Product Description
This classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations: vector algebra and calculus, tensor calculus, and the notation devised by Cartan, which employs invariant differential forms as elements in an algebra due to Grassman, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis. ... Read more

Product Description
At last: geometry in an exemplary, accessible and attractive form! The authors emphasise both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications. They also show students the fundamental concepts and the difference between important results and minor technical routines. Altogether, the text presents a coherent high school curriculum for the geometry course, naturally backed by numerous examples and exercises. ... Read more

Customer Reviews (6)

excellent introduction to geometry as a segue into higher mathematics
Serge Lang needs no introduction as a mathematician or a writer of mathematics.Some of his books are excellent and some are less well written.This book is well written- it is clear, it is logical, and it tries to explain/motivate the important ideas of the book.I used it to teach my daughter geometry and found it well organized with an adequate number of exercises.What I liked best about it was that one can consider it as an introduction to mathematical thinking. By that I mean it tries to teach one not just some facts about geometry, but how mathematicians think about geometry,how mathematicians go about finding theorems in geometry and then how mathematicians go about proving those theorems.It is an excellent book for someone who wants to learn about what mathematics in a wayso that they can understand and appreciate rigorous proofs.

Kindle Price a rip-off!
I teach Geometry with this book, and initially one of the reasons I wanted the Kindle was so that I could download this book. I downloaded the sample not longer after getting my Kindle, but I wasn't ready to pay the price for a number of reasons. At the time (about 3 months ago) it was about $17.00!!!! Now the Kindle version costs what I can get the hardcover for. This is ridiculous! What could have possibly happened in 3 months to nearly triple the Kindle version price?!? I am VERY disappointed.

Needless to say, I am now NOT buying the Kindle version.

By the way, the three stars is because I am giving Amazon 1 star for changing the price like this and I give the book itself 5 stars. That averages to 3.

Well-written but does not include everything necessary in high school geometry.
Although the book's approach is good, it omits a lot of theorems, mostly those involving circles.The book emphasizes too much coordinate geometry.I recommend this book for self-study, but it is clearly not intended to be a textbook to cover all the material in a standard high school geometry course.

An unorthodox high school geometry text.
I found this text interesting because it does not follow the standard approach to high school geometry.In a standard high school geometry text, the material is developedfrom Euclid's postulates (axioms) and common notions in the manner that he did in the Elements, albeit in modern language.These books generally cover much the same material, although some include right triangle trigonometry and transformations.The authors of this text choose to introduce their own postulates, which leads to a quite different development of the material and alternative ways of proving standard theorems.Having previously read a standard development of geometry, I found reading it developed in an alternate way fascinating.

The authors omit some topics in a standard geometry course, including inequalities, theorems about tangents, secants, and chords of circles, and concurrence theorems.The presentation of other topics is truncated.Instead, they include material on dilations, vectors, the dot product, transformations, and isometries.Right triangle trigonometry is not included.Another way in which this text differs from standard texts is that proofs are written in paragraph form, which is standard practice among mathematicians, rather than in the two column statement and reason format favored by geometry teachers for pedagogical reasons.I should caution you that some of the terminology and notation is also nonstandard, which could pose problems for you in your subsequent reading or examinations.Consequently, I recommend that you read a standard text before working through this one.

The text begins with a discussion of lines and angles.Postulates are introduced.However, some statements initially stated as postulates about distance and parallel lines are later proved as theorems.Then coordinates are introduced, allowing the authors to use algebraic arguments throughout the text.From there, the authors cover area, the Pythagorean Theorem, the distance formula, circles, perpendicular bisectors, triangles, polygons, and triangle congruence.Dilations are used to explain similarity.Volume formulas are derived for some standard figures.The authors present fascinating geometric arguments that enable them to obviate the need to use calculus to find some of the limits involved in the derivations.The book concludes with nonstandard topics, including vectors, the dot product, transformations, and isometries.This material is the greatest strength of the text, which concludes with a proof that any isometry can be expressed as the composition of at most three reflections.

The writing is generally clear, but there are errors.In one proof, there is a triangle whose three vertices are actually collinear.The authors do not distinguish between the Angle-Side-Angle congruence postulate for triangles and the Angle-Angle-Side Theorem for congruence of triangles, arguingthat since the sum of the measures of a triangle is always 180 degrees, the measures of two angles of a triangle determine the third.Where this causes problems is that when they express that triangles are congruent, corresponding vertices do not necessarily match, which can be confusing.

The problems in the text are both interesting and tractable.The problems in the final section of the text and those listed as Additional Exercises are more challenging.There are no answers to the problems in the text.A solution manual, Solutions Manual for Geometry: A High School Course: by S. Lang and G. Murrow, written by Philip Carlson is available separately.Also, a problem involving similar triangles and another that hinges on the Side-Angle-Side congruence postulate for triangles are introduced before the relevant topics.

I recommend using this text as a supplement to a standard course.That way you will be familiar with standard terminology and notation.You will also know what a standard course covers and the usual way in which the theorems are proved.That will help you appreciate the nonstandard material covered in this text and the alternative proofs that are presented.

