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    $155.56 $108.93
    1. Calculus With Analytic Geometry,
    $102.00 $45.00
    2. Topology (2nd Edition)
    $105.33 $69.98
    3. Calculus (8th Edition)
    $105.00 $78.95
    4. Basic Mathematical Skills with
    $84.84 $82.00
    5. Geometry for Enjoyment & Challenge
    $10.17 $8.33 list($14.95)
    6. The Golden Ratio : The Story of
    $100.00 $44.59
    7. Differential Geometry of Curves
    $93.56 $67.99
    8. Elementary Geometry for College
    $6.09 list($19.95)
    9. Geometry and Trigonometry for
    $28.99 list($118.00)
    10. College Algebra and Trigonometry
    $39.95 $31.00
    11. The Geometer's Sketchpad: Student
    12. Geometry of Differential Forms
    $13.59 $10.00 list($19.99)
    13. Geometry for Dummies
    $55.00 $52.69
    14. Geometry, Topology and Physics
    $75.00 list($106.50)
    15. Geometry (Mathematics Series)
    $139.95 $111.96
    16. Handbook of Discrete and Computational
    17. Trigonometry Problems: From the
    $79.95 $58.98
    18. Elliptic Curves (Graduate Texts
    $59.95 $40.47
    19. The Shape of Space
    $96.00 $72.87
    20. Roads to Geometry, Third Edition

    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 (2002-01-01)
    Publisher: Not Avail
    Sales Rank: 18446
    Average Customer Review: 4.59 out of 5 stars
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    Book Description

    Designed for the three-semester 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 computer-generated graphics (Third Edition), to include exercises involving the use of computers and graphing calculators (Fourth Edition), to be available in an interactive CD-ROM 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 all-new set of text-specific videos.

    • P.S. Problem-Solving Sections, an additional set of thought-provoking exercises added to the end of each chapter, require students to use a variety of problem-solving skills and provide a challenging arena for students to work with calculus concepts.
    • Getting at the Concept Exercises added to each section exercise set check students' understanding of the basic concepts. Located midway through the exercise set, they are both boxed and titled for easy reference.
    • Review Exercises at the end of each chapter have been reorganized to provide students with a more effective study tool. The exercises are now grouped and correlated by text section, enabling students to target concepts requiring review.
    • The icon "IC" in the text identifies examples that appear in the Interactive Calculus 3.0 CD-ROM and Internet Calculus 2.0 web site with enhanced opportunities for exploration and visualization using the program itself and/or a Computer Algebra System.
    • Think About It conceptual exercises require students to use their critical-thinking skills and help them develop an intuitive understanding of the underlying theory of the calculus.
    • Modeling Data multi-part questions ask students to find and interpret mathematical models to fit real-life data, often through the use of a graphing utility.
    • Section Projects, extended applications that appear at the end of selected exercise sets. may be used for individual, collaborative, or peer-assisted assignments.
    • True or False? Exercises, included toward the end of many exercises sets, help students understand the logical structure of calculus and highlight concepts, common errors, and the correct statements of definitions and theorems.
    • Motivating the Chapter sections opening each chapter present data-driven applications that explore the concepts to be covered in the context of a real-world setting.

    ... Read more

    Reviews (17)

    5-0 out of 5 stars Calculus With Analytic Geometry
    This is an excellent book with lots of examples. First a concept is introduced, then an example given, and then the student can work problems relating to the section to reinforce the concepts presented.

    Easy to read, and nice progression of topics.

    4-0 out of 5 stars Good book but NOT for a math major
    I have to agree that larson's calculus is a very comprehensive calculus text. It includes a lot of material and applications.

    If you are going to selfstudy calculus, i have some advices:
    1 Not every section is necessary. Some sections are mainly about applications in mechanical engineerings(actually, most applications). If you are not interested in ME, just skip them.

    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.

    5-0 out of 5 stars Refer to other editions 0618141804
    Checkout the 7th edition without a CD. Slightly different listing. Copied below....
    * Hardcover: 182 pages ; Dimensions (in inches): 11.25 x 1.75 x 9.00
    * Publisher: Houghton Mifflin Company; 7th edition (July 1, 2001)
    * ASIN: 0618141804
    * In-Print Editions: Hardcover (7th Bk&Cdr) | Paperback (4th) | All Editions
    * Average Customer Review: Based on 16 reviews. Write a review.
    * Sales Rank: 857,204
    (Publishers and authors: improve your sales)

    4-0 out of 5 stars Good but problems were too easy
    Not bad at all! I found the book's explanations pretty easy to understand.

    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.

