphism (he calls them "topological equivalences") by considering topological transformations in the plane. Using the notion of topological equivalence he defines the notions of cell, path, and Jordan curve. Compactness and connectedness are then defined, along with the general notion of a topological space.

Elementary notions from differential topology are then considered in chapter 2, with the reader encountering for the first time the connections between analysis and topology, via the consideration of the phase portraits of differential equations. Brouwer's fixed point theorem is proved via Sperner's lemma, the latter being a combinatorial result which deals with the labeling of vertices in a triangulation of the cell. Gradient vector fields, the Poincare index theorem, and dual vector fields, which are some elementary notions in Morse theory, are treated here briefly.

An excellent introduction to some elementary notions from algebraic topology is done in chapter 3. The author treats the case of plane homology (mod 2), which is discussed via the use of polygonal chains on a grating in the plane. Beginning students will find the presentation very understandable, and the formalism that is developed is used to give a proof of the Jordan curve theorem. Then in chapter 4, the author proves the classification theorem for surfaces, using a combinatorial definition of a surface.

The author raises the level of complication in chapter 5, wherein he studies the (mod 2) homology of complexes. A complex is defined somewhat loosely as a topological space that is constructed out of vertices, edges, and polygons via topological identification. He proves the invariance theorem for triangulations of surfaces by showing that the homology groups of the triangulation are same as the homology groups of the plane model of the surface. This is an example of the invariance principle, and the author briefly details some of the history of invariance principles, such as the Hauptvermutung, its counterexample due to the mathematician John Milnor, and Heawood's conjecture, the latter of which deals with the minimum number of colors needed to color all maps on a surface with a given Euler characteristic. Integral homology is also introduced by the author, and he shows the origin of torsion in the consideration of the "twist" in a surface.

In the last part of the book, the author returns to the consideration of continuous transformations, tackling first the idea of a universal covering space. Algebraic topology again makes its appearance via the consideration of transformations of triangulated topological spaces, i.e. simplicial transformations. He shows how these transformations induce transformations in the homology groups, thus introducing the reader to some notions from category theory. The elaboration of the invariance theorem for homology leads the author to studying the properties of the group homomorphisms via matrix algebra, and then to a proof of the Lefschetz fixed point theorem. The book ends with a brief discussion of homotopy, topological dynamics, and alternative homology theories.

The beginning student of topology will thus be well prepared to move on to more rigorous and advanced treatments of differential, algebraic, and geometric topology after the reading of this book. There are still many unsolved problems in these areas, and each one of these will require a deep understanding and intuition of the underlying concepts in topology. This book is a good start.

Splendidly intuitive yet rigorous
This covers the basics of algebraic topology with simplexes, covering in essence the fundamental ideas behind of the work of Poincare, Brouwer, and Alexander. He proves the Jordan curve theorem, classifies all compact surfaces, and the relationship with vector fields. The homology groups are defined and used.

There are excellent examples, clear writing, and humour. An outstanding introduction.

One nice feature is that he bases his notions of continuity on "nearness" not epsilon-delta.

An excellent read
Ignore those that suggest this book is too "elementary". This is a wonderful text that concretizes the more abstract notions of algebraic topology. True, it should not be your only text on algebraic topology, and the proofs are not as rigorous as a pedant might want, but it clearly conveys the geometric underpinnings of topology and deserves a space on any topologist's bookshelf.

Not for resolute students of algebraci/diff. topology.
I believe the two existing reviews are over-ratng. True, the book is accessible to anyone without prior knowledge of topology/algebra, but the treatment is too "elementary". For example, the author doesn't even introduce the word "mod 2 homology". If you are resolutely to study algebraic (or differential) topology, this is NOT the book to "study". Try Bredon or Fomenko-Novikov or May. For the subject covered, look for the book by Stillwell.

Esoteric Fun
Way back in 1980 I took a course at Oberlin College from Professor Henle in which he used this book (his own) as the text. Up until then I had been wavering as to a major, whether it should be in the hard sciences or Math. Michael Henle, his course, and this textbook decided me. I majored in Math.The book gives a very hands on, concrete approach to what is a very abstract realm. An example that comes immediately to mind is the proof of the classification of manifolds, which comes down to a sequence of clever cut and paste operations on a large sheet with labeled edges. This text also has a curious sense of humor subtly hidden through it. Just look in the index under 'Man in the moon'. I dare you!The exercises, which consist mostly of writing proofs, where there is very little notation and all your ideas have to be written out long-hand, are incredibly valuable for developing a logical mind. At least they were for me, back in 1980. ... Read more

Book Description

One of the most popular artists of the 20th century, M. C. Escher, leaves a rich legacy. The centennial celebration of his birth, held in Rome and Ravello in 1998, gave testimony to the keen interest and new insight into his work, and showcased a number of comtemporary artists and scientists whose work is directly inspired by that of Escher. This book contains 40 of their articles, richly illustrated with original art works in addition to well-known and little-known works by Escher. A CD-ROM complements the articles, containing color illustrations of work by contemporary artists, movies, animations, and other demonstrations. ... Read more

Reviews (3)

Book and guide are great, publisher tests are for weenies
I am teaching from this book this year, having taught from the second edition for the last several years. I wouldn't use any other geometry book besides Mr. Jacobs'. There are some typos in the 1st printing of the 3e, but nothing serious.