Alternatively, you could work through the text Geometry by Edwin E. Moise and Floyd L. Downs, Jr. That text, which is known for its challenging problems, is comprehensive enough to cover both the material in a standard course and much of the nonstandard material in this text.

a very well written text
The text goes through all usual syllabus of high school geometry.All the subjects discussed have very important and basic applications.The authors don't try to give solid mathematical proofs to all theorems; but they just want to concieve the student in the best way possible and they have suceeded in doing so.I think this would work as a very interesting reading to anyone who really wants to learn about fundamentals of geometry. ... Read more

Product Description
Geometry is both elegantly simple and infinitely profound. People in many professions find that they need to be able to draw geometric shapes accurately, regardless of artistic ability. In Drawing Geomentry, Jon Allen shows readers how to draw two-dimensional geometric shapes in simple step-by-step instructions and provides step-by-step instructions for constructing two-dimensional geometric shapes, which can be readily followed by a beginner. The book also serves as an invaluable source book for students and professionals.

Contains 26 color and 118 line illustrations. ... Read more

Product Description
This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra.

The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory.

The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry. ... Read more

Customer Reviews (1)

Trees, not forest
First, a calibration: I am a total neophyte to algebraic geometry, and haven't taken a university algebra course since a few decades ago when I was a physics major. This book is one of several on the subject (along with some books on commutative algebra) that I'm using to get an amateur's orientation.

As so often happens, this book looked great in the bookstore. It is thin, reasonably well-illustrated compared to other books in the field, and even helps you gets your toes wet in sheaves, category theory and some other neat topics.

That said, I believe the prerequisites in the preface (university algebra, with a complex variables course optional) are understated; e.g. it helps to know something about fibres, lifts and other topics from geometry. It might be relevant that these notes were prepared at a German university; you should consider that "undergraduates" there are heading toward the equivalent of a US M.S. degree, not B.S./B.A.

More detrimental is that the presentation slogs from one proof to another and too rarely pauses for breath to consider the "big picture" significance of what you're proving. Notwithstanding that Joe Harris's "Algebraic Geometry: A First Course" is even less of a piece of cake for me than it might be for you, his style is a breath of fresh air when it comes to enlightening you as to some geometric context and payoff for all this effort. Other supplements I found helpful include Reid and Schenck.

PS in 2008: I very belatedly found the terrific "An Invitation to Algebraic Geometry," by Karen E. Smith &al. (Springer 2000, corrected printing 2004). This is the hands-down best introduction to the subject, IMHO. ... Read more

Product Description
The author demonstrates how solving geometric problems amounts to fitting parts together to solve interesting puzzles. Students discover relationships that exist between parallel and perpendicular lines; analyze the characteristics of distinct shapes such as circles, quadrilaterals, and triangles; and learn how geometric principles can solve real-world problems. Titles in BarronÂ's Painless Series are written especially for middle school and high school students who are having a difficult time with a specific subject. In many cases, a student is confused by the subjectÂ's complexity and details. Still other students simply finds a subject uninteresting, an attitude that usually results in lower grades. Painless titles offer informal, student-friendly approaches to each subject, emphasizing interesting details, supplementing the text with amusing insights, and outlining potential pitfalls clearly and step by step. Students begin to understand how disparate details all fit together to form a clear picture. Timelines, ideas for interesting projects, and Â"Brain TicklerÂ" quizzes in many of these titles help to take the pain out of study and improve each studentÂ's grades. ... Read more

Customer Reviews (6)

Not recommended
My son went through Painless Algebra and it was a good book. Naturally, we tried to use this book from the same author. Disappointed. The book is simply not well written. This sounds very general but it's an appropriate way to "generalize" it.

For example, on pages 13-14, it introduces concepts of inductive proofs and deductive proofs. The introduction itself is pointless and cluelessly done at the beginning of the book. On pages 14-16, it gives almost 20 geometric symbols without explanation of concepts behind the symbols. For someone new to geometry, it's just too much. On Chapter 2, page 23, it introduces the concept of angle. Then on page 30, without any mention of degrees of a line and a circle so far, the book uses exactly these two concepts to get the measurement of an angle larger than 180 degree ("reflex angle"). Then strangely, on the next section, the book introduces the concepts of right angle, obtuse angle, straight angle, etc, which should be done earlier. Also, the book simply does not put any emphasis on right angle, which I believe that a clear understanding of the concept is extremely important to get real traction on geometry (for example, trig is almost exclusive on right triangles).

Another example on last chapter. On page 261, it gives midpoint formula, without any explanation why. Several pages late, it gives the distance formula, without explanation again. Then after introduction of these two relatively difficult formulas, the book takes great pain to show how to graph a line by plotting points, which is pretty easy to understand and to do. Like in Painless algebra, the book insists to graph three points to get a line, while two points are suffice. It's laughable to talk about graphing a line so late in a book when such concepts of trapezoids, area, volume, chords, tangents, and Pythagorean Theorem, etc. have been covered way earlier.

