An Introduction to Mathematical Cosmology [Hardcover]

J. N. Islam (Author)

Book Description

Publication Date: December 17, 2001 | ISBN-10: 0521496500 | ISBN-13: 978-0521496506 | Edition: 2

This book provides a concise introduction to the mathematical aspects of the origin, structure and evolution of the universe. The book begins with a brief overview of observational and theoretical cosmology, along with a short introduction of general relativity. It then goes on to discuss Friedmann models, the Hubble constant and deceleration parameter, singularities, the early universe, inflation, quantum cosmology and the distant future of the universe. This new edition contains a rigorous derivation of the Robertson-Walker metric. It also discusses the limits to the parameter space through various theoretical and observational constraints, and presents a new inflationary solution for a sixth degree potential. This book is suitable as a textbook for advanced undergraduates and beginning graduate students. It will also be of interest to cosmologists, astrophysicists, applied mathematicians and mathematical physicists.

Editorial Reviews

Review

"The writing style is clear, concise, and quite technical.... Recommended." Choice

Book Description

This book provides a concise introduction to the mathematical aspects of the origin, structure and evolution of the universe. After a brief overview of cosmology and general relativity, the book moves on to discuss more advanced topics. This new edition takes into account the advances that have been made in the field in recent years, and includes much new material. Suitable as a textbook for beginning graduate students, the book will also be of interest to cosmologists, astrophysicists, applied mathematicians and mathematical physicists.

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Product Details

• Hardcover: 262 pages
• Publisher: Cambridge University Press; 2 edition (December 17, 2001)
• Language: English
• ISBN-10: 0521496500
• ISBN-13: 978-0521496506
• Product Dimensions: 9.1 x 6.1 x 0.7 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #3,493,107 in Books (See Top 100 in Books)

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6 of 6 people found the following review helpful:

3.0 out of 5 stars More of a Review Than an Introduction, November 1, 2000

By 

Andy Gregory (Cleveland England) - See all my reviews

This review is from: An Introduction to Mathematical Cosmology (Paperback)

This book presents a review the basics of mathematical cosmology. For example a review of basic general relativity (a co-ordinate approach) is presented early on (Chapter 2). There are no exercises or problems. You could not learn general relativity from this.The discussion of the geometric and kinematic properties of the RW metric were good. Sufficient material is presented for reviews of standard cosmological models in chapters 3 and 5 although the material concerning the relativistic Friedmann models is covered much more clearly in Foster and Nightingale with the same end results and nice do-able exercises.. Chapter five presents a review of models with a cosmological constant.Some exact solutions (original work by the author) are presented. Rather frustratingly, solutions of some equations are presented with no hints at all as to how they are arrived at. Some approximate relationships are stated without suggesting how they are taken.This makes independent study of the book frustrating at times.There are two chapters later on that present the material from the mathematical supplement to Weinberg's 'three minutes' book in more detail. These are quite fun and could be dipped into independently. I bought this book 'hardback at paperback price - 14.95' which was fair. I would not pay the full price for this book - save up and get Weinberg's Gravitation and Cosmology or get it from the library. It is not really suitable for independent study.

5 of 6 people found the following review helpful:

5.0 out of 5 stars Interesting mathematical treatment of topics in cosmology, December 27, 2004

By 

Jill Malter ([e-mail]) - See all my reviews

This review is from: An Introduction to Mathematical Cosmology (Paperback)

Some books on cosmology specialize in stating the concepts while keeping the mathematics to a minimum. Others state everything in more mathematical terms. Yet others are textbooks which get one to practice the mathematics. This book takes a different approach from any of these.

To understand cosmology, one needs to know some mathematics. And that would be true even if we knew all the answers to our questions. Given that there are actually multiple models of the universe that are being used and debated, it is even more important to see the mathematics that gets used to characterize them.

Still, this is not a textbook with problem sets. It is more of a review text in some areas (particularly general relativity), and a supplementary book in others. It addresses several important topics in cosmology in useful detail.

The book begins with an overview of cosmology and a review of general relativity. Then Islam spends a significant amount of time on the Robertson-Walker metric, with two different derivations of it. Next, we look at Friedman models of the universe. And then, we look at observational cosmology, with estimates and ranges for the Hubble constant and the resulting age of the universe (which hopefully comes out larger than the ages of the stars and galaxies).

After that, Islam discusses models with a cosmological constant. That's a good idea given that in the last few years, we have obtained more and more evidence for the existence of this (or of a dark energy term). He then includes an interesting chapter on singularities.

After this, there are chapters on the early universe. That means the temperature of the early universe and big bang nucleosynthesis. And we find out about the amounts of primordial helium and deuterium (I think these are still very intriguing issues). The author also shows us a variety of inflationary models (I had fun comparing this chapter with what Roger Penrose said about inflation in "The Road to Reality"). Islam then gives a brief account of quantum cosmology, including a mention of the Hartle-Hawking proposal for the wave function of the "ground state" of the universe.

The book concludes with a chapter about the distant future of the universe, including black hole evaporation and proton decay. While such a section may seem speculative and unsophisticated, I think such topics are a genuine part of cosmology.

This is a useful book, and I recommend it as a supplement to almost any cosmology text.

1 of 4 people found the following review helpful:

5.0 out of 5 stars Loved every page, September 22, 2010

By 

mh311 - See all my reviews

This review is from: An Introduction to Mathematical Cosmology (Hardcover)

I picked this book up in the science library. Now I'm studying astrophysics. Get the picture?