Geometry 2nd Edition by David A. Brannan (PDF)

Description

This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors’ Manual, which can be downloaded from www.cambridge.org/9781107647831.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I am a physicist and wish I had had a good undergraduate class in geometry to lay the visual foundation for much of the rest of the undergraduate math I took. This book has been a great book for establishing that foundation as well as clearly explaining the underlying language, concepts and relationships between the different geometries.This is a good place to start to really understand linear algebra, tensor analysis, transforms and differential geometry.I recently learned that before 1900, much more emphasis was placed on geometry study in undergraduate math curriculums than we get today. This book has helped to fill in what physicists have lost in not having more geometry in their undergraduate math curriculums.I used GeoGebra (an excellent, free, virus/malware free graphics application available online) in helping me visualize both the problems and the examples which was helpful in finding mistakes in calculations for the problems.

⭐I enjoyed this book and it felt like I could easily understand the material.

⭐* Physical properties of the bookThe thing that attracts me about this volume is the beautiful paper its printed on. The book is weighty, and VERY well bound considering its in paperback. Also it is printed in font size that is readable even to those who need spectacles.* Is it introductory, intermediate, or higher undergraduate level?No book can cover everything in a subject. So deciding the level its pitched at is important. Overall the balance of its explanations are starting just in A- level territory, and largely between first-year / second- year crossover studies in Geometry. The earlier parts of the book is Euclidean / Affine geometry for the first 5 chapters, and the sixth and above are Spherical geometries topics.* The authors traits throughout the book Within each of the sections, that has a steady well – designed incline in difficulty. Throughout it has a belting way of using many, many diagrams and graphs to get the ideas over to the willing to stick with it reader.* The balance of the book before chapter 6Its not an insult to say it starts in a- Level arena in the first chapters, the stuff in Conics and ellipse, parabola and hyperbola topics is expressively explained and thoroughly described graphically and in texts. I loved the ways set theory and theorems is intertwined with the affine transformations and projected geometries. Its just (i.m.h.o) Its hard to find a more descriptive manner to explain these concepts and still be useful!Also it has the useful graphical diagrams of whats going in with finding solutions to equations in the second and third dimensions using intersections between graphical planes. Its beautifully described and yet able to stand up to examination.The fun continues with explorations into expanding the projective conics surfaces in R^3 with a equation that can be used and applied in matrices 3 x 3. As this enables studies including extending the planes to include infinity. Its a model of clarity to included Mobius methods to include the extended planes and Riemann sphere and complex disks.* The balance of the book after chapter 6From chapter 6 begins ‘Non-Euclidean and Half Plane Geometries / Projective Geometries’ and it explores a denser subject in rewarding ways as it inherits the earlier information to work on the fresh explanations. Topics explored with spherical triangles, lengths of spherical translations lines / reflections / translations and areas in spherical triangles including the extended complex plane. The theoretical proofs start to become more prevalent. The level of explanations after begins to reduce as the authors bring the topics to a close by edging into Kleinian view of geometries. And in the back of the book, Appendix 3 has many fully worked examples of the problems set in the book.* SummaryThe book is beautifully printed. It explores the Geometry topics with high clarity by using diagrams and lots of supporting text in practical ways. Its well designed for the mostly first year / lesser second year undergraduate student. It will give the student a chance to help themselves in a potentially difficult area of Mathematical studies.

⭐Good use of matrices to show the principles of transformation geometry. Also coversspherical trigonometry. Ideas clearly presented throughout.

⭐Le point fort de ce livre est son plan avec son approche systématique de la géométrie. En résumé ça donne:Géométrie euclidienne -> Géométrie Affine -> Géométrie Projective -> Géométrie Hyperbolique -> Géométrique Sphérique -> Lien en toutes ces géométriesOn ne peut pas faire plus clair, et c’est le seul livre (en français ou anglais) qui a cette approche.Il est très abordable. Ce livre convient en effet à tout étudiant universitaire ou amateur de géométrie.Il se paye même le luxe d’avoir des exercices corrigés.Remarque: il n’aborde pas la géométrie différentielle directement (courbes & surfaces) mais c’est tout à faire normal car le livre est déjà épais et c’est un très gros sujet. Prenez donc un livre tel que le Do Carmo Curves & Surfaces qui complétera parfaitement celui-ci.This is an excellent book, to learn modern Geometry and classical Geometry from a modern point of view ( Erlanger program from Klein ). And modern geometry is the base, to study not only other mathematical topics, like differential geometry or topology, but also many topics in physics, like quantum physics.

⭐la maniera moderrna e coinvolgente in cui ha presentato gli argomenti e per alcune importanti novita d’impostazione metodologica.

⭐

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