Similar examples are plenty. To summarize again, this book is not well written. For beginner, to find another book to start; for students to get better understanding of geometry, find a book more systematic and deeper in presentation of concepts, formulas.

REVIEW FROM THE AUTHOR
I am the author of PAINLESS GEOMETRY and PAINLESS ALGEBRA.I read past reviews about the errors in the book and for that I apologize.I want you to know that the new edition of the book published in 2009 is essentially error free. I have put a lot of thought into creating PAINLESS GEOMETRY so that it could teach geometry painlessly.Each example and exercise was chosen to teach both obvious and hidden lessons.I have taught high school and college math, served as a school principal and have written twenty math books. I thnk PAINLESS GEOMETRY is the easiest and best constructed book on the market.I hope you give it a try.

Math Wiz Simplified
Great tool for young mathematicians new to Geometry.Supplements school textbooks -- exercises in the book facilitate review of concepts learned in class.

Have you used this book?
I've been meaning to write a review to respond to those on this page for a while.I guess I have used so many math books that contain an error or two that I just can't possibly throw away such a good book over that.

The fact is that we homeschool and my son LOVED this book which we picked up at the library.It is full of wonderful, hands-on work and SIMPLE explanations that make geometry easier to understand than most other books we tried - yes, truly understand because you not only had it explained well, but also "did" something on paper or folding paper to experience it.

He enjoyed it so much that when I picked up another Painless book at the used book store, he wanted to start it that day, rather than waiting 'til next semester.

So I don't know if y'all just glanced at the book or really tried it, but this family tried it and loved it - and I own a red marker so I can cross out the one incorrect answer I found in my edition!

Not Very Good
On page 16, it is stated that the area of a circle is pi times the diameter.Is there anybody out there who DOESN'T know that the area of a circle is pi times the square of the radius?That error wouldn't such a big deal, except that there are plenty more to come.I don't recommend this book to anyone. ... Read more

Product Description
Learn geometry at your own pace

What are congruent circles? How do you find the hypotenuse of a triangle?What is the sum of the angles in a decagon?How can you apply geometric equations to your daily life?With the unbeatable study companion Geometry: A Self-Teaching Guide, you’ll discover the answers to these questions and many more.

This thorough primer presents an easy-to-follow, proven method for grasping the key concepts of geometry.You’ll progress step by step through plane, solid, and analytic geometry and then move on to geometric applications for calculus.You’ll build your problem-solving skills along the way through detailed examples, reviews, exercises, and answer explanations.The clearly structured format of Geometry makes it fully accessible, providing an easily understood, comprehensive overview for everyone from high school students to adult learners to math mavens.

Like all Self-Teaching Guides, Geometry allows you to build gradually on what you have learned--at your own pace.Questions and self-tests reinforce the information in each chapter and allow you to skip ahead or focus on specific areas of concern.Packed with useful, up-to-date information, this clear, concise volume is a valuable learning tool and reference source for anyone who wants to improve his or her understanding of basic geometry. ... Read more

Customer Reviews (5)

Riddled with Errors!
I was disappointed as I worked through the first two chapters of this book. It is simply riddled with errors. At first, I thought it was just me, but as the errors become more and more blatant, I realized that it was the book and not my inability as a student. One example problem (from Page 44) "Triangle CDE is congruent to Triangle C'D'E'. If angle D=48 degrees and angle E = 17 degrees, find the measure of angle F." It turns out that there would be no angle F in that triangle! If there were just one or two errors in the book, I could let it go, but I've found one such error on almost every page! I'm giving up on this book. It seems like it would have been a good text, but the abundance of errors makes it pretty much useless.

Save your money and don't buy this book. I got the now out of print "Geometry & Trigonometry for Calculus" by Peter Selby, so I'm going to try that next.

Disappointing
Rampant with errors.Mislabeled exercises, poorly illustrated diagrams with bad measurements, plain-old typos, and simple calculations done wrong, often several times in a row.

The truth is, every math book has errors that can appear obvious when it is a rare anomaly, but when the same mistake is made over and over, it just gets confusing.On pages 50 and 51, for example, the area of a triangle is repeatedly miscalculated by dividing the base in half twice (the base should be divided once), which gives what appears to be a valid (though wrong) answer.The arithmetic is correct, but the key concept is completely botched.This is only one example of many I have spotted.

I agree with other reviewers, this is more than simple oversight.For a so-called "self-teaching guide," this is negligent.

A great little text...
This is a great little text with numerous illustrations but with a lot of errors.If you have taken geometry in the past or else are singularly hardheaded you will not be thrown by some of these mistakes that appear even in the self test sections.It is a great review, but remember to trust your own mind while studying the material.

OK
Geometry: A Self-Teaching Guide. This is not a bad text, but as a previous reviewer noted, it does have many errors (and I was also confused by the trapaziod section); on the other hand, most recent high school and college texts suffer from the same lack of craftsmanship. A final complaint is that there is no mention of proofs, which I was hoping to learn. I do like the fact that the book is straightforward and, once you learn how to account for the editing errors, it will give you a good grasp of the practical aspects of geometry very quickly. With this book and a good grasp of algebra you will be more than ready for trig.

