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Modern Geometry with Applications (Universitext), by George A. Jennings
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This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.
- Sales Rank: #1871989 in Books
- Published on: 2008-06-13
- Original language: English
- Number of items: 1
- Dimensions: 9.17" h x .46" w x 6.10" l, .65 pounds
- Binding: Paperback
- 204 pages
From the Back Cover
This is an introduction to the theory and applications of modern geometry. It differs from other books in its field in its emphasis on applications and its discussion of Special Relativity as a major example of a non-Euclidean geometry. Besides Special Relativity, it covers two other important areas of non-Euclidean geometry: spherical geometry (used in navigation and astronomy) and projective geometry (used in art). In addition, it reviews many useful topics from Euclidean geometry, emphasizing transformations, and includes a chapter on conics and planetary orbits. Applications are stressed throughout the book. Every topic is motivated by an application and many additional applications are given in the exercises. The book would be an excellent introduction to higher geometry for those students, especially prospective mathematics teachers, who need to know how geometry is used in addition to its formal theory.
Most helpful customer reviews
4 of 4 people found the following review helpful.
An inspiring inducement to study more geometry
By jeremy
I really enjoyed this book. The first thing I saw in it was the beautiful generalization of the Pythagorean Theorem by Pappas of Alexandria which inspired me to create a dynamic version of that proof in Geometer's Sketchpad. I also enjoyed the planimeter proof which is a very nice application of first year calculus.
This year, as a high school teacher, I have been teaching spherical geometry using this text. It was a lot of fun using the cross product to get dual triangles and the exercises are just right. It was fun to graph dual triangles on the sphere using Maple--a nice project for students. I also like his introduction to map making--the treatment of conformal mappings with its dilation of infinitesimal triangles was intriguing.
Although I am using Courant-Robbins for projective geometry, I like the way Jennings introduces the subject via perspective drawing and he also goes into algebraic curves at the end of that chapter.
I'm not crazy about the section on relativity. It doesn't have Lorentz or Loedel diagrams and doesn't discuss proper time. I like to see the development of the Lorentz equations using hyperbolic trig functions which makes their derivation more natural.
I don't agree with the reviewer who pans this book for being non-rigorous. This book does a fine job of introducing some fascinating geometry and will, if anything, inspire students to study more in-depth treatments of the same material. I think it develops a fine mathematical intuition, whereas too much rigor may very well have the opposite effect.
I give it five stars because it does a good job of addressing the needs of bright high school students and inspiring them. I missed this book when one of my students ran off with it and was glad I could find a replacement copy.
13 of 15 people found the following review helpful.
Excellent elementary introduction to modern geometry
By G.B.S
I am a Ph.D student in the field of symplectic geometry and topology. This book introduces the foundations of modern geometry in a beautiful and a very clear way,and I am saying this having some experience with geometry and topology books. If you are a skilled high school student or an under graduate student for mathematics or related area,this is a good book to start with in understanding what is modern geometry. The level of the book is about undergraduate level using very elementary notions. The content of the book is: Euclidean geometry and its logical foundations(so one could understand the motivation of the other geometries), Sphirical geometry,conic sections,Projective geometry,and the ending chapter is about the geometrical foundations of special relativity. The approach is not theorem-proof style but rather a more intuitive approch!. This is a recommended book.
3 of 5 people found the following review helpful.
No
By Kevin C
This was the assigned textbook for a second-year Geometry course I took during my undergrad. I did exceptionally well in the course, but not because of this textbook. On the contrary, the only time I ever used this textbook was when I had homework assigned out of it or I tried to decipher the book with the aim of supplementing my notes from class - the latter of which it was nearly useless for. Instead of going into detail, I'll list the pros and cons.
Pros:
-For those with little math background who just want to know what "modern geometry" is and is used for, this might be helpful.
-The section of Euclidean and spherical geometries are acceptable (except for some extensive hand-waving in the latter area).
-It's cheap.
Cons:
-The section on isometries is a complete joke. For a textbook that comes back to them time and time again to use them in proofs this is unacceptable.
-The author often goes for an "draw a picture" approach to proofs - usually on more complicated details.
-I was really looking forward to the section on projective geometry...
Conclusion: If you're in pure Math, there's no point buying this textbook. It will just frustrate you and you'll end up learning everything off of Wolfram Mathworld or if you're learning Geometry in a classroom, you'll go see your prof. during his office hours every time he assigns you homework.
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