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1. Calculus With Analytic Geometry, Seventh Edition by Ron Larson  
list price: $155.56
our price: $155.56 (price subject to change: see help) Asin: 0618239723 Catlog: Book (20020101) Publisher: Not Avail Sales Rank: 18446 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Designed for the threesemester course for math and science majors, the Larson/Hostetler/Edwards series continues its tradition of success by being the first to offer both an Early Transcendental version as well as a new Calculus with Precalculus text. This was also the first calculus text to use computergenerated graphics (Third Edition), to include exercises involving the use of computers and graphing calculators (Fourth Edition), to be available in an interactive CDROM format (Fifth Edition), and to be offered as a complete, online calculus course (Sixth Edition). Every edition of the book has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. The Seventh Edition also expands its support package with an allnew set of textspecific videos.
... Read more Reviews (17)
Calculus With Analytic Geometry Easy to read, and nice progression of topics.
Good book but NOT for a math major If you are going to selfstudy calculus, i have some advices: 2 Don't go too fast. If you don't have time, just skip some sections of the end of each chapters. Especially at the end of the book. Chapter 14 is quite confusing. Read them slowly, understand piece by piece. If you are a math major, particularly pure math, this is not a book for you. You need a book that talks more about theory.
Refer to other editions 0618141804
Good but problems were too easy The CD I really did not use. Some of you probably got more use out of it. But the text and diagrams are well enough done that I found the CD unnecessary. The only criticism is that perhaps some of the problems could have been harder/more challenging.
Calculus 
2. Topology (2nd Edition) by James Munkres  
list price: $102.00
our price: $102.00 (price subject to change: see help) Asin: 0131816292 Catlog: Book (19991228) Publisher: Prentice Hall Sales Rank: 48786 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (23)
Standard Topology Text
A Great Work Having a course in analysis would certainly make the book flow since otherwise it would just to be a mental exercise rather than an extension of familiar concepts. The exercises are very well thought out and are meant to be solved by all students given that they have some diligence. They truly help in turning a fog of concepts into concrete understanding.
great!
Excellent Topology Book Later at graduate school, Munkres was also used in a topology class at the beginning graduate level. Highlights were taken from the first section (point set topology), and a large focus of the class was on the algebraic topology in the second section of the book. Sometimes I had difficulty following exactly what the professor was doing at the blackboard, but I could always understand what was going on when I consulted Munkres. I would stress that this is only to be used as an introduction to algebraic topology, as there is nearly no development of homology groups and other algebraic concepts. However, it gives a very good presentation for the fundamental group. As a whole it would be a very good addition to your mathematical library.
Wonderful text in a poor binding The only drawback, and it is a serious one, is the binding. For a wellselling book $[...] worth, one could expect a *decent* binding, but the outcome is a *shame*. With time, the covers of my copy got ridiculously bent outwards, quite like if was cooked in my oven (which I didn't, of course). ... Read more 
3. Calculus (8th Edition) by Dale Varberg, Edwin J. Purcell, Steven E. Rigdon  
list price: $105.33
our price: $105.33 (price subject to change: see help) Asin: 0130811378 Catlog: Book (19990927) Publisher: Prentice Hall Sales Rank: 5427 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description This the shortest mainstream calculus book available. The authors make effective use of computing technology, graphics, and applications, and provide at least two technology projects per chapter. This popular book is correct without being excessively rigorous, uptodate without being faddish. Maintains a strong geometric and conceptual focus. Emphasizes explanation rather than detailed proofs. Presents definitions consistently throughout to maintain a clear conceptual framework. Provides hundreds of new problems, including problems on approximations, functions defined by tables, and conceptual questions. Ideal for readers preparing for the AP Calculus exam or who want to brush up on their calculus with a nononsense, concisely written book. ... Read moreReviews (12)
Buy Swokowski's Calculus instead. I've been using the book for two semesters in a distance learning program. In this setting, where the reader needs to learn from the book rather than from an instructor, the book is inadequate. It's single strength  brevity  doesn't make up for its weaknesses: mystifying explanations, worked examples that omit important steps, and errors. Many times, this book made me laugh out loud when, after literally hours of effort, I finally understood what the authors were trying to communicate. There is no way I could have completed my classes had I not had Swokowski to refer to. Beyond these weaknesses, the book is loaded with throwaway Horatio Algerisms ("Skill at this, like most worthwhile activities, depends on practice.") and hokey humor ("We have no desire to let this text suffer from the standard ailment of older texts, called 'revisionitis.'") These give the book a dated, musty feel: it's as if you are looking back at how calculus used to be taught 40 years ago. Finally, six weeks into the first semester, the binding failed, converting the book into an expensive, 900page, looseleaf folder. Overall, not a book I enjoyed spending time with.