Geometry: A Self-Teaching Guide
This review is based on the first chapter.

The authors/editors did a poor job reviewing this book for errors.I checked the publisher's website and they do not provide online corrections.Being a self-teaching guide it contains self-tests, but when the answers are wrong it is very confusing to the learner.

The discussion on trapezoids is confusing because they only illustrate isosceles trapezoids (but just call them "trapezoids" ) this gives the impression at all trapezoids are isoceles with base angles of equal value. ... Read more

Product Description
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields.

The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view.

Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics. ... Read more

Customer Reviews (13)

Excellent review of math for (particle) physicists
I bought this book to supplement my knowledge of mathematics which frequently is involved in understanding Particle physics concepts. The book is terse, but peppered with examples and insights about the definitions, and so far it is really fun to read. Seems like a good investment.

Too many errors to be useful for study
Reading all the glowing reviews of this book, I wonder whether the reviewers actually tried to use the book to understand the material, or just checked the table of contents. There are so many misprints, throughout, that one wonders if the book was proofread at all. Some of the mistakes will be obvious to every physicist - for example, one of the Maxwell equations on page 56 is wrong - others are subtle, and will confuse the reader. The careful reader, who wants to really understand the material and tries to fill in the details of some of the derivations, will waste a lot of time trying to derive results that have misprints from intermediate steps which have different misprints! Some chapters are worse than others, but the average density of misprints seems to be more than one per page.
The book might be useful as a list of topics and a "road map" to the literature prior to 2003, but that hardly justifies the cost (or the paper) of a whole book.

Geometry Topology and Physics: A condesed view
This book provide a complete and useful review of geometrical instuments of mathematical physics from the beginnig to the most advanced topics of interest. It can be used by students at the beginnig of thei studies in this topics, and it's found to be a useful gallery for higher level students (or scholar).

An excellent book
This is the best book of its type, that is, a book that contains almost all if not all the advance mathematics a theoretical physicist should know. I have studied chapters 2-9 and it has the perfect balance between rigorous presentation of topics and practical uses with examples. The level is for advance graduate students. The range of topics covered is wide including Topology topics like Homotopy, Homology, Cohomology theory and others like Manifolds, Riemannian Geometry, Complex Manifolds, Fibre Bundles and Characteristics Classes. I believe this book gives you a solid base in the modern mathematics that are being used among the physicists and mathematicians that you certainly may need to know and from where you will be in a position to further extent (if you wish) into more technical advanced mathematical books on specific topics, also it is self contained but the only shortcoming is that it brings not many exercises but still my advice, get it is a superb book!

A great reference book.
No doubt, the interplay of topology and physics has stimulated phenomenal research and breakthroughs in mathematics and physics alike.

Unfortunately, there is so much mathematics to master that the average graduate physics student is left bewildered.....until now.

The text is an excellent reference book. I emphasize reference. The book presupposes an acquaintance with basic undergraduate mathematics including linear algebra and vector analysis.

The author covers a wide range of topics from tensor analysis on manifolds to topology, fundamental groups, complex manifolds, differential geometry, fibre bundles etc.

The exposition in necessarily brief but the main theorems and IDEAS of each topic are presented with specific applications to physics. For example the use of differential geometry in general relativity and the use of principal bundles in gauge theories, etc.

Unfortunately, there are very few exercises necessitating the use of supplementary texts. However, to the author's credit appropriate supplementary texts are provided. The author goes to great lengths to show which texts inspired the chapters and follows the same line of presentation.

Perhaps the greatest attribute of the text is to take disparate branches of mathematics and coallate them under one text with applications to physics. In doing so one gains a better grasp of how the fields of mathematics interact in the domain of physics. ... Read more

Product Description

For courses in Geometry or Geometry for Future Teachers.

This popular book has four main goals: 1. to help students become better problem solvers, especially in solving common application problems involving geometry; 2. to help students learn many properties of geometric figures, to verify them using proofs, and to use them to solve applied problems; 3. to expose students to the axiomatic method of synthetic Euclidean geometry at an appropriate level of sophistication; and 4. to provide students with other methods for solving problems in geometry, namely using coordinate geometry and transformation geometry. Beginning with informal experiences, the book gradually moves toward more formal proofs, and includes special topics sections.

Customer Reviews (3)

A solid introduction to geometry that emphasizes learning through problem solving
One of the problems a number of math students face is learning how to think about the problems they face.They simply never develop the necessary tool set that will allow them to understand what the problem is asking and what they should do to attack it.Once they have an answer, they are not sure if they have found the correct answer.This is a fine BASIC text for college and high school students who want to get a handle on dealing with geometry.If you have a deep mathematics background and are looking for an advanced college text on geometry, this is probably not for you.

