A Course in Modern Geometries (Undergraduate Texts in Mathematics) Corrected Edition

by Judith N. Cederberg (Author)

5 customer reviews

ISBN-13: 978-1402006678

ISBN-10: 0387969225

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A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 introduces Euclid's geometry and the basic ideas of non-Euclidean geometry. The synthetic approach of Chapters 1 - 2 is followed by the analytic treatment of transformations of the Euclidean plane in Chapter 3. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3 - 4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. Each chapter includes a list of suggested sources for applications and/or related topics.

A Course in Modern Geometries (Undergraduate Texts in Mathematics)

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Product Details

Series: Undergraduate Texts in Mathematics
Hardcover: 232 pages
Publisher: Springer; Corrected edition (November 3, 1995)
Language: English
ISBN-10: 0387969225
ISBN-13: 978-1402006678
Product Dimensions: 0.8 x 6.5 x 9.8 inches
Shipping Weight: 12.8 ounces
Average Customer Review: 2.6 out of 5 stars See all reviews (5 customer reviews)
Amazon Best Sellers Rank: #3,463,879 in Books (See Top 100 in Books)
- #135 in Books > Science & Math > Mathematics > Geometry & Topology > Non-Euclidean Geometries
- #2042 in Books > Textbooks > Science & Mathematics > Mathematics > Geometry

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Customer Reviews

2.6 out of 5 stars

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Most Helpful Customer Reviews

20 of 20 people found the following review helpful

Good first chapter but that's it

By nennafir on November 28, 2007

Format: Hardcover

I chose this book to replace the official textbook for a course where we had been using Blau's Foundations in Geometry (which I was not entirely satisfied with.)

From Amazon, I was able to look at some excerpts from the first chapter which impressed me, so I ordered the text for the class.

The first chapter is well written and talks about the importance of models in showing consistency and independence of axioms. it contains some nice examples.

After that the book more or less falls apart. Chapter 2 talks about the inadequacies of Euclids original axiomatic system and then refers to some possible other axiomatic systems in appendices. In the second section of Chapter 2 while Euclid's problems are being discussed, there is an exercise to show that Pasch's Axiom 1 and 2 are equivalent. The exercise is impossible because the author has not defined what it means to be interior to a triangle, or even remotely addressed the issue.

For the remainder of Chapter 2, the author abandons any axiomatic framework at all and just proves various theorems about Eucilidean and hyperbolic geometry. Since axioms are not stated and terms are not adequately defined, I am not sure what the author is doing in this Chapter. To be honest, I think she is doing nothing at all. The chapter ends with an intuitive discussion of elliptic geometry.

Chapter 3 talks about geometric transformations of the Euclidean plane. It is also full of imprecise definitions, impossible exercises, and other issues. For example, in Definition 3.10 the author states "A group of transformations that keep a given line c invariant and whose translations form an infinite cyclic subgroup is known as a _frieze group_ with axis c.Read more ›

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Great book, must have.

By Huey on December 29, 2012

Format: Hardcover Verified Purchase

Great for learning introductory geometry at the advanced level. The book is concise and thorough, the proofs given are clear and easy to follow.

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0 of 1 people found the following review helpful

Worst textbook that I have ever had in my College life

By Pasang on November 13, 2012

Format: Paperback

This book is the worst book that my professor has ever chose for my math class. The definitions and theorems in this book has lack of explanations, and there are very few examples. But also the solutions of the examples doesn't make sense at all(especially on chapter 3). I want to tell my professor not to get this book for students in future. I really hate this book.

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4 of 9 people found the following review helpful

Very readable and well written!

By Physicsmind on June 5, 2008

Format: Hardcover

I studied Dr. Cederberg's text a while ago while I was at St. Olaf College. Being an ambitious youth, I was always trying to seek out the "best" book in a field to study. However, it's certainly difficult to learn from the masters if one doesn't have a solid background in the basic materials. I learned Calculus from G. Hardy's "Pure Math" but found it extremely difficult to comprehend (though it was a rewarding try). Then I turned to Spivak for a more modern treatment. In geometry, I went the opposite way: studying Cederberg's book first before moving to the more advanced one. I like her clear presentation and especially the part on matrix representations of groups of transformations. This book would be a valuable source for teachers of geometry.

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0 of 15 people found the following review helpful

Bad

By Thu Tran on December 23, 2009

Format: Hardcover Verified Purchase

The book was broken in half when it arrived. It was not because of delivery.

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