This book is more relaxed on proof-writing than the 2e, and so I have added some proofs from the 2e to supplement it. There are also a few exercises each lesson from the 2e that require more algebra, and so I use those, too. Another instructor could do as well if they added SAT problems from a SAT practice book.

The teacher guide is spectacular, providing a richness in both the history of geometry and its application. Did you know that the Greeks not only knew how far away the moon was, but also that its orbit is a bit elliptical? (Who needs technology to be smart?)

The publisher generated tests are not written by Mr. Jacobs, and are frankly for weenies. If the publisher doesn't remedy that situation I'll be writing my own for next year. When the tests are changed, the book will have my 5-star rating. If you're homeschooling, use the summary and review as the chapter tests.

Geometry: Seeing, Doing, Understanding
"I have just spent a couple of hours browsing through Harold Jacob's GEOMETRY, and I think I've fallen in love again. This book is really lovely. What a treat. I didn't want to put it down. Harold has really done a masterful job of bringing in so much stuff -- culture, puzzles, challenges, current events, etc., and his use of cartoons and similar things that appeal to kids (like me!) is the best. This is a very rich and compelling guide through the central ideas of geometry. Harold has created a roadmap that will let learners experience the thrill and wonder and discovery of important geometrical truths. As a fellow author, I am inspired to work even harder to try to reach his standard of excellence. Congratulations to Harold and his editors on an OUTSTANDING contribution to mathematics learning." -

Better than the Best?
Amazon reviews let you know what teachers and students think about texts. Type in the following ISBNs to see the reviews of the second edition (ISBN 071671745X) of this text or of the author's Mathematics: A Human Endeavor (ISBN 071672426X). These comments on the third edition are based on close reading, not classroom experience. With an initial review up, I hope to see what others have to say.

I taught at Reed, Wellesley, and Bard Colleges and watched the reform mathematics program develop when I was associate director of the Mathematical Association of America, in Washington, DC. Geometry is my research area. I worked in publishing as an editor for more than 20 years. I have read every word of this book and worked all of the exercises because I was its freelance editor. I am a knowledgeable, interested party.

The third edition towers over the second edition, which is described by its most recent Amazon reviewer, Edward Lee, as "the best geometry text in existence, bar none" (January 25, 2003). Begin by noticing the use color throughout, then notice how color has been used to make key material in the text and diagrams stand out more clearly. Detailed comparisons will show you that every part of the book has been scrutinized and reworked, adding a host of new examples and exercises, fine-tuning the concepts and wording. Coordinates are used throughout, so that analytic methods are now another tool rather than the subject of a special chapter, late in the book.

Chapter 1, An Introduction to Geometry is completely new and shows the reader how geometry has been used from the dawn of history, in the East and the West, to design cities, measure the earth's circumference, design pyramids, and figure land taxes. This last brings us to the final lesson of this chapter, "We Can't Go on Like This." Here the student discovers that the Egyptian tax assessor's formula, though plausible, does not work. Something may look sensible and even be used, but we need to be careful and check things. Not everything that is plausible is true. And so we are off to Chapter 2 on deductive reasoning, and then on to all of geometry, including solid geometry (Chapter 15) and non-Euclidean geometry (Chapter 16) --- optional in most first courses.

Jacobs put all of his art into this revision. It is his best effort. Donald J. Albers begins his foreword "This is one of the great geometry books of all time. ... It is the finest example of instructional artistry I have ever encountered."

Geometry is a wild and beautiful subject. Think of it as a continent you might visit and explore. The lessons in this book are station stops on your tour. At each stop, Jacobs gives you a sense of what there is to see and explore. The exercise sequences are side trips for individuals or groups. It is these jaunts that give you a real feel for the place, they build the muscle you need for further exploration and show you small wonders or glimpses of distant peaks. Albers calls these exercises "the beating heart of the book."