good but solutions manual is a must have
Classic "Attachable" book (a). being able to feel attachment for. This book satisfies all the above conditions [and (d)]. The style is very accessible to everyone who knows algebra. Math lovers who want to go beyond algebra should buy this book. Now, its particular uniqueness are the followings: mine has been separated into many stapled pages, though I personally like to sort them whenever I touch the book; examples are enough to illustrate introduced theorems. Of course, it doesn't end up with downtoearth proofs. Wherever that might happen, it says so, and theorems that can not be proven with attainable knowledge are "left for advanced Calculus courses." Consequently, all presented proofs are quite rigorous in understandability. (c) will follow for appropriate readers. Good to start with, and will be one of your old friends.
Calculus 8th Edition Varberg, Purcell, Rigdon
Perhaps the best out there...but that's not saying much... I feel that this book in many ways is the best. Keep in mind, however, that this isn't saying much. For the most part, calculus (and math in general) textbooks are somewhat difficult to learn from. This stems from the fact that we students like to see lots of worked out example in order to "get" it (buy Schaum's outline or REA's Problem Solver for lots of worked examples). In many cases, a calculus book like this will give you, perhaps, one example for a given procedure and leave it to you to deduce the rest. Still, I like the fact that this book contains the material for Calc. I, II, and III. If nothing else, it saves us some money. One final comment: as another reviewer on amazon has already noted, the binding on this book is quite poor. I have seen many other students in my class with books in which the pages have started falling out. Perhaps Prentice Hall should provide us with a better binding for a hundred bucks. ... Read more 
4. Basic Mathematical Skills with Geometry w/MathZone by DonaldHutchison, BarryBergman, StefanBaratto  
list price: $105.00
our price: $105.00 (price subject to change: see help) Asin: 0073016055 Catlog: Book (20040420) Publisher: McGrawHill Science/Engineering/Math Sales Rank: 17242 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (1)
try doing the tests on MathZone 
5. Geometry for Enjoyment & Challenge by Richard Rhoad, George Milauskas, Robert Whipple  
list price: $84.84
our price: $84.84 (price subject to change: see help) Asin: 0866099654 Catlog: Book (19910601) Publisher: Mcdougal Littell/Houghton Mifflin Sales Rank: 18448 US  Canada  United Kingdom  Germany  France  Japan  
6. The Golden Ratio : The Story of PHI, the World's Most Astonishing Number by MARIO LIVIO  
list price: $14.95
our price: $10.17 (price subject to change: see help) Asin: 0767908163 Catlog: Book (20030923) Publisher: Broadway Sales Rank: 1405 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description
Reviews (40)
Pursuing the Mysteries of the Ubiquitous Number Phi Then he describes the role of the Greek mathematicians Plato and Euclid, and the Italian mathematician Leonardo Fibonacci in the history of phi, together with the geometrical and arithmetical wonders connected to this number. One example of the wonders is the relation between the Fibonacci sequence and phi. The Fibonacci sequence 1, 1, 2, 3, 5, 8, ... is defined as a series of numbers in which each term is the sum of the two preceding terms. The ratio of successive numbers of this sequence approaches phi as we go farther and farther down the sequence. Next come the topics of phi found in nature and used in arts. The logarithmic spiral, which goes hand in hand with the Golden Radio, appears in the sunflower, the flight of a falcon, galaxies, etc. The author's study of many historical attempts to disclose the Golden Ratio in various works of art, pieces of music and poetry comes to the conclusion that ... (I have to refrain from writing the ending of the "detective story"). In the final chapter Livio considers the question: What is the reason that mathematics and numerical constants like phi play such a central role in topics ranging from fundamental theories of the universe to the stock market? Noting that the discussion about this question can fill the entire volume, the author gives a brief (but very understandable) description of the modified Platonic view and the natural selection interpretation. He also presents his personal opinion, which adopts complementarity of the above two views. This chapter whets readers' appetite for a possible next book on this topic to be written by Livio. I strongly recommend "The Golden Ratio" to scientists, artists and laypersons that are interested in the wonders of numbers and mathematics and in their relations to arts and nature.