    5-0 out of 5 stars Calculus
    I've worked with several calculus books over many years and this is the CLEAREST and most staightforward of all. It makes the concepts seem so obvious and simple, where many other books make them appear arcane and mysterious (even to me, and I love this stuff.) It's a joy to read and work with. ... Read more

    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 (1999-12-28)
    Publisher: Prentice Hall
    Sales Rank: 48786
    Average Customer Review: 4.74 out of 5 stars
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    Book Description

    This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures.GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness.Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory.For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications. ... Read more

    Reviews (23)

    5-0 out of 5 stars Standard Topology Text
    Most people have a favorite color, fewer people have a favorite baseball team, and even fewer people have a favorite topology textbook. Granted I've only had an extensive relationship with this particular textbook, but given the reviews I've read and other recommendations I've recieved, I would have to go on record and vouch for this book.

    When I took topology this text was recommended and our lectures were based on a book (which was required) compiled by the teacher. Often times, we found the lectures/required text to be lacking and were glad to have this text to refer to.

    I've seen this book used for both point-set and algebraic topology courses, or some combination of the two. The coverage of point-set is fairly complete while the algebraic section covers introductory material (homotopy, fixed point theorem, lifts, fundamental groups, etc.). The breakdown of the material is approximately 65% Point-set and 35% algebraic thus making it a good choice for someone taking Point-set but personally motivated to glance ahead to some of the algebraic stuff.

    Two particular strengths: A thorough introduction to basic concepts of analysis, and, because you don't see many of them around, a good introductory treatment of Algebraic Topology.

    5-0 out of 5 stars A Great Work
    Taking a first course in topology could not be better complemented. This clear exposition of point set and algebraic topology is so well written that it could even be used for self study. Motivation from the professor is always helpful, but Munkres actually goes quite far in providing a reason for the topics in question. Furthermore, the examples clarify many of the presented concepts and even show some of the misconceptions a student may have.

    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.

    5-0 out of 5 stars great!
    Not much to add here... there are enough easy problems that I can get the hang of something, but also some really tough ones at the end of each problem section. The proofs and examples in the text are really good guides to doing the problems also. In some sections there are counterexamples for, say, the converse of a theorem which are always really pathological. At the beginning of each section there is some discussion on what to expect, why the stuff is important, what to do with it, etc. Even though I had a really good prof for the topology course I did this book was very helpful out of the classroom.

    5-0 out of 5 stars Excellent Topology Book
    My introduction to Munkres was in an independent study of point set topology in my final semester of undergraduate work. A professor assigned me problems from the book, but my learning was largely self motivated. I found that it was an excellent book for independent study. The text was clear and readable and the exercises helped to cement the concepts that are introduced in the reading.

    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.

    5-0 out of 5 stars Wonderful text in a poor binding
    As far as contents is concerned, this is a wonderful textboot for self-studying topology. Full of examples and a bit slow-paced, it describes even the 'clever' proofs (like Tichonoff's theorem) so that it makes their core ideas come naturally. The selection of topics is superb (algebraic topology has a much wider coverage than in the 1st edition).

    The only drawback, and it is a serious one, is the binding. For a well-selling 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 (1999-09-27)
    Publisher: Prentice Hall
    Sales Rank: 5427
    Average Customer Review: 3.5 out of 5 stars
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    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, up-to-date 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 no-nonsense, concisely written book.

    ... Read more

    Reviews (12)

    2-0 out of 5 stars Buy Swokowski's Calculus instead.
    It's hard to believe that this puzzling, error-filled book is in its 7th edition.

    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 throw-away 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, 900-page, loose-leaf folder. Overall, not a book I enjoyed spending time with.

    4-0 out of 5 stars good but solutions manual is a must have
    This is a good book for calculus. I usually go to class and do not undestand the professor because he speaks a different language then come home and figure it out from the book. The solutions manual is a must have for this course unless you have an excellent teacher or tudor. I find it helpful to check my problems half-way through completing them to make sure I am on the right track. And when I do not understand the text book instructions, the solutions manual usually puts me on track.

    5-0 out of 5 stars Classic "Attachable" book
    Requirements for all books should be;

    (a). being able to feel attachment for.
    (b). clearly understandable to readers in the assumed level.
    (c). benefitial to buy and read.
    (d).[equivalent to (a), (b), and (c)]. unique.

    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 down-to-earth 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.

    1-0 out of 5 stars Calculus 8th Edition Varberg, Purcell, Rigdon
    This book stinks. Most of the positive reviews came from mathematicians not from students that have to study from this book! My fear of calculus is worsen after using this book. For someone who try to make it though college and working her tails off this book isn't helping. I'm not saying that it have to be easy, but there are so many erros in this book that I wasted my time trying to figured it out how to solve some problem that isn't even correct! Many students told me that have they not been taking calcus before, they probably won't pass the class. This book doesn't give good method of how it goes from point A to point B. There were a number of times where I would stare at the pages, wondering how the book came up with the answers, (was it magic). Another very annoying thing about this book is giving the easiest example problems that it can. This can really screw me over when it gives an oversimplified example for a theorem, and then in the problem set, there isn't any guide of how I can solve it. There were alot of problems that I couldn't even start because this book didn't give me adequate explanations or examples! Bottom line is, I don't think I'm that stupid, but this book really hurt myself esteem.