Here is a side trip you can explore now: Take a lopsided quadrilateral and erect equilateral triangles on its sides so that their third vertices point alternatingly into and out of the quadrilateral. Connect these four new vertices in the order of the sides of the quadrilateral they are derived from. You will see that no matter what your original quadrilateral was, the new quadrilateral is of a very special sort. The exercise is straightforward, and the result is surprising. Some readers may want to understand the geometry that lies behind this observation. That goal is like the wish to scale a distant peak. Many may feel the call, but only some will set out and reach the summit. Geometric proofs, sometimes so mysterious, are our search for an answer to the question "Why?"

A Teacher's Guide with solutions to all the exercises, lesson plans, reduced size images of the transparency masters, and commentaries on the subject is available. There is also a separate Test Bank. The Transparency Masters, for teachers who use an overhead projector, are available on a CDROM.

In 10 years, I expect to see a crop of geometers who cut their teeth on this book. In the meantime, I expect to see many reviews from students and teachers on this site. Let this be the beginning. ... Read more

Book Description

Increasingly, researchers in many branches of science are coming into contact with Bayesian statistics or Bayesian probability theory. By encompassing both inductive and deductive logic, Bayesian analysis can improve model parameter estimates by many orders of magnitude. It provides a simple and unified approach to all data analysis problems, allowing the experimenter to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. This book provides a clear exposition of the underlying concepts with large numbers of worked examples and problem sets. The book also discusses numerical techniques for implementing the Bayesian calculations, including an introduction to Markov Chain Monte-Carlo integration and linear and nonlinear least-squares analysis seen from a Bayesian perspective. In addition, background material is provided in appendices and supporting Mathematica notebooks are available, providing an easy learning route for upper-undergraduates, graduate students, or any serious researcher in physical sciences or engineering. ... Read more

Book Description

These two volumes contain survey papers given at the 1991 international symposium on geometric group theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. Volume I contains reviews of such subjects as isoperimetric and isodiametric functions, geometric invariants of a groups, Brick's quasi-simple filtrations for groups and 3-manifolds, string rewriting, and algebraic proof of the torus theorem, the classification of groups acting freely on R-trees, and much more.Volume II consists solely of a ground breaking paper by M. Gromov on finitely generated groups. ... Read more

Book Description

Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational varieties at a level appropriate for graduate study. Kollár's original course has been developed, with his co-authors, into a state-of-the-art treatment of the classification of algebraic varieties. The authors have included numerous exercises with solutions, which help students reach the stage where they can begin to tackle related contemporary research problems. ... Read more

Book Description

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, geometrical constructions and finite field extensions, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. The text is intended for junior- to senior-level mathematics majors. Robin Hartshorne is a professor of mathematics at the University of California at Berkeley, and is the author of Foundations of Projective Geometry (Benjamin, 1967) and Algebraic Geometry (Springer, 1977). ... Read more

Reviews (4)

This book and course is not for the faint of heart!
This is without exception the hardest math course I have ever taken. Your understanding of the concepts is pertinent. I had to read the 1st chapter over five times just to understand projective geometry. Hartshorne tries to simplify the material but only so much can be done. It is just a hard course, period. The book does contain many example and logical proofs but be ready to burn the midnight candle on this one.

A stunning book
Hartshorne is a leading mathematician known for work in rather abstract geometry (see his book ALGEBRAIC GEOMETRY). He takes Euclid's ELEMENTS as great mathematics, no mere genial precursor, and collates it with Hilbert's FOUNDATIONS OF GEOMETRY.

Of course Harshorne proves that Euclid needed the parallel postulate, by exhibiting a non-Euclidean geometry. He gives a very pretty compass and straight-edge Euclidean theory of circles, which then turns into the Poincare plane model for hyperbolic geometry. He also proves that Euclid needed the method of exhaustion for volumes of solids: he gives the agreeably simple Dehn invariant proof that even a cube and a tetrahedron of equal volumes are not decomposable into congruent parts. It is a famous proof, rarely seen, and a beautiful use of the modern algebraic viewpoint in classical geometry. I had always supposed it must be hard but it is not.

Hartshorne also develops the contested "geometric algebra" of Euclid as a modern axiomatic algebra. Many commentators have shown it is wrong to think Euclid was doing "algebra" in the sense of a disguised theory of the roots of quadratic polynomials. But (unless and until Fowler's THE MATHEMATICS OF PLATO'S ACADEMY changes my mind) I think it is reasonable to say Euclid is doing algebra in this sense.