Golden Indeed! Writing about science in a way that is both knowledgeable and understandable for the common reader is an infamous hurdle, but Livio leaps over it with the greatest of ease, giving clear explanations of every potentially difficult matter and providing the scientific proofs in the appendices, for those more mathematically inclined. Overall, though, it is the great humanity of Livio's worldview that shines through the book and makes it, at least for me, one of the most memorable reads of the year.
A Difficult Mathematical Concept Revealed It is little wonder that such numbers as the Golden Ratio were considered magical. The never ending, never repeating number that cannot ever be expressed as a fraction has an uncanny tendency to show up in the oddest places, not only galactic structure and nautilus shells, but in plant parts and composition of paintings and music. Unfortunately magical numerology can lead to farfetched relationships, as to the socalled number of the beast (666), and to academicism in art. Just because the Golden Ratio results in a pleasing relationship in a composition we are not tied to always measure art on how well it fits that ratio! Livio has illuminated the history of the Golden Ratio in such a way that much of the associated themes can be understood by the reasonably educated laymen. While some of the book can be tough sledding for most of us nonmathematicians, the gist is available to all with some effort. Read this book to learn about the history of interpretation and misinterpretation of mathematical concepts.
A great guide to an amazing number Livio explains the original formulation of this number by Euclid and proceeds to address the various times in history in which it may have been employed by architects, artists and musicians. I think this is a really good book if you're interested in reading about the most "irrational of all irrational numbers".
Mathematically Profound 
7. Differential Geometry of Curves and Surfaces by Manfredo Do Carmo  
list price: $100.00
our price: $100.00 (price subject to change: see help) Asin: 0132125897 Catlog: Book (19760201) Publisher: Prentice Hall Sales Rank: 109376 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Reviews (10)
Excelent exposition !
Excellent introduction to differential geometry
Very Difficult
too wordy
Outdated classic in the field 
8. Elementary Geometry for College Students by Daniel, C. Alexander, Geralyn M. Koeberlein  
list price: $93.56
our price: $93.56 (price subject to change: see help) Asin: 061822176X Catlog: Book (20020701) Publisher: Houghton Mifflin Company Sales Rank: 351807 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description The Third Edition of Elementary Geometry for College Students covers the important principles and realworld applications of plane geometry with additional chapters on solid geometry, analytic geometry, and trigonometry. The text's largely visual approach, strongly influenced by both NCTM and AMATYC standards, begins with the presentation of a concept followed by the examination and development of a theory, verification of the theory through deduction, and finally, application of the principles to the real world. Designed with the appropriate pacing and appearance for collegelevel students, this text offers a welcome alternative for instructors who, in the past, have had to use secondarylevel texts for this course.
