An Elementary Approach to Homological Algebra (Monographs and Surveys in Pure and Applied Mathematics) [Hardcover]

L.R. Vermani (Author)

Book Description

Publication Date: May 28, 2003 | ISBN-10: 1584884002 | ISBN-13: 978-1584884002 | Edition: 1

Homological algebra was developed as an area of study almost 50 years ago, and many books on the subject exist. However, few, if any, of these books are written at a level appropriate for students approaching the subject for the first time.

An Elementary Approach to Homological Algebra fills that void. Designed to meet the needs of beginning graduate students, it presents the material in a clear, easy-to-understand manner. Complete, detailed proofs make the material easy to follow, numerous worked examples help readers understand the concepts, and an abundance of exercises test and solidify their understanding.

Often perceived as dry and abstract, homological algebra nonetheless has important applications in many important areas. The author highlights some of these, particularly several related to group theoretic problems, in the concluding chapter. Beyond making classical homological algebra accessible to students, the author's level of detail, while not exhaustive, also makes the book useful for self-study and as a reference for researchers.

Product Details

• Hardcover: 328 pages
• Publisher: CRC Press; 1 edition (May 28, 2003)
• Language: English
• ISBN-10: 1584884002
• ISBN-13: 978-1584884002
• Product Dimensions: 9.5 x 6.3 x 0.9 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,145,660 in Books (See Top 100 in Books)

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4 of 5 people found the following review helpful:

5.0 out of 5 stars Maybe not Elementary, July 31, 2005

By 

Jason Schorn "j schorn" (Spokane, WA) - See all my reviews
(REAL NAME)   

This review is from: An Elementary Approach to Homological Algebra (Monographs and Surveys in Pure and Applied Mathematics) (Hardcover)

The depth of knowledge required in order to fully appreciate the subject is indeed deep. One must possess a solid foundation in basic algebra at the level of Rotman or Hungerford. That is, you must have spent some serious time in the trenches sweating through a vast array of quality problems. Furthermore, it would be beneficial if the reader had a passing acquaintance with algebraic topology; say the later chapters of Munkres' text. Having this background will make your journey through this text more palatable and much smoother. In general, this is a very nice concise text and the author does an admirable job highlighting the core topics. In my opinion, the area in which this text is lacking is in the exercises-they are either trivial or they do not work towards extending the material-after all the sole purpose of including exercises is to test the reader's ability to "do" mathematics. Of course one could argue that because this is an "elementary" text, and hence necessarily "elementary" readers, that such problems are appropriate. But this brings me to my point, namely, Homological Algebra is not an elementary subject that should be introduced to pre-graduate level students and, to some extent, first or second year graduate students. Why? Simple, the normal run-of-the-mill student will not see the big picture.

With that said, I do recommend this text and I did enjoy reading this text. Again, for someone who has had some quality exposure to algebra I firmly believe you can make your way through the entire book and, by the end, begin to "see" the big picture of where and how Homological Algebra fits in.