    3-0 out of 5 stars Perhaps the best out there...but that's not saying much...
    I am in something of a unique position to critique this book. You see, I have, due to the fact that I attended different schools and therefore had different teachers for Calculus I, II, and III, been forced to buy three different ... calculus textbooks.

    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 (2004-04-20)
    Publisher: McGraw-Hill Science/Engineering/Math
    Sales Rank: 17242
    Average Customer Review: 4.0 out of 5 stars
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    Book Description

    Maintaining its hallmark features of carefully detailed explanations and accessible pedagogy, this edition also addresses the AMATYC and NCTM Standards. In addition to the changes incorporated into the text, a new integrated video series and multimedia tutorial program are also available. Designed for a one-semester basic math course, this successful worktext is appropriate for lecture, learning center, laboratory, or self-paced courses. ... Read more

    Reviews (1)

    4-0 out of 5 stars try doing the tests on MathZone
    The book and the publisher's MathZone show a nice attempt at integrating the power of the Internet with a traditional maths text. The material is for high school readers. You can of course treat the book just as a conventional text, and refrain from accessing MathZone. In this respect, the book is well polished, being in its 6th edition, and very logically internally consistent. As befits Euclidean geometry.

    Now if you do want to use MathZone, what to do at the website? Perhaps the most fruitful approach, if you are disciplined enough, is to take those tests offered there. In addition to doing the exercises in the book, of course. The tests are a valuable metric of how well you comprehend the material. The authors and publisher have put a lot of time into MathZone. Go for it! ... Read more

    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 (1991-06-01)
    Publisher: Mcdougal Littell/Houghton Mifflin
    Sales Rank: 18448
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    6. The Golden Ratio : The Story of PHI, the World's Most Astonishing Number
    list price: $14.95
    our price: $10.17
    (price subject to change: see help)
    Asin: 0767908163
    Catlog: Book (2003-09-23)
    Publisher: Broadway
    Sales Rank: 1405
    Average Customer Review: 3.9 out of 5 stars
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    Book Description

    Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!

    The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose.Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.
    ... Read more

    Reviews (40)

    5-0 out of 5 stars Pursuing the Mysteries of the Ubiquitous Number Phi
    Mario Livio, a cosmologist and art aficionado at the Hubble Space Telescope Center and the author of the previous book "The Accelerating Universe," wrote a lot about the irrational (never-ending, never-repeating) number phi, or the Golden Ratio, whose value is 1.6180339877... The story starts from these questions: Who discovered the Golden Ratio? Was phi used in the design of a Babylonian stela and Egyptian pyramids? The author pursues the answers to these questions, writing a series of his thoughts like a detective story.

    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.

    5-0 out of 5 stars Golden Indeed!
    Following in the steps of his earlier, just as fascinating account linking cosmology and the arts ("The Accelerating Universe"), Mario Livio continues to prove he is one of the most original, exciting and literate writers of popular science today. "The Golden Ratio" is a witty and learned journey generally following the trail of the number Phi, but stopping along the way to take in subjects as diverse as philosophy, history, art, religion, the sciences, architecture, etc.

    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.

    5-0 out of 5 stars A Difficult Mathematical Concept Revealed
    As a non-mathematician I appreciate any help I can get in understanding the more esoteric parts of math. The Golden Ratio is just such a concept. Fortunately, Mario Livio has shown much light on this remarkable corner of geometry in his book "The Golden Ratio."

    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 far-fetched relationships, as to the so-called 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 non-mathematicians, the gist is available to all with some effort.

    Read this book to learn about the history of interpretation and misinterpretation of mathematical concepts.

    4-0 out of 5 stars A great guide to an amazing number
    Livio's book is really an interesting look at a number similar to pi in that's an irrational number which displays itself in various places in nature, from the arrangement of petals on a flower to the logarithmic spirals of galaxies.

    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".

    5-0 out of 5 stars Mathematically Profound
    Broad streams of literary, historical, aethsetic and religious thought are pooled together in a concise and well-illustrated review of this powerful proportion, which recurs in the natural world in surprising places both large and small. Clearly presented mathematical proofs give the book a solid backbone. Mathematical ideas are expressed in the book through a combination of prose, appendix proofs, and plentiful illustrations & diagrams. This allows readers of varying mathematical ability and learning styles to appreciate the beautiful ideas that Livio gracefully presents. A must for serious lovers of proportion & geometry, architects, mystics, painters, graphic designers and mathematicians. ... Read more

    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 (1976-02-01)
    Publisher: Prentice Hall
    Sales Rank: 109376
    Average Customer Review: 3.8 out of 5 stars
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    Reviews (10)

    5-0 out of 5 stars Excelent exposition !
    I used this book during my MsC in Math at University of Brasilia, Brazil. Manfredo gives a detailed exposition about the local and global properties of a surface and introduces the abstract surfaces at the end of the book. I really recommend this book for a first course in Differential Geometry and it gives a good knowledge to read the Riemannian Geometry(Manfredo).