... Read more Reviews (1)
A Wretched and Horrid Book "Elementary Geometry for College Students," by Daniel C. Alexander (of Parkland College) and Geralyn M. Koeberlein (of MahometSeymour High School), has taught me nothing more than NOT to trust a textbook written by a couple of hack authors from unknown schools with a blatant disregard for meticulously explaining important vital and "elementary" steps as to how to arrive to certain statements, reasoning, deducing, measurements, and so much more NEEDED in successfully acheving full reign over geometry. For example, the origins of postulates and proofing are never explored, but slammed in your face, convoluting both topics along with breaking down statements from deducing a particular shape, its angles and measurements. The book's attempts at explaining triangles, convex polygons, congruent triangles, and properties of parallelograms are all but slandered together (with steps in basic algebraic mathematical equations arrogantly skipped over and presumed upon to you) without any form of thorough reason or explained steps bothered in explaining. Important theorems are disarrayed throughout with quickstep problem examples without helpful or detailed reasoning as to how the answer was ever achieved. The authors have obviously assumed a college student has had some form of pregeometry course prepping, and expect both instructor and student to know the advanced fundamentals without considering the beginner geometry student at all (just from judging by example and "solutions" given in each section). As a result, students will fail miserably, along with angering frustration, and discontent wonderment over what purpose geometry may ever serve toward a reallife career. Perhaps trying "Geometry for Dummies" by the infamous IDG publishing company would be a much suitable levelage to this otherwise detrimental book attempting to teach an important equation to the universe of mathematics. By far, this textbook is the worst and most horrible book in teaching the subject of geometry!! To professors searching a geometry book for your students: PLEASE avoid this book at all costs! You and your students don't need a textbook that presumes you know it all before diving into shapes, proofing, deducing, theorums, solids, and so forth. Most surely, there are much more superior books to this wretched and horrid title worthy of its decommissioning. ... Read more 
9. Geometry and Trigonometry for Calculus (Wiley SelfTeaching Guides) by Peter H.Selby  
list price: $19.95
(price subject to change: see help) Asin: 0471775584 Catlog: Book (19750418) Publisher: Wiley Sales Rank: 90991 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (12)
The Pleasure of Finding Things Out Looking to fill that void I got this book and its companion introductory volume, Peter Selby and Steve Slavin's "Practical Algebra: A SelfTeaching Guide", and am extremely relieved to find out mathematical illiteracy can be remedied with the right tools. These books not only taught me the basics of algebra and geometry, but more importantly, gave me a glimpse of how mathematical ideas are developed. Concepts that appeared to me to be mystical elaborations now seem full of reason and purpose, thanks to the selfcontained nature of these two books and the step by step construction of ever more complex themes. The authors focus not on mechanical repetition but on understanding, on making sense to the student, so everything fits in in a meaningful way, instead of appearing as a loose aggregation of disjointed bits. I really got a lot of enjoyment out of learning all the material, and finding out what a wonderful world of ideas this knowledge opens up. Of course, being a great book doesn't mean being a flawless book, and this one indeed has its shortcomings. First, this two volumes do not cover logarithms at all, so you'll have to look for that subject elsewhere. Also, the plain geometry, analytic geometry, and conic sections chapters have insufficient exercises, so you'll probably want to get an additional text to get some more practice in those areas. Finally, even though the books are a very good and wellrounded introduction, they do not go into much depth in any area. On the other hand, the introduction to limits is truly great. If your knowledge of mathematics has ever held you back professionally or personally, this is a great place to start changing that!!
EXCELLENT! Wish I would have had this author teaching me. Mr. Peter H. Selby is an excellent author. You flow through his pages without having to read over paragraphs several times in order to understand the sense of his explanations without stress and fatigue. There is no guessing nor ambiguous wording. It is difficult to put down his book for the day. I look forward to his future books.
Bummer
good as a companion only Unless you want a refresher, I'd go somwhere else, maybe a dummies or idiots guide instead.
There aren't enough exercises.. 
10. College Algebra and Trigonometry (2nd Edition) by Margaret L. Lial, John Hornsby, David I. Schneider  
list price: $118.00
(price subject to change: see help) Asin: 0321057554 Catlog: Book (20001108) Publisher: Addison Wesley Sales Rank: 345551 US  Canada  United Kingdom  Germany  France  Japan  
11. The Geometer's Sketchpad: Student Edition : Version 4 by Key Curriculum Press  
list price: $39.95
our price: $39.95 (price subject to change: see help) Asin: 1559535288 Catlog: Book (20020801) Publisher: Key Curriculum Press Sales Rank: 196302 US  Canada  United Kingdom  Germany  France  Japan  
12. Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201) by Shigeyuki Morita, Teruko Nagase, Katsumi Nomizu  
list price: $53.00
our price: $53.00 (price subject to change: see help) Asin: 0821810456 Catlog: Book (20010901) Publisher: American Mathematical Society Sales Rank: 449934 US  Canada  United Kingdom  Germany  France  Japan  
Book Description The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the ChernWeil theory. The book can serve as a textbook for undergraduate students and for graduate students in geometry. ... Read more 
13. Geometry for Dummies by WendyArnone  
list price: $19.99
our price: $13.59 (price subject to change: see help) Asin: 0764553240 Catlog: Book (20010915) Publisher: For Dummies Sales Rank: 13620 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Well, don't fret. You're in the same boat as almost everyone else. Geometry has about a million (a rough estimate) uses in real life – for example, you may have some home improvement projects you want to tackle; you have to know how to cut the wood at certain angles to make them fit together. ( Bet you didn't realize that carpenters have to be experts at geometry as well!) With a basic knowledge of geometry, building some bookshelves for your kid's room becomes so much easier. Geometry For Dummies can give you that basic understanding of geometry, and you might actually have a little fun along the way. Written in a breezy, easytounderstand, nontextbooklike style, this book helps you with all your geometrical dilemmas. In Geometry For Dummies, you'll find out about the following topics and more:
So whatever your reason for wanting to learn geometry – a home improvement project, helping your kid with his or her homework, or just a fascination with funny shapes – Geometry For Dummies is just what you need to recall what you learned in school and put it to good use. ... Read more Reviews (5)
...an excellent approach!!!
