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Modern Geometry with Applications (Universitext) 2nd Edition Edition

by George A. Jennings (Author)
3.5 out of 5 stars 4 customer reviews
ISBN-13: 978-0387942223
ISBN-10: 038794222X
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Product Details

  • Series: Universitext
  • Paperback: 204 pages
  • Publisher: Springer; 2nd Edition edition (June 12, 1997)
  • Language: English
  • ISBN-10: 038794222X
  • ISBN-13: 978-0387942223
  • Product Dimensions: 6.1 x 0.5 x 9.2 inches
  • Shipping Weight: 10.6 ounces (View shipping rates and policies)
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #420,380 in Books (See Top 100 in Books)

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13 of 15 people found the following review helpful
Excellent elementary introduction to modern geometry
By G.B.S on March 9, 2004
Format: Paperback
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.
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4 of 4 people found the following review helpful
An inspiring inducement to study more geometry
By jeremy on May 9, 2012
Format: Paperback Verified Purchase
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.
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3 of 5 people found the following review helpful
No
By Kevin C on February 14, 2011
Format: Paperback
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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4 of 7 people found the following review helpful
Amateurish
By Viktor Blasjo on March 20, 2007
Format: Paperback
Chapter 1 on Euclidean geometry displays the author's poor taste as well as his profound misconception of what it means to prove something. We learn on page 19 that the area of a triangle is (1/2)(base)(height). The only justification for this is that it is "often" clear by cutting and pasting. Fine. We don't have to prove every little thing. But then there follows a "proposition 1.8.1" in which Jennings supposedly "proves", by using this formula, that moving the tip of a triangle along a line parallel to the base doesn't change its area. Jennings is also very fond of isometries and use them to "prove" SAS congruence. Since the discussion of isometries is purely descriptive, with no claims to axiomatic status, this essentially amounts to saying that "the triangles are congruent because I say so", no matter how much it is padded with fancy language (let T be the isometry such that this-and-that, etc.). Although this proof is questionable, at least here Jennings is in the company of Euclid (I.4). But Jennings quickly proves himself unworthy of such dignified company by proving SSS using the cosine theorem, which is certainly not Euclid's proof (I.8). Some other parts of the book are less disastrous, especially when Jennings borrows lots of material from Courant & Robbins and Hilbert & Cohn-Vossen. Still, Jennings almost manages to destroy even these beautiful things through thoroughly tasteless exposition; the proofs typically consist of elaborate justifications of trivial details by mountains of useless symbolism while the key ideas are not addressed at all ("It is important to note that [something completely trivial]: this is because blah, blah, blah, define L(z_4*), blah, blah, blah. It is clear that [important step], so we're done."). It is also ridiculous to claim that "projective geometry blossomed during the eighteenth [century]" (p. 115).
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