    4-0 out of 5 stars Excellent introduction to differential geometry
    I found this book to be a good introduction to differential geometry for undergraduates. All concepts are clearly and concisely developed and explained well. Also, the details of advanced calculus and analysis required for the book are covered very well in appendices. My only reservation is that the problems can be very difficult at first. For someone interested in really exploring and learning differential geometry, however, this is not a problem.

    2-0 out of 5 stars Very Difficult
    Although some claim it is classic, don't expect it to be readable. The book's definitions cna be quite confusing, and it is often difficult to understand many of the definitions or problems without a great deal of effort. If you are using this book for a class, I would reccomend getting a more readable text for reference.

    3-0 out of 5 stars too wordy
    Many people say that this is an excellent book on elementary Differential Geometry,so I borrowed one.I read most of chapter1-4,but I do not find it clear enough.Maybe I have been confused by so many examples.It is too wordy for me.It can be more concise.I recommend the book of Klingenberg,which is used as my textbook.Klingenberg'book is a little dense and does not contain enough exercises.But your professor will give you some.

    1-0 out of 5 stars Outdated classic in the field
    While many consider this text the classic in the field, I think that it's time to find something a bit more modern. do Carmo often skips steps in his proofs or examples that he deems "obvious" but that my professor even had to spend a good deal of time trying to figure out how to bridge the gap. The writing style and terminology are beginning to show their age, and the exercises are particularly incomprehensible. Also, the few examples that are actually included don't give any insight into doing the exercises, which seem to be written primarily as a way for do Carmo to include topics that he couldn't squeeze into the body of the text. The hints in the back of the book are often too vague to provide any useful insight into solving the problem, especially for someone not familiar with geometry. Hope that you don't have to use this text for a first course in differential geometry, and if you do, hope that the professor writes his/her own exercises. ... Read more

    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 (2002-07-01)
    Publisher: Houghton Mifflin Company
    Sales Rank: 351807
    Average Customer Review: 1 out of 5 stars
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    Book Description

    The Third Edition of Elementary Geometry for College Students covers the important principles and real-world 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 college-level students, this text offers a welcome alternative for instructors who, in the past, have had to use secondary-level texts for this course.

    • Videotapes, professionally produced for this text and hosted by Dana Mosely, offer a valuable resource for further instruction and review.
    • Reminder marginal notes reinforce theorems or formulas from previous chapters to help students progress through the course.
    • Enhanced Chapter Openers introduce students to the principle notion of the chapter and provide real-world context.
    • Discovery features designed to reinforce the inductive approach of this text include activities that enable students to discover geometry concepts on their own and section tools that provide students with hands-on application of concepts.
    • Applications throughout text reinforce the connection of geometry to the real world. A Look Beyond chapter-ending sections provide engaging sketches, sometimes with historical background.
    • Summaries of constructions, postulates, and theorems are provided to reinforce learning. In addition, a numbering system for postulates and theorems presents a user-friendly structure.

    ... Read more

    Reviews (1)

    1-0 out of 5 stars A Wretched and Horrid Book
    Entering geometry for the first time ever can be an almost initimidating venture, especially for the first time geometry student. After conquering other mathematical courses successfully (like algebra and statistics), I presumed entering "Elementary Geometry for College Students," based on being given exceptional required texts from previous courses, would be a breeze. Oh how wrong I was!

    "Elementary Geometry for College Students," by Daniel C. Alexander (of Parkland College) and Geralyn M. Koeberlein (of Mahomet-Seymour 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 quick-step 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 pre-geometry 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 real-life 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 Self-Teaching Guides)
    by Peter H.Selby
    list price: $19.95
    (price subject to change: see help)
    Asin: 0471775584
    Catlog: Book (1975-04-18)
    Publisher: Wiley
    Sales Rank: 90991
    Average Customer Review: 3.58 out of 5 stars
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    Book Description