Book is adequate
A Textbook, with a tinge of humour For every theorem or postulate this book teaches about, right next to it is a short explanation along with a simple diagram used as an example. This book goes from simple geometry, all the way into a bit of trigonometry. It is basically like a textbook, but with lots of humour and simple explanations that separates it from the rest of the other geometry books. This book probably covers everything that is taught in 10th Grade, but without all the exercises. It teaches and explains geometry, but if you are looking for a book full of exercises, this is not the book for you. It should give us more problems or equations to solve, and that is why it lacks 5stars. That is its only downfall. If you are reading this before you get into geometry, be prepared to know all the material and be bored to death. This is not exactly a bad thing though :) .
Thanks Amazon[.com]
Making the DRY drinkable I suspect however geomerty and real dummies don't mix well. Read this book and surprise yourself, maybe you're not a dummie after all. ... Read more 
14. Geometry, Topology and Physics (Graduate Student Series in Physics) by Mikio Nakahara  
list price: $55.00
our price: $55.00 (price subject to change: see help) Asin: 0750306068 Catlog: Book (20031001) Publisher: Institute of Physics Publishing Sales Rank: 71824 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Reviews (7)
Flat spheres and more
Just a "better than nothing" book If you are a physics graduate who needs a nice guide to "understand" the aspects and skills of geo / top, I would recommend the following: (1) Milnor's Topology from the Differentiable Viewpoint, and (2) Kreysig's Differential Geometry. The first one was old, and so it does not assume much knowledge about the topic. The latter is a kindofBible for the topic, and all solutions are provided for the problems. These two books will help you a lot if you care about the meaning, not only for those classroom exams or just showing off that you know something about it. Frankel is the next to put on your bookshelf as a detailed and rigorous development for your preparation to be a theoretical physicist. If you have only a rough idea about topology, Hocking and Steen are the best choices, and they are Dover!! Anyway, if I could find a cheap used Nakahara, I would get it as a reference.
Best in its genre There seem to be a few books on the market that are very similar to this one: Nash & Sen, Frankel, etc. This one is at the top of its class, in my opinion, for a couple reasons: (1) It's written like a math text that covers physicsrelated material, not a book about mathematics for physicists. I prefer this; you may not. As a consequence, this book is more rigorous than its alternatives, it relies less on physical examples, and it cuts out a lot of lengthy explanation that you may not need. Of course, there are drawbacks to all of these "features"  you need to decide what you need and what's best for you. (2) It's most comprehensive, with Frankel coming in second, and Nash & Sen least comprehensive (though they have quite a bit on Fibre bundles and related topics). Nakahara has a chapter on complex manifolds, which is absent from the other two. Nakahara also concludes with a nice intro to string theory, which is absent from the other two as well (though nothing you couldn't find in Polchinski or the like). Actually  I modify this slightly. Frankel covers less subjects than Nakahara, but with more depth (though also more wordiness  I quit Frankel about 2/3 through because it wasn't succinct enough and I got tired of it). Depending on your tastes, I would recommend this book before the other two. It presupposes that you have an understanding of algebra (groups, rings, fields, etc.) but it has an introduction to the necessary components of topology within. Frankel has presupposes both algebra and topology; Nash & Sen presupposes only algebra.
