Modern Geometry with Applications (Universitext) [Paperback]

George A. Jennings (Author)

Book Description

Publication Date: June 10, 1994 | ISBN-10: 038794222X | ISBN-13: 978-0387942223

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.

Product Details

• Paperback: 212 pages
• Publisher: Springer (June 10, 1994)
• Language: English
• ISBN-10: 038794222X
• ISBN-13: 978-0387942223
• Product Dimensions: 9.1 x 6.1 x 0.6 inches
• Shipping Weight: 10.6 ounces (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,117,919 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 11 people found the following review helpful:

5.0 out of 5 stars Excellent elementary introduction to modern geometry, March 9, 2004

By 

G.B.S "17" (Europe) - See all my reviews

This review is from: Modern Geometry with Applications (Universitext) (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.

4 of 5 people found the following review helpful:

2.0 out of 5 stars Amateurish, March 20, 2007

By 

Viktor Blasjo - See all my reviews
(REAL NAME)   

This review is from: Modern Geometry with Applications (Universitext) (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).

3 of 4 people found the following review helpful:

2.0 out of 5 stars No, February 14, 2011

By 

Kevin C - See all my reviews

This review is from: Modern Geometry with Applications (Universitext) (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 own class notes using parts of the textbook - the latter of which it was nearly useless for. Instead of going into detail, I'll list the pros and cons.

Pros:

-To some less mathematically literate individuals 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 "intuitive" 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. In studying pure mathematics you develop a standard of rigour in your own proofs and expect to see something comparable from authors of your primary learning material; this textbook does not inspire that.