    Geometry & Trigonometry for Calculus By Peter H. Selby If you need geometry and trigonometry as a tool for technical work … as a refresher course … or as a prerequisite for calculus, here’s a quick, efficient way for you to learn it! With this book, you can teach yourself the fundamentals of plane geometry, trigonometry, and analytic geometry … and learn how these topics relate to what you already know about algebra and what you’d like to know about calculus. You’ll work your way through geometry, numerical trigonometry, methods of trigonometric analysis, analytics, and limits—all the way up to the "front door" of calculus. Geometry and Trigonometry for Calculus is one of the Wiley Self-Teaching Guides. It’s been tested, rewritten, and retested until we’re sure you can teach yourself the concepts of geometry and trigonometry. And it’s programmed—so you work at your own pace. No prerequisites are needed. Objectives and self-tests tell you how you’re doing and allow you to skip ahead or find extra help if you need it. Frequent reviews and practice exercises reinforce what you learn. Wiley Self-Teaching Guides Astronomy, Moche Basic Physics, Kuhn Chemistry: Concepts and Problems, Houk How to Succeed in Organic Chemistry, Gordon Basic Electricity, Ryan Electronics, Kybett Ecology, Sutton Energy for Life, Allamong Plant Anatomy, Stevenson Quick Medical Terminology, Smith Human Anatomy, Ashley Dental Anatomy and Terminology, Ashley Math Skills for the Sciences, Pearson Thinking Metric, 2nd ed., Gilbert Using Graphs and Tables, Selby Geometry and Trigonometry for Calculus, Selby Quick Calculus, Kleppner BASIC, 2nd ed., Albrecht BASIC for Home Computers, Albrecht ANS COBOL, 2nd ed., Ashley Structured COBOL, Ashley Fortran IV, Friedmann, Greenberg & Hoffberg ATARI BASIC, Albrecht TRS-80 BASIC, Albrecht Job Control Language, Ashley Flowcharting, Stern Introduction to Data Processing, 2nd ed., Harris Background Math for a Computer World, Ashley Probability, Koosis Statistics, 2nd ed., Koosis Finite Mathematics, Rothenberg Practical Algebra, Selby Quick Arithmetic, Carman Math Shortcuts, Locke Study Skills: A Student’s Guide for Survival, Carman Psychological Research: How to Do It, Quirk Psychology of Learning, Royer Choosing Success: TA on the Job, Jongeward Successful Time Management, Ferner Communication for Problem Solving, Curtis Skills for Effective Communication, Becvar Clear Writing, Gilbert Punctuation, Markgraf Vocabulary for Adults, Romine Spelling for Adults, Ryan Reading Skills, Adams Art: As You See It, Bell Your Library —What’s in It for You? Lolley Quickhand, Grossman Quick Typing, Grossman Consumer Math, Locke ... Read more

    Reviews (12)

    4-0 out of 5 stars The Pleasure of Finding Things Out
    Like many people, I didn't learn anything in any significant way in high school, so later in life I found out I lacked the necessary mathematical skills to pursue my interests in science.

    Looking to fill that void I got this book and its companion introductory volume, Peter Selby and Steve Slavin's "Practical Algebra: A Self-Teaching 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 self-contained 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 well-rounded 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!!

    5-0 out of 5 stars EXCELLENT! Wish I would have had this author teaching me.
    There is no such thing as a student who is "slow" in understanding. There is however a teacher who does not master the art of communicating. A good student memorizes in order to pass a grade. A slow student is normally bugged by the "why" of everything. However I have had the honor of solving engineering problems for students from MIT and other top Universities because my professors were able to explain the "why" to 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.

    1-0 out of 5 stars Bummer
    Content is fine. Binding is not.
    The book is falling apart.

    1-0 out of 5 stars good as a companion only
    If you want to test your knowledge of geometry and trig after reading another text book, this is good. However, this is not a standalone book. It offers problems and answers, but very little in examples and explanations of why.

    Unless you want a refresher, I'd go somwhere else, maybe a dummies or idiots guide instead.

    2-0 out of 5 stars There aren't enough exercises..
    The best and most enjoyable way to learn math is through practice, and although Peter H. Selby articulately explains the concepts presented in this book, there just aren't enough exercises for you to "teach yourself" the subject. A given section on plane geometry will give you about 15 abstract principles followed by 5 easy practice exercises. I have learned from this book, but in order to do so, I've had to make flashcards and do lots and lots of rereading to help me memorize the vocabulary and rules. This book would be okay for someone who just needs a quick refresher, but if you really want to learn the material, I would suggest buying separate 350-400 page books for each subject. ... Read more

    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 (2000-11-08)
    Publisher: Addison Wesley
    Sales Rank: 345551
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    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 (2002-08-01)
    Publisher: Key Curriculum Press
    Sales Rank: 196302
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    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 (2001-09-01)
    Publisher: American Mathematical Society
    Sales Rank: 449934
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    Book Description

    Since the times of Gauss, Riemann, and Poincaré, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms.

    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 Chern-Weil 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 (2001-09-15)
    Publisher: For Dummies
    Sales Rank: 13620
    Average Customer Review: 4.2 out of 5 stars
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    Book Description

    You know that geometry is a math thing, right? You remember that much from school. You also probably remember that it has something to do with circles, squares, diameters, angles, and all those other terms that floated in (and probably right out of ) your head as you were cramming for all those geometry tests way back when. But your math teacher probably never told you that you'd actually use that stuff in real life – if he had, maybe you would have paid more attention!

    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, easy-to-understand, non-textbook-like style, this book helps you with all your geometrical dilemmas.