However, if you want to learn the basics on how to think about geometry and a lot of help on how to solve a variety of geometric problems, this is a terrific text and will be a big help.I enjoy the way the text engages the student from the very beginning and asks him or her to THINK.It isn't a bunch of material to memorize.What the authors do is build the student's understanding through problem solving.If the student will take the time to work the problems and not give up on the problems he or she finds difficult, the understanding will come and will be more ingrained in his or her thought processes than would happen through memorization.

There are lots of geometric drawings, as one would hope, and there are a number of applications of geometry to real life and that should help the student, as well.Again, this is meant as a basic geometry text and can be suitable for a good high school student as well as non-majors in college that want to get an introduction to the basics of geometry.

not college level
This book is pitched at an extremely low level
quite beyond anything in the 'math for poets'
category - often dropping below even that of high
school.Indeed, the book compares unfavorably
with the canonical hs text by Jacobs.To give
just one example, it takes the authors 273 pages
to get to the ideaof cross multiplication [a staple
in the repertoire of any decent middle school
student].In particular, math majors as well
as anyone interested in the subject should
steer clear of this and consider instead books by
Pedoe, Court, Coxeter, etc.If you are looking
for a problem oriented approach to geometry, try
the relevant offering in the Schaum's series
[acknowledged masters of this approach].
In the meantime, let's not sacrifice any more trees
for products as weak as this.

An outstanding introduction to geometric thought
This is one of the few introductory level texts I have seen that gives some of the real flavor of mathematics, without being too challenging for beginning students.The initial section on problem solving is modelled on the famous book by Polya, "How to solve it," and has many simple but thought-stimulating problems.The following sections develop plane and solid geometry with many illustrated problems and interesting historical notes.The final chapters carefully introduce geometric proofs.There are also review sections on simple algebraic manipulations and basic logic, as well as a short section on the implications of alternate parallel postulates.Overall, the text has a well thought out development of basic skills and concepts, and enough interesting tidbits from more "advanced" topics to challenge the imagination of any student. ... Read more

Product Description
Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1. ... Read more

Customer Reviews (6)

An Introduction with Mathematical Integrity
Gregory Naber is to be commended for writing a thorough introduction to gauge field theory in which the mathematics is presented with clarity and rigor.For the professional mathematician who is interested in physics, or for the graduate student who prefers to see the mathematics "done right" in advanced applications to physics, Naber's wonderful two-volume set stands apart from its major competitors, nearly all of which were written by physicists, for physicists.

Despite the attention to mathematical rigor, it is clear that Naber intended his books to be accessible to a dual audience of physicists and mathematicians. For the physicists, he has included gentle introductory chapters on topological spaces, homotopy groups, principal bundles, manifolds and Lie groups, and differential forms. For mathematicians, the chapters on physical motivation, gauge fields and instantons, Yang-Mills-Higgs theory, Spinor structures, etc., provide unusually accessible introductions to some difficult physics materials.

Chapter 0 of the first volume is worth the price of both books, as it leads the reader, in 26 succinct pages, to a compelling appreciation ofthe natural "fit" of the Hopf Bundle to the task of providing a quantum mechanical analysis of the exterior of a single magnetic monopole.For outsiders who have become incredulous about the increasingly sophisticated uses of topology and geometry in theoretical physics, this example provides some much-needed assurance.As the reader quickly learns, the use of connections on principal fiber bundles is neither gratuitous nor mathematical overkill:indeed, the bundle machinery emerges quite NATURALLY as the simplest and best mathematical tool, perfectly fitted to the special problem at hand.

Any serious reader will want to buy both volumes of this set:Topology, Geometry, and Gauge Fields:Foundations (volume 1), and Topology, Geometry, and Gauge Fields:Interactions (volume 2).These books take their place alongside the work of authors such as Jerrold Marsden, Theodore Frankel, Barrett O'Neill, and Walter Thirring, all of whom write about modern mathematical physics in a way that does not obscure the true role of the mathematics.

correction to dost
The review "Easy reading, complete proofs, plenty of exercises, October 29, 2005 by Rehan Dost is of the first volume, Foundations, not this volume which is Interactions. Naber's books are crafted to bridge physics, undergraduate mathematics and graduate mathematics. This is one more of his beautiful volumes in applied mathematics.

Easy reading, complete proofs, plenty of exercises
This text is by far the best introductory text marrying basic concepts of physics with pure mathematics.

Some background in the basic concepts of vector calculus, linear algebra, complex numbers and group theory is required.

The author begins by motivating the mathematics by the pursuit of finding a vector potential to represent a magnetic monopole. We see that the topology of R3-0 precludes such a vector potential from existing. We see here a simple example of how the topology of a space affects the physics associated with it.
The importance of the vector potential as something other than a convenient computational tool is highlighted by a reference to essential inclusion in quantum mechanics. Thus we NEED such a potential.