Excellent book Most of the topics are intepreted in terms of their topological/geomtrical structure (and the interplay between those two), but that's what the title of the book says. So you will learn things again in new ways, and gain a powerful new set of tools. If nothing else, it gives you a nice warm fuzzy feeling when you read other field/string theory books that glosses over the mathematics. One minor rant : the notation of the book can be better. I personally uses indices to keep track of the type of objects (eg. greek index=components of tensors, no index=a geometrical object etc..), but Nakahara drops indices here and there "for simplicity". But that's my personal rant. Good book. Buy it.
A must for any theoretical physicist 
15. Geometry (Mathematics Series) by Harold R. Jacobs  
list price: $106.50
(price subject to change: see help) Asin: 071671745X Catlog: Book (19870101) Publisher: W.H. Freeman & Company Sales Rank: 106561 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Reviews (5)
The best geometry textbook in existence, bar none. This book introduces logical proofs right at the beginning; you may have some difficulty convincing your kids or yourself that you need to work out all these silly logic puzzles in order to begin studying geometry, but you do. From there on, the book is a sheer joy to read, full of interesting and tricky problems, clear explanations, and of course those famous B.C. and Peanuts clips.
Worked every problem
A Very Good Geometry Book
Jacobs sugarcoats the process of rigorous proof!
My favorite high school geometry text 
16. Handbook of Discrete and Computational Geometry, Second Edition by Jacob E. Goodman, Joseph O'Rourke  
list price: $139.95
our price: $139.95 (price subject to change: see help) Asin: 1584883014 Catlog: Book (20040415) Publisher: Chapman & Hall/CRC Sales Rank: 669866 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (1)
Very comprehensive overview of computational geometry There are a few articles overviewing Voronoi diagrams, such as the one on Voronoi diagrams and triangulations. The applications of Voronoi diagrams are many, and include tumour cell diagnosis, biometry, galaxy distributions, and pattern recognition. This article is a little short considering the importance of the subject. The article on shortest paths and networks is somewhat disappointing since there is no indepth discussion on network routing algorithms. The article on computational topology highlights some of the results in this very important area. Many problems in topology have been tackled recently using computers, particularly the work of the mathematician A.T. Fomenko. Computational topology is a relatively young field, having been in existence only since the early 1990's. The applications are enormous, ranging from meshing, morphing, feature extraction, data compression, and in many scientific areas such as computational medicine, chemistry, and astrophysics. It can also be used in computer security via graphical passwords. It is an immense help in visualizing complicated topological objects, such as Lens spaces, horned spheres, and thickened knots. The article does not touch on the use of MayerVietoris sequences to design efficient divideandconquer schemes for computing the homology of higherdimensional complexes. The interplay between topology and finding better algorithms in computational geometry is one that will flourish no doubt in years to come. The last section of the book covers applications with the most interesting article being the one on sphere packing and coding theory. The algorithms in sphere packing have direct applicability to error correctiong codes over the field GF(q). The author of this article does touch briefly on general algebraicgeometric codes, which is good considering their importance in applications. The last article appropriately discusses available software for computational geometry. Although the list of Web sites is quite extensive, there are many more available since this book was first printed. A very fine addition to the literature on computational geometry and should be on everyone's shelf who is interested in this important area. ... Read more 
17. Trigonometry Problems: From the Training of the USA Imo Team by T. Andreescu  
list price: $30.00
our price: $30.00 (price subject to change: see help) Asin: 0817643346 Catlog: Book (20041130) Publisher: Birkhauser Boston Sales Rank: 649205 US  Canada  United Kingdom  Germany  France  Japan  
Book Description 103 Trigonometry Problems contains highlyselected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school mathematics techniques. Key features: â€¢ Presentation evolves through gradual progression in problem difficulty to build and strengthen students' mathematical skills and techniques â€¢ Provides indepth enrichment of problemsolving tactics and strategies, along with practical testtaking techniques, to better prepare students for possible participation in various mathematical competitions â€¢ Topics covered include: trigonometric formulas and identities, their applications in the geometry of the triangle, trigonometric equations and inequalities, and substitutions involving trigonometric functions Advanced high school students, undergraduates, and mathematics teachers engaged in competition training will gain both skills and strategies from this cogent problemsolving resource. ... Read more 