    In Geometry For Dummies, you'll find out about the following topics and more:

    • Understanding lines and angles
    • Working up a geometry proof
    • All those funny shapes: circles, rectangles, triangles, and the ever versatile polygon
    • Having your Pi and eating it, too
    • Taking the next step into trigonometry
    • Doing someone a solid: Exploring prisms, pyramids, cylinders, cones, and spheres
    • Top Ten list of cool careers that use geometry and tips for making geometry easier
    • Appendices with formulas, theorems, and other helpful geometry resources

    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)

    5-0 out of 5 stars excellent approach!!!
    The title of this book already presents a sort of contradiction, which made me laugh when I first saw it on the shelf. I bought it to solidify and deepen my understaning of this beautiful branch of science and to give me confidence in my ability to teach such beauty to young minds, eager or not. I have found it both entertaining and informative and would recommend it to anyone who has ever felt overwhelmed by the "axiomatic method" which saturates most geometry texts. If you appreciate the power and precision of mathematics and also appreciate the human nature of realistic humor, please buy this book!!!

    3-0 out of 5 stars Book is adequate
    This boox is adequate for Honors students...
    Try find some other book.
    But it's really good for practice

    4-0 out of 5 stars A Textbook, with a tinge of humour
    If you want to learn about geometry, but don't want to look through a thick, school like textbook, this is the perfect book!

    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 5-stars. 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 :) .

    5-0 out of 5 stars Thanks Amazon[.com]
    I was surfing the web, beacuase I am a computer programmer of old and know all about webspace and word processing and things. Well, anyway I found this book very helpful, especially for teaching other people, something I find very challenging. I have always been a struggler when it comes to maths and as a general rule didn't understand a word of it. But now I can get up in front of my class with confidence and teach them about squares and triangles and things without having to send people out the room for doing nothing.

    4-0 out of 5 stars Making the DRY drinkable
    I recall with anguish over 37 years ago, my 10th grade geometry class, dry as a Wadi in the Sahara. I slept through the first course obtaining a grade worthy of my snoring through an hour a day of irrelevance.
    Today some math teachers are asking why math has to be dull or academic. This book is one which revives my faith a math teacher may indeed have real blood pumping in their veins.
    This book I'd recommend to some teenagers and more so for adults, those 18 years and up who slept through geometry in high school.
    I also recommend the basics of geometry start in school much earlier than grade 10.

    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 (2003-10-01)
    Publisher: Institute of Physics Publishing
    Sales Rank: 71824
    Average Customer Review: 4.29 out of 5 stars
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    Reviews (7)

    4-0 out of 5 stars Flat spheres and more
    Highly stimulating and extremely hard to read, written for mathematicians in physics. However, the chapter on Riemannian Geometry can be worked through, up to a point, without any knowledge of exterior differential forms, and is notable if for only one fact alone: a simple calculation is provided that explains explicitly that spheres in four and eight dimensions (3-spheres and 7-spheres) are flat with torsion! I don't know another reference that a physicist without special background in math can consult to understand this highly nonintuitive fact.

    2-0 out of 5 stars Just a "better than nothing" book
    It's not the best way to learn geometry / topology for physics. It's better than nothing, though, if you are familiar with the topics already. There are many "holes" in Nakahara's book, which you would spend much more time and hard working in a "big" library. than you should to fill in. It's not worth that money and struggle. It's the last one you should consider about owning.

    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 kind-of-Bible 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.

    5-0 out of 5 stars Best in its genre
    I suppose I should preface this by saying that I read this book *after* reading similar books, so my ability to understand this book is probably better than others, but that said, I think that my comparative evaluation is free from this bias...

    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 physics-related 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.

    5-0 out of 5 stars Excellent book
    A very nice blending of rigor and physical motivation with well chosen topics. Plenty of examples to illustrate important points. Especially noteworthy is its description of actions of lie algebras on manifolds : the best I have read so far.

    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.

    5-0 out of 5 stars A must for any theoretical physicist
    With an excellent balance between mathematical rigor and pedagogical simplicity, Nakahara remarkably captures in a single volume much of the mathematics a physicist will ever need. (If he wrote a few chapters on group theory, 'much' might be replaced with 'all'). Containing as much as it does, it is not something to breeze through. Depending on your mathematical background, you may only want to read a few chapters (and if the Homology chapter is tripping you up, just keep moving). But invest the time with it, and you will be rewarded with a solid grasp of the mathematical pictures underlying most modern physics. And once you read it and see physics from this perspective, you'll be amazed you had ever thought you understood the physics it describes. It should be said, though, that some of the latter chapters, in particular 12, are horribly sloppy. There are dozens upon dozens of errors, many at a deep conceptual level. Nonetheless, it is a monumental text, and I recommend it heartily. ... Read more

    15. Geometry (Mathematics Series)
    by Harold R. Jacobs
    list price: $106.50
    (price subject to change: see help)
    Asin: 071671745X
    Catlog: Book (1987-01-01)
    Publisher: W.H. Freeman & Company
    Sales Rank: 106561
    Average Customer Review: 5 out of 5 stars
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    Reviews (5)

    5-0 out of 5 stars The best geometry textbook in existence, bar none.
    A very clear, very entertaining textbook for a high-school course on geometry.

    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.

    5-0 out of 5 stars Worked every problem
    I have no experience with other geometry books--although I did use the Schaum book and other "outline" help books early in the school year as a reference. Actually Jacobs was easier to use than the "outline" help books. Many problems skate close to calculus (limits are introduced) and analytic geometry. Some problems are quite nearly elegant. Highly recommended.