The author now asks whether there is a "trick" or device to get around this difficulty. The device are principal bundles and connections. For example the potentials noted above must keep track of the phase of a charged test particle as it moves thru the field of a magnetic monopole. We need a "bundle" of circles ( representing the phase at each point ) over S2 ( the author explains why we need only consider S2 instead of R3-0, briefly we need only keep track of 2 of the 3 spherical co-ordinates ).
Thus a curve in S2 thought of as the particles trajectory will have to be "lifted" to the bundle space by a lifting procedure called a connection.
In a more general setting elementary particles have an internal structure ( spin etc ) which becomes apparent during interactions although may not be apparent in uniform motion thru a vacuum. Since the phase of the particle does not alter the modulus when calculating probabilities these do not change. However, when the particles interact phase differences are important. We need to keep track of such phases as the particles interact.

Thus we need a "bundle" over a 4-manifold ( keeps track of the particles space-time path ) to keep track of such internal states. One sees we also need a group to transform states into one another ( usually incorporated into the bundle ). Connections then model physical phenomena which mediate changes in the internal states.
We see that some connections satisfy the Yang-Mills equations and using the appropriate equivalence relation form Moduli spaces.

Now that may seem like alot to digest with only a spattering of mathematical maturity.

The beauty of the book is that the author starts from FIRST principles.

Chapter 1 introduces topological concepts of topology, continuity, quotient topology, projective spaces, compactness, connectivity, covering spaces and topological groups.

Chapter 2 introduces concepts of path lifting, fundamental groups, contractability, simple connectedness, covering homotopy theorem, higher homotopy groups

Chapter 3 introduces principle bundles, transition functions, bundle maps and principle bundles over spheres.

Chapter 4 introduces manifolds, derivatives on manifolds, tangent/cotangent spaces, submanifolds, vector fields, matrix lie groups, vector valued 1- forms, 2 forms and Riemann metrics

Chapter 5 gets to some physics with gauge fields and connections, curvature, Yang-Mills functional, moduli spaces, Hodge dual , matter fields and covariant derivatives.

At each step the author carefully provides complete proofs and easy exercises to ensure understanding.

It was a pleasure to read the book and complete the exercises. At no point did I feel frustration or boredom.

Don't waste your money
This review refers only to the book printing quality not to the contents.

I had purchased some books from Springer in the past (Like Arnold Mathematical Methods of Classical Mechanics, Lang Algebra etc..) and found them beautifully edited: good binding, paper etc..

And to my surprise I was very disappointed with the overall quality of this book, poor binding -glued instead of sewn- bad quality paper -forming waves at the binding spine, etc..

You pay for a quality item, a book you can use for years, and you get a hardbound crap that you can not left open in a table without holding it tight risking to lose the pages after a few days of use in the process.

I find this unacceptable in books costing 60$+. Sadly I find this to occur very often, publishers should be more careful with their printings and custumers should demand a better quality.

Don't waste your money.

A reader.

MATH AND TOPOLOGY
Topology is very important scince in the fields of mathematics. And it using in many of another sinceis. ... Read more

Product Description

Product Description
Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane conics, cubics and the group law, affine and projective varieties, and nonsingularity and dimension. He stresses the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book contains numerous examples and exercises illustrating the theory. ... Read more

Customer Reviews (3)

Exceptionally good book; but make sure this is what you need
This book is intended to provide us with a short (135 pages), down to earth and fluently motivated introduction to algebraic geometry. And it does a great job. While the author does not clearly state his intentions in advance, I think it would be safe to assume that this is meant to accompany a more standard text on the subject (Hartshorne, Harris, Shafarevich, etc), and that the author's main goal was to give the quickest possible route to the heart of the subject, making sure the reader stays interested throughout rather than that he is presented with the firmest logical structure. I would like to stress that despite of what I wrote so far, this book does present rigorous proofs and clear definitions.

The style is friendly, straightforward and unpretentious. Everything is well motivated, and one occasionally gets to hear the author's personal perspective or view about a certain topic. I will quote two examples. When discussing the Zariski topology, the author writes "The Zariski topology may cause trouble to some students; since it is only being used as a language, and has almost no content, the difficulty is likely to be psychological rather than technical". This was very calming for me to read, as I have been previously struggling with the "deep meaning" of the Zariski topology, and no book has had the honesty to tell me that I shouldn't worry that much about it. As a second example of the author's style, after a Q.E.D. in page 53 the author explains that "The proof of (b) is a typical algebraist's proof: it's logically very neat, but almost completely hides the content: the real point is that ..."

Chapter 1 begins with the concrete example of conics, intended to motivate the later definitions of the projective plane. Next elliptic curves and their group law is discussed. The chapter ends with a brief survey of the genus of curves.

Chapter 2 is more technical; its purpose is to build the algebraic foundations needed for Hilbert's Nullstellensatz. Among topics covered are Noetherian rings, Hilbert's Basis Theorem, algebraic sets, the Zariski topology, prime ideals and a nice motivation for the Nullstellensatz. Next coordinate rings, morphisms, varieties and other standard topics are introduced.

Chapter 3, titled "Applications", uses the previous material to discuss some nice geometric topics. I especially enjoyed the section on the 27 lines on a cubic surface.