18. Elliptic Curves (Graduate Texts in Mathematics) by Dale Husemoller  
list price: $79.95
our price: $79.95 (price subject to change: see help) Asin: 0387954902 Catlog: Book (20040101) Publisher: SpringerVerlag Sales Rank: 727518 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description This new edition contains three new chapters which explore recent directions and extensions of the theory of elliptic curves and the addition of two new appendices.The first appendix, written by Stefan Theisan, examines the role of CalabiYau manifolds in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory. Dale Husemöller is a member of the faculty at the Max Planck Institute of Mathematics in Bonn. ... Read more Reviews (1)
An excellent update to the first edition. Chapter 18 is a brief summary of the modular elliptic curves conjecture and Fermat's Last Theorem from mostly an historical perspective. The author reviews the material from prior chapters that relate to the modular curve conjecture. The Tate module of an elliptic curve plays a central role, with its structure as an ladic Galois module allowing the author to formulate an alternative version of the modular curve conjecture. The author shows that the modular elliptic curve conjecture is equivalent to the assertion that every ladic representation arising from a Tate module of an elliptic curve over the rational numbers Q comes from a modular form of weight 2, which is a Hecke eigenfunction. It is fascinating that the connection between elliptic curves and Fermat's Last Theorem was only pointed out as late as 1986 by the mathematician Gerhard Frey. The relation of the 'Frey curve', as it is now called, to Fermat's Last Theorem is discussed by the author, and he shows how it is reduced to the modular elliptic curve conjecture for semistable curves. In chapter 19, the author introduces the reader to CalabiYau varieties, which are higher dimensional analogs of elliptic curves, and which have become very important in highenergy physics. The reader will have to have some background in the theory of complex manifolds to appreciate this chapter, but the author does a quick survey of the relevant topics. Of particular importance in this discussion are the Kahler manifolds, which can be thought of as complex manifolds with a metric that is an analog of the Euclidean metric in the real case, i.e. the metric is Hermitian and is closed. After a further review of characteristic classes the author gives several equivalent definitions of CalabiYau manifolds, and several examples in (complex) dimension one, two, and three. He also gives examples of CalabiYau manifolds that arise from projective and weighted projective spaces, and their generalizations, the toric varieties. A brief remark is made concerning the existence of 'mirror' CalabiYau manifolds, these latter objects currently the subject of intense research. Just as in the case of real manifolds, it is of interest to find invariants for CalabiYau manifolds that will assist in their classification. The author does this for the case of surfaces that are CalabiYau, and this naturally leads to the analog of the Euler characteristic in the guise of the famous RiemannRoch theorem. The RiemannRoch theorem though is not proven, but the author does show explicitly how to obtain the formula for the genus for the structure sheaf on the scheme defined by the ideal sheaf. A brief introduction to K3 surfaces is given. These surfaces are very important in physical applications and in fourdimensional topology. Finally, in the last chapter of the book, the author studies families of elliptic curves. This is done in the context of the theory of schemes, and the author makes some connections with physics. The author gives a very brief review of scheme theory, starting with the notion of a 'local ringed space', which is a topological space with a sheaf of rings defined on it such that the stalks are local rings for every point in the space. Local ringed spaces include smooth and complex analytic manifolds as special cases, and codify both the algebraic and analytic properties of the objects studied. An affine scheme is then defined as a locally ringed space isomorphic to the spectrum of a ring. A scheme is a locally ringed space locally isomorphic at each point to an affine scheme. The isomorphism classes of elliptic curves have the structure of a scheme. Elliptic fibrations of surfaces over curves are studied in terms of their effective divisors, which are analogs of the canonical divisors used in the Enriques classification of surfaces. The Euler characteristic is then computed in terms of the effective divisor. The author then shows that a K3 surface with a Picard number at least 5 has an elliptic fibration. This is generalized to the case of CalabiYau varieties using the concept of a 'numerically effective' divisor. Some explicit examples of CalabiYau hypersurfaces in fourdimensional weighted projective are then given. These examples were found by string theorists, and the author therefore devotes an appendix that describes how CalabiYau manifolds are used in high energy physics. The appendix is very short, and a perusal of the literature of string theory will reveal the overwhelming importance of CalabiYau manifolds. String theory has evolved into Mtheories and membrane theories, but both of these involve heavy use of algebraic geometry, and many of the constructions are generalizations of what is known for the case of elliptic curves. ... Read more 