    5-0 out of 5 stars A Very Good Geometry Book
    A good geometry book for high school students. It teaches everything one needs to know about basic euclidean geometry with intuitive lessons and clear explinations of all the content. One thing to note though is that you need a strong understanding of the algerbraic principals of equality, and the fact that the teachers edition is very hard to come by.

    5-0 out of 5 stars Jacobs sugar-coats the process of rigorous proof!
    I really enjoyed reading this text. This book is very sensitive to students who are encountering proof for the first time. Jacobs does a great job in building the subject. His motivations and also the humor in text is what makes this book so enjoyable to read. What's more amazing is that he still maintains all the rigor that is critical for advance studies in mathematics.

    5-0 out of 5 stars My favorite high school geometry text
    Jacobs is a great teacher and he has written a book that contains much of the essence of that teaching. He presents the material well, with entertaining hooks and careful exposition. There's a good mix of approaches (transformational, intuitive, and rigorous) and a good mix of problems (easy, medium, hard, a few really hard). It's the best balanced of all the geometry texts I've seen. The one drawback is that it doesn't respond to modern trends of using more discovery-based inductive approaches, or using tools like Geometer's Sketchpad or Cabri. Michael Serra's _Discovering Geometry_ is a good source of problems and activities if you wish to supplement your course with this sort of thing. ... Read more

    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 (2004-04-15)
    Publisher: Chapman & Hall/CRC
    Sales Rank: 669866
    Average Customer Review: 4 out of 5 stars
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    Book Description

    The second edition of the Handbook of Discrete and Computational Geometry is a thoroughly revised version of the bestselling first edition. With the addition of 500 pages and 14 new chapters covering topics such as geometric graphs, collision detection, clustering, applications of computational geometry, and statistical applications, this is a significant update. This edition includes expanded coverage on the topics of mesh generation in two and three dimensions, aspect graphs, center points, and probabilistic roadmap algorithms. It also features new results on solutions of the Kepler conjecture, and honeycomb conjecture, new bounds on K sets, and new results on face numbers of polytopes. ... Read more

    Reviews (1)

    4-0 out of 5 stars Very comprehensive overview of computational geometry
    This book, written by many well-known experts in the field, is a fine compendium of articles on the most active areas of computational geometry. Each article is supplemented with a glossary of terms needed for understanding the relevant concepts and frequently contains a list of open problems. An overview of the convex hull of a collection of random points in Euclidean n-space is given in one of the articles on discrete aspects of stochastic geometry, where also a very interesting discussion of generalizations of the Buffon needle problem is given.

    There are a few articles overviewing Voronoi diagrams, such as the one on Voronoi diagrams and triangulations. The applications of Voronoi diagrams are many, and include tumour cell diagnosis, biometry, galaxy distributions, and pattern recognition. This article is a little short considering the importance of the subject.

    The article on shortest paths and networks is somewhat disappointing since there is no in-depth discussion on network routing algorithms.

    The article on computational topology highlights some of the results in this very important area. Many problems in topology have been tackled recently using computers, particularly the work of the mathematician A.T. Fomenko. Computational topology is a relatively young field, having been in existence only since the early 1990's. The applications are enormous, ranging from meshing, morphing, feature extraction, data compression, and in many scientific areas such as computational medicine, chemistry, and astrophysics. It can also be used in computer security via graphical passwords. It is an immense help in visualizing complicated topological objects, such as Lens spaces, horned spheres, and thickened knots. The article does not touch on the use of Mayer-Vietoris sequences to design efficient divide-and-conquer schemes for computing the homology of higher-dimensional complexes. The interplay between topology and finding better algorithms in computational geometry is one that will flourish no doubt in years to come.

    The last section of the book covers applications with the most interesting article being the one on sphere packing and coding theory. The algorithms in sphere packing have direct applicability to error correctiong codes over the field GF(q). The author of this article does touch briefly on general algebraic-geometric codes, which is good considering their importance in applications.

    The last article appropriately discusses available software for computational geometry. Although the list of Web sites is quite extensive, there are many more available since this book was first printed.

    A very fine addition to the literature on computational geometry and should be on everyone's shelf who is interested in this important area. ... 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 (2004-11-30)
    Publisher: Birkhauser Boston
    Sales Rank: 649205
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    Book Description

    103 Trigonometry Problems contains highly-selected 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:

    • Presentation evolves through gradual progression in problem difficulty to build and strengthen students' mathematical skills and techniques

    • Provides in-depth enrichment of problem-solving tactics and strategies, along with practical test-taking techniques, to better prepare students for possible participation in various mathematical competitions

    • 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 problem-solving 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 (2004-01-01)
    Publisher: Springer-Verlag
    Sales Rank: 727518
    Average Customer Review: 5 out of 5 stars
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    Book Description

    This book is an introduction to the theory of elliptic curves, ranging from its most elementary aspects to current research.The first part, which grew out of Tate's Haverford lectures, covers the elementary arithmetic theory of elliptic curves over the rationals.The next two chapters recast the arguments used in the proof of the Mordell theorem into the context of Galois cohomology and descent theory.This is followed by three chapters on the analytic theory of elliptic curves, including such topics as elliptic functions, theta functions, and modular functions.Next, the theory of endomorphisms and elliptic curves over infinite and local fields are discussed.The book then continues by providing a survey of results in the arithmetic theory, especially those related to the conjecture of the Birch and Swinnerton-Dyer.