I would highly recommend this book to anyone not very familiar with algebraic geometry; for instance, it could be a good reading to decide if you want to take a more serious study (e.g. a university course) of the subject. If I were to suggest only one text for someone who just wants to know what algebraic geometry is all about, it would definitely be this one.

Unreadable but well-organized
It is difficult to see who this book is aimed at.Perhaps the extremely gifted undergraduate who can fill in sketchy, incomplete, difficult proofs, but has also taken courses?My professor (a topologist) even had a difficult time presenting the material as-is and solving the exercises, as very few examples were given, hence it was unclear exactly what was required for a satisfactory proof of the questions as stated.Reid, probably in an effort to save space, delegates difficult steps of proofs to the reader by declaring them "obvious," making the book practically unreadable to the average undergraduate student.The notation is used strangely and the typesetting is awkward.

The proof of the 27-lines theorem is interesting and a decent capstone for the introductory subject.However, I did not feel as though I had deepened my knowledge of algebraic geometry as a result, only having learned the bare minimum to approach one useless (albeit entertaining) theorem.

If you have to use this book I recommend buying another one to supplement the background knowledge and to figure out how to complete the proofs.

baked just right for the first timers !
There are many good books on the subject of algebraic geometry, so what was the use of one more - asks the author in the preface to this book.But there are none -at the UG level- which for the first time reveal to theyounger mathematicians the secrets of this vast and growing subject. Thebook treats every new concept with the rigour that keeps in mind the levelit is meant for, and yet maintains its mathematical "beauty" -setting firmly the basics for those who would want to take up this courseat an advanced level as well as keeping the more casual mathematics readerinterested. ... Read more

Product Description

Product Description
Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane conics, cubics and the group law, affine and projective varieties, and nonsingularity and dimension. He stresses the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book contains numerous examples and exercises illustrating the theory. ... Read more

Customer Reviews (3)

Exceptionally good book; but make sure this is what you need
This book is intended to provide us with a short (135 pages), down to earth and fluently motivated introduction to algebraic geometry. And it does a great job. While the author does not clearly state his intentions in advance, I think it would be safe to assume that this is meant to accompany a more standard text on the subject (Hartshorne, Harris, Shafarevich, etc), and that the author's main goal was to give the quickest possible route to the heart of the subject, making sure the reader stays interested throughout rather than that he is presented with the firmest logical structure. I would like to stress that despite of what I wrote so far, this book does present rigorous proofs and clear definitions.

The style is friendly, straightforward and unpretentious. Everything is well motivated, and one occasionally gets to hear the author's personal perspective or view about a certain topic. I will quote two examples. When discussing the Zariski topology, the author writes "The Zariski topology may cause trouble to some students; since it is only being used as a language, and has almost no content, the difficulty is likely to be psychological rather than technical". This was very calming for me to read, as I have been previously struggling with the "deep meaning" of the Zariski topology, and no book has had the honesty to tell me that I shouldn't worry that much about it. As a second example of the author's style, after a Q.E.D. in page 53 the author explains that "The proof of (b) is a typical algebraist's proof: it's logically very neat, but almost completely hides the content: the real point is that ..."

Chapter 1 begins with the concrete example of conics, intended to motivate the later definitions of the projective plane. Next elliptic curves and their group law is discussed. The chapter ends with a brief survey of the genus of curves.

Chapter 2 is more technical; its purpose is to build the algebraic foundations needed for Hilbert's Nullstellensatz. Among topics covered are Noetherian rings, Hilbert's Basis Theorem, algebraic sets, the Zariski topology, prime ideals and a nice motivation for the Nullstellensatz. Next coordinate rings, morphisms, varieties and other standard topics are introduced.

Chapter 3, titled "Applications", uses the previous material to discuss some nice geometric topics. I especially enjoyed the section on the 27 lines on a cubic surface.

I would highly recommend this book to anyone not very familiar with algebraic geometry; for instance, it could be a good reading to decide if you want to take a more serious study (e.g. a university course) of the subject. If I were to suggest only one text for someone who just wants to know what algebraic geometry is all about, it would definitely be this one.

Unreadable but well-organized
It is difficult to see who this book is aimed at.Perhaps the extremely gifted undergraduate who can fill in sketchy, incomplete, difficult proofs, but has also taken courses?My professor (a topologist) even had a difficult time presenting the material as-is and solving the exercises, as very few examples were given, hence it was unclear exactly what was required for a satisfactory proof of the questions as stated.Reid, probably in an effort to save space, delegates difficult steps of proofs to the reader by declaring them "obvious," making the book practically unreadable to the average undergraduate student.The notation is used strangely and the typesetting is awkward.

The proof of the 27-lines theorem is interesting and a decent capstone for the introductory subject.However, I did not feel as though I had deepened my knowledge of algebraic geometry as a result, only having learned the bare minimum to approach one useless (albeit entertaining) theorem.