19. The Shape of Space by Jeffrey R. Weeks  
list price: $59.95
our price: $59.95 (price subject to change: see help) Asin: 0824707095 Catlog: Book (20011215) Publisher: Marcel Dekker Sales Rank: 437998 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Reviews (4)
A clear, friendly introduction to topology This book is an ideal introduction to topology for beginners with little or no mathematical background. It introduces topological manifolds (especially 2 and 3manifolds) and their applications to cosmology and the shape of space. It is filled with diagrams, examples and exercises with full solutions at the end of the book. The book assumes almost no knowledge of mathematics or physics, and is thus suitable for highschool and beginning college students. It is a must read for students contemplating a career in pure mathematics or theoretical physics, and who want to get a taste of the applications of pure mathematics to the physical world. For those wishing to go a step further on the subject of the shape of space, the author published a paper (Nature 425, 593  595, 09 October 2003) claiming that the universe is a dodecahedral 3manifold, based on cosmic microwave background measurements. This book may be a nice introduction for this paper and for subsequent papers that will surely ensue, trying to describe the shape of space.
Topology for everyone
Loads of fun Weeks starts out by explaining surfaces and the quotient space descriptions of the torus and klein bottle. Later chapters describe 3manifolds, fibre bundles(!), and the 8 geometries relevant to Thurston's geometrization conjecture. The focus of the book is on applying these concepts to investigating the shape of our spatial universe. This is a particularly apt goal, given that many times in the book the reader is asked to imagine living in various kinds of spaces. He has a very good set of exercises designed to increase one's visualization powers. For example, in the chapter on 3manifolds, he has the reader color various covering space pictures of 3manifolds like the 3torus, according to some specifications; this really helps one understand how covering maps work. As someone who was familiar with topology before reading the book, I can say that the book has definitely increased my understand of 3manifolds, which is more than I can say for most topology books. In particular, I found the material on fibre bundles very enlightening.
Straight talk about curved space Jeffrey Weeks, a MacArthur ("genius grant") fellow and a consultant to NASA on cosmological observations, believes that there's no reason why a liberal arts student or a high schooler shouldn't be able to have a solid understanding of the answers to these questions, even though some of them are at the edge of research in cosmology and threemanifolds, and others have traditionally not been part of the math curriculum before graduate school. The math is presented at an elementary level, but it is genuine mathematics. Readers in the intended audience must be prepared to roll up their sleeves; there are exercises, and there are formulas, and their minds will be stretched. But there are no prerequisites other than a little firstyear algebra, and the discussion stays at a vividly concrete level, with a plethora of diagrams to aid the swelling imagination. High schoolers will benefit from some guidance getting through it; it's appropriate for undergraduate selfstudy. More mathematically sophisticated readers, even those who've taken a course in algebraic topology or differentiable manifolds, will find the book a lively read, but will still probably learn a thing or two. I, for one, was startled to be shown a Moebius strip that was twosided! (The trick is to embed it in a nonorientable threespace.) The payoff is in the final two chapters, which detail programs of astronomical observation that could well tell us the precise topology and geometry of the universe, and explain just how they would do it. One chapter is devoted to a technique based on correlating distances between galactic clusters, and the other to a statistical search for correlated arcs of great circles in the cosmic microwave background. Both observations will probably be completed within the next decade. It's an exciting prospect. Buyers note: I believe the Amazon characterization of this as a paperback is in error. I bought the second edition in hardcover at the same list price. In its (successful) attempt to avoid intimidation, it uses a large typeface, so it would fill out some 200 pages in a more typical math format. ... Read more 
20. Roads to Geometry, Third Edition by Edward C. Wallace, Stephen F. West, Edward Wallace, Stephen West  
list price: $96.00
our price: $96.00 (price subject to change: see help) Asin: 0130413968 Catlog: Book (20030717) Publisher: Prentice Hall Sales Rank: 89085 US  Canada  United Kingdom  Germany  France  Japan  
Book Description 
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