    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 Calabi-Yau 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)

    5-0 out of 5 stars An excellent update to the first edition.
    Anyone who has studied elliptic curves appreciates their beauty and the richness of the mathematics that arises from such a study. This book, first published in 1987, has three additional chapters that reflect some major applications of elliptic curves since then. Indeed, the resolution of Fermat's Last Theorem due to Andrew Wiles and the use of a generalization of elliptic curves, called Calabi-Yau manifolds, in string theory have all taken place since the time of publication. The review here will be confined to these chapters.

    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 l-adic 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 l-adic 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 Calabi-Yau varieties, which are higher dimensional analogs of elliptic curves, and which have become very important in high-energy 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 Calabi-Yau manifolds, and several examples in (complex) dimension one, two, and three. He also gives examples of Calabi-Yau 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' Calabi-Yau 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 Calabi-Yau manifolds that will assist in their classification. The author does this for the case of surfaces that are Calabi-Yau, and this naturally leads to the analog of the Euler characteristic in the guise of the famous Riemann-Roch theorem. The Riemann-Roch 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 four-dimensional 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 Calabi-Yau varieties using the concept of a 'numerically effective' divisor. Some explicit examples of Calabi-Yau hypersurfaces in four-dimensional weighted projective are then given. These examples were found by string theorists, and the author therefore devotes an appendix that describes how Calabi-Yau 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 Calabi-Yau manifolds. String theory has evolved into M-theories 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 (2001-12-15)
    Publisher: Marcel Dekker
    Sales Rank: 437998
    Average Customer Review: 5 out of 5 stars
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    Reviews (4)

    5-0 out of 5 stars A clear, friendly introduction to topology
    Is space finite or infinite? Does it have borders? What shape does it have? These are among the most pressing and interesting questions in astrophysics and cosmology today. To answer (or at least understand) these questions, one must possess an understanding of topology, a branch of mathematics dealing with properties of shapes that are not changed upon deformation.

    This book is an ideal introduction to topology for beginners with little or no mathematical background. It introduces topological manifolds (especially 2- and 3-manifolds) 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 high-school 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 3-manifold, 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.

    5-0 out of 5 stars Topology for everyone
    Jeffrey wrote this book with the high school student in mind, but even as a second year student in Mathematics I found this book quite informative. Most textbooks in Analysis or Topology do not give you an intuitive feel for the subject. I recommend this book for anyone taking a course in Topology, even Graduate students.
    This book is well written with many illustrations and exercises to help you get an intuitive understanding of 3 Dimensional manifolds. This helped me a lot in my second year Analysis class as I had an intuitive notion of manifolds taught in class.
    At the same time the book is easy enough for high school students who always wondered what a Mobius strip or a Klein bottle was but did not find any books on it. This book would make Topology interesting for everyone. I give it a five star rating.

    5-0 out of 5 stars Loads of fun
    But this book can also be quite serious, although it may take someone with an extensive math background to see this. The book seems aimed primarily at high-schoolers, but graduate students in topology can definitely benefit from reading it.

    Weeks starts out by explaining surfaces and the quotient space descriptions of the torus and klein bottle. Later chapters describe 3-manifolds, 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 3-manifolds, he has the reader color various covering space pictures of 3-manifolds like the 3-torus, 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 3-manifolds, which is more than I can say for most topology books. In particular, I found the material on fibre bundles very enlightening.

    5-0 out of 5 stars Straight talk about curved space
    What is the universe as a whole shaped like? Does it curve back on itself? Does it meet itself at the other side without curving? Is its Flatland analogy a plane, or a sphere, or a doughnut, or a Klein bottle? What other, stranger geometries become possible with the added dimension? And if the universe has one of these exotic shapes, how could astronomers ever know for sure?

    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 three-manifolds, 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 first-year 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 self-study.

    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 two-sided! (The trick is to embed it in a non-orientable three-space.)

    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 (2003-07-17)
    Publisher: Prentice Hall
    Sales Rank: 89085
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    Book Description

    This new book clarifies, extends, and unifies concepts discussed in basic high school geometry courses. It gives readers a comprehensive introduction to plane geometry in a historical context.Chapter topics include axiomatic systems, axiom sets for geometry, neutral geometry, Euclidean geometry of the plane, analytic and transformational geometry, non-Euclidean geometries, and projective geometry.For anyone in need of a refresher course in geometry. ... Read more

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