If you have to use this book I recommend buying another one to supplement the background knowledge and to figure out how to complete the proofs.

baked just right for the first timers !
There are many good books on the subject of algebraic geometry, so what was the use of one more - asks the author in the preface to this book.But there are none -at the UG level- which for the first time reveal to theyounger mathematicians the secrets of this vast and growing subject. Thebook treats every new concept with the rigour that keeps in mind the levelit is meant for, and yet maintains its mathematical "beauty" -setting firmly the basics for those who would want to take up this courseat an advanced level as well as keeping the more casual mathematics readerinterested. ... Read more

Product Description
Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: http://mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems ... Read more

Customer Reviews (1)

first edition
I have a copy of the first edition which has an interesting treatment of projective geometry. The 2cd edition appears to cover even more. ... Read more

Product Description

Product Description

Customer Reviews (1)

Thought provoking
Let me say first off that George Hersey is obviously an expert in his field and writes very well.The problem for me is that he is comfortable enough with his subject that his observations run to the "poetic".While this is a good thing for readers equally knowledgeable in the disciplines that he traverses while writing this book it was not good for me.

To aid anyone interested in this book let me say I am a male in my 60's
with an MFA in the fine arts.Although I read prodigiously I am virtually untrained in music theory, and I left off my math studies after advance algebra.So, although I continue to work at expanding my education in these two subjects, and am retaining Hersey's book with the hopes of returning to it periodically as I come up to the line on these studies, it
is beyond me right now...at least for it to be appreciated at the deserved depth.

I believe that anyone with some experience with the history of architecture, projective geometry, and music theory will find this book a treasure trove of aesthetic enjoyment and information.Such a person will also have fun contemplating some of the new and original interpretations that Hersey injects into the material. ... Read more

Product Description

Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers, and useful to people working in the applied fields.

Product Description

Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.

... Read more

Customer Reviews (3)

Geometry Book
This book has a few errors and is not very descriptive. However, it is a course requirement. So, I guess it has to be okay.

Geometry with a twinkle in the eye
This is probably the only math book I've actually read in its entirety. Moise delivers what could be very dry material with a lightness and sense of humor that kept me poking on through the book. The connections to otherareas of math, especially (and not surprisingly) non-Euclidean geometries,is a big plus. I also liked the occasional historical interludes. There area few spots where you may not see good pointers to the figures provided,but in general it is very clear what the author is referring to. Theproblem sets and Moise's own explanations afford excellent practice for the"proof-challenged," as well. I keep this book on my shelf as"ready reference." I wish Moise had written more math books!

The new Elements
Beginning by the elementary axioms the author builds all the great geometry theorems and formulas. Like a great romance, after begin to read you don't want stop until end. ... Read more

Product Description
An ingenious problem-solving solution for befuddled math students.

A bestselling math book author takes what appears to be a typical geometry workbook, full of solved problems, and makes notes in the margins adding missing steps and simplifying concepts so that otherwise baffling solutions are made perfectly clear. By learning how to interpret and solve problems as they are presented in courses, students become fully prepared to solve any obscure problem. No more solving by trial and error!

• Includes 1000 problems and solutions
• Annotations throughout the text clarify each problem and fill in missing steps needed to reach the solution, making this book like no other geometry workbook on the market
• The previous two books in the series on calculus and algebra sell very well ... Read more

Customer Reviews (5)

Geometry self help book
Geometry self help books are good for those who need extra tutoring to understand geometry problems.

Lots of great problems, but not for math classes
These books do indeed have a tons of good math problems, but I was hoping to use them as reproductions for my math class.Each page of problems has the entire worked out solution included with the problem, so there is not much mystery as to the answer.The solutions are detailed, and readable with a cartoon look to them.I might use some of the problems, but I wish I could xerox them for my students.

Terrific Book!
Exceptional book for high school student taking an honors geometry class..have bought a few over time and most are just lists of problems with answers in back..but this one actually goes step by step thru a well orchestrated sequence of problems and does a terrific job explaining them. Great coverage of the years content + good preview of basic algebra materials needed to be succesful in Geo.

another excellent help book in the "Humongous" math book series
This is another great help book in the "Humongous" math book series.There are so many problems that are solved with step by step explanations, diagrams and notes in easy to find areas of geometry.It is a great book for getting help and explanations for any particular problem area a student may encounter.The "Humongous" math series books are by far the best math books I have ever looked at.

Used this book for tutoring a student in geometry this summer
I used this book in conjunction with the Jurgenson and Brown Geometry textbook this summer to tutor a student who needed to pass an entrance exam in geometry so that he could take Algebra II next semester.He passed with a 95.

I'm a math teacher and tutor, and own the entire Humongous series.I've also been a professional indexer, and I can tell you that I appreciated the care taken with the index (and also the large font used - a nice treat, in comparison with the usual tiny-print indexes!).

There *is* a chapter on logic and proofs, but it's not extensive.However, proofs don't seem to have the emphasis they had back when I studied geometry in the 60's, so it shouldn't be a problem for the modern student.

It's odd that Amazon doesn't provide a view of the table of contents for this book.
I found a website that does provide one - go here:
[...]

I definitely recommend this book for those wishing to learn geometry.It even begins with refresher material on the algebra and rational numbers you'll use in geometry.

... Read more