Well beyond Euclid
Hartshorne is a famous algebraist and one main contribution of this text is to show fascinating interrelations between classical geometries and modern algebra (of course the book contains lots of pure geometry as well). Example 1: Many texts show the impossibility of the classical problems of constructibility by straightedge and compass (by observing that the coordinates of any point so constructed lie in the smallest extension field of the rationals Q closed under taking square roots of positive numbers). Hartshorne's is the only text that goes further, solving the analogous problem when the straightedge is marked (real roots of cubic and quartic equations must also be allowed); Archimedes observed that any angle can be trisected with these tools. Example 2. Dehn's solution to Hilbert's Third Problem is given, whereby any two polyhedra equivalent under dissection must have equal Dehn invariants, and it shown that a tetrahedron has different invariant than a cube. Example 3. In hyperbolic geometry, Hilbert's arithmetic of ends is developed and applied. Example 4. Pejas' algebraic classification of Hilbert planes is discussed.

Hartshorne's text overlaps mine in correcting Euclid's errors, developing rigorous foundations for Euclidean and Non-Euclidean geometries, and covering much history, presented delightfully. He gives a thorough discussion of area and the open problems in that theory. He concludes with a nice chapter on polyhedra.

Hartshorne's New Book, "Geometry: Euclid and Beyond", is a Masterpiece!
I told my wife: "If I have to give up all my books but one, then this is the one I'd keep; no question about it." (More comments later.) ... Read more

Book Description

This collection has been inspired by the work of Roger Penrose.It gives an overview of current work on the interaction between geometry and physics, from which many important developments in research have emerged.This volume collects together the contributions of many important researchers, including Sir Roger himself, and gives an overview of the many applications of geometrical ideas and techniques across mathematics and the physical sciences.From the area of pure mathematics papers are included on the topics of classical differential geometry and non-commutative geometry, knot invariants, and the applications of gauge theory.Contributions from applied mathematics cover the topics of integrable systems and general relativity.Current research in experimental and theoretical physics inspired chapters on string theory, quantum gravity, the foundations of quantum mechanics, quasi-crystals and astrophysics.The collection also includes articles on quantum computation, quantum cryptography and the possible role of micro-tubules in a theory of consciousness. ... Read more

Reviews (2)

makes a good mousepad
This book makes the greatest mousepad I've ever had. Good book.

A fantastic book for those who can understand it.
A great book, about some of the coolest and most cutting edge theories out there. Certainly not for the layman though. Most of the chapters are filled with equation after equation however those with advanced math and a good math program will have lots of fun. This book is the real deal! Read it all and you just might fry your brain! It would get five stars if it was better organized. The best use of this book is for quick reference if you have a specific idea or question about the topics contained and don't or can't get to the internet. Not a must buy but worth the money. ... Read more

Book Description

Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area, both for mathematicians and theoretical physicists.

The author's goal is to provide an easily accessible introduction to the subject. The book contains detailed accounts of the basic concepts and the many exercises illustrate the theory. Appendices to various chapters allow an outlook to recent research directions.

Daniel Huybrechts is currently Professor of Mathematics at the University Denis Diderot in Paris.

Book Description

Teach Yourself Trigonometry is suitable for beginners, but it also goes beyond the basics to offer comprehensive coverage of more advanced topics. Each chapter features numerous worked examples and many carefully graded exercises, and full demonstrations of trigonometric proofs are given in the answer key.

Reviews (3)

Excellent, methodical approach for the self-taught
I teach myself a lot from books. Some books provide little, some a lot. With this book you walk away with a usable knowledge of trigonometry AND invaluable knowledge of how your calculator performs mathematical operations.
I've tok trig in high school, but the subject wasn't presented in such an organized and methodical approach. The overview in Chapter 1 provided insights that eluded me in high school. Chapter 2 provided detailed knowledge of my pocket computer and knowledge of it's use to solve trig problems that I never realized before. The examples and solutions provide feedback that the lessons were learned and owned. The subsequent chapters methodically build consistent, solid, usable knowledge. Mr. Abbot continually enables you to compare table-based calculations with your calculator calculations, building your confidence in your ability to do both. IF you've wrestled with other approaches to learning trig, this is THE book to get you through it.
I have read Mr. Abbott's Calculus book and find his approach conducive to my learning.

reader from texas
The book would ahve been good except before you even get into the material very good there are problems with wrong answers or very confusing explantions. If this much is wrong at the beginning what about later in the book when you get into the stuff you don't know.

Clear discussion but book marred by lots of typos
This book is very well written and a lot of thought was given by the authors as to the presentation of the material and how much background to assume the reader has. I would give the book five stars based on the writing. However, the writers were not well served by the editor, as there are many typos, maybe as many as one every other page. It appears that the proof reading was done by someone without a math background, as many of the errors are obvious, such as an equal sign being omitted, turning an equality into a product. Or the length of the sides of a right triangle being given so that the hypotenuse is not the longest side. Sometimes the answers to questions are messed up, which is very frustrating. Hopefully when the book is republished, it will be given the care it deserves. ... Read more