A Mathematical Bridge: An Intuitive Journey in Higher Mathematics [Hardcover]

Stephen Fletcher Hewson (Author)

Book Description

Publication Date: August 2003

An alternative introduction to the highlights of a typical undergraduate mathematics course, this book starts from very simple levels or principles and develops in an intuitive and entertaining way. The aim is to motivate and inspire the reader to discover and understand some of the truly amazing mathematical structures and ideas which are often swamped, or usually pass unnoticed or are not fully grasped, in a higher mathematics course.

Editorial Reviews

Review

As a teacher of undergraduate mathematics I found this book to be a valuable resource ... the material is presented in an uncluttered clear style that will enable undergraduates to use the book for reinforcement and/or alternative viewpoints on the mathematics they are learning. The exercises for the reader are about at the right level for an undergraduate and the mathematics covered is not just pure mathematics but essential topics in mathematical physics and probability theory. -- Mathematical Reviews

This book is written in a way that is suitable not only for the student looking forward and the graduate in reflective mode, but also for schoolteachers seeking material on which to base their accounts of mathematics ... The book concludes with a substantial body of exercises that aims to reinforce and extend the material. -- Times Higher Education

This nicely written book invites the reader to an interesting journey into the challenging, difficult, but exciting world of undergraduate mathematics ... It has a wide selection of exercises for each chapter, suggestions for further reading, and appendices with useful background material. Reading this passionately written text shall be very helpful for those who mistakenly believe that higher mathematics is a dull and hard to understand subject. -- Zentralblatt MATH

Review

As a teacher of undergraduate mathematics I found this book to be a valuable resource ... the material is presented in an uncluttered clear style that will enable undergraduates to use the book for reinforcement and/or alternative viewpoints on the mathematics they are learning. The exercises for the reader are about at the right level for an undergraduate and the mathematics covered is not just pure mathematics but essential topics in mathematical physics and probability theory.

See all Editorial Reviews

Product Details

• Hardcover: 548 pages
• Publisher: World Scientific Pub Co Inc (August 2003)
• Language: English
• ISBN-10: 9812385541
• ISBN-13: 978-9812385543
• Product Dimensions: 9.1 x 5.9 x 1.2 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 3.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #4,967,479 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

15 of 15 people found the following review helpful:

5.0 out of 5 stars An excellent and unusual book, June 1, 2004

By A Customer

This review is from: A Mathematical Bridge: An Intuitive Journey in Higher Mathematics (Paperback)

This is a really unusual math book. The author attempts -- and, in my opinion, by and large, succeeds in -- the task of presenting pretty much most of the core elements of an undergrad math course in a descriptive and intuitive way -- he starts from counting and ends up with quantum mechanics!! This book differs from most math books by focusing foremost on the reasons why different mathematical structures exist, with the formalism following afterwards, by which time it is often quite obvious.

This book would not replace standard proof -- theorem style textbooks but supplements them very nicely by providing loads of insight and intuition -- things which usually can only be determined over time by practice. As such I'd recommend it to anyone who requires a substantial math element in their degree, and I wish that I had had a copy before I started analysis etc. at college.

One point to note is that although the text is often almost conversational, the book is really crammed with information and insights -- to read it properly requires a lot of hard work and thought. If you are just after a read about math without needing or wanting to know the details, then I would recommend that you look elsewhere.

7 of 7 people found the following review helpful:

3.0 out of 5 stars Good Idea for a Book, but Rife with Errors (See Update), May 25, 2006

By 

Romann M. Weber (Los Angeles, CA) - See all my reviews
(REAL NAME)   

This review is from: A Mathematical Bridge: An Intuitive Journey in Higher Mathematics (Paperback)

There are relatively few books on mathematics and theoretical physics that are decidedly user-friendly. Fewer still endeavor to approach their subject from a perspective significantly different from the standard textbook approach. I was therefore eager to examine Hewson's "A Mathematical Bridge," with its promise of an "intuitive journey," to see whether it could offer some fresh insights on material I already knew and perhaps shine some light on some less familiar material. I even decided to take notes while going through the book to record any ideas that the material might evoke. Sadly, my notes up to this point are largely made up of the book's errata. As a previous reviewer mentioned, some of it is simply typographical (and that does not excuse the book's editors from their oversight), though the errors that glare to the mathematically trained could serve to confuse the less prepared reader. There are also numerous errors of English that I find particularly troublesome for a book that should have been adequately proofread. Far more troublesome, however, are what appear to be errors of notation, algebraic errors, and a few faulty mathematical arguments. There are also a few other things in the book that disagree with other sources (one example being the 2x2 matrix definition of quaternions, which switches around the matrix representations of i, j, and k relative to the order presented by Arfken). Just within the book's first 80 pages, I have compiled a list of errors spanning five handwritten pages, not a very promising sign. It is a shame, since I believe the layout of the book and the plan of the covered material are both very sound. Especially considering the book's expense, I cannot recommend it to the lay reader, and I think the mathematician will only tire of its faults. I can only hope that a future edition will address and correct the errors present in this volume. For now, it is merely a book of unrealized potential, but one worthy of being given another chance.

UPDATE, 12/11/2008: The review above refers to the first edition of the book. I see that a second edition is currently planned for release in spring 2009. The good news is that the publisher's errata list for this title addresses most (but, unfortunately, not all) of my complaints from the first edition, so this should be a much-improved book when it comes out. Again, I must say that the plan followed in this book is very good; it was just its density of errors that kept me from rating it highly. Although I have not yet seen the second edition (but I hope to), I think that the Amazon reader can safely add one star to my original rating for the second edition (new rating: four out of five).

17 of 22 people found the following review helpful:

3.0 out of 5 stars Good overall, but too many small errors/typos, April 2, 2004

By A Customer

This review is from: A Mathematical Bridge: An Intuitive Journey in Higher Mathematics (Paperback)

I have not yet finished this book, but I am quite pleased with it overall. However, the author makes a number of what seem to be typos, which the editor seems to have failed to catch--mostly in the mathematical equations which show up every now and then. For example, at one point he writes R (the set of real numbers) rather than N (the set of natural numbers)--there is really quite a large difference, and the N and R keys aren't particularly close to each other on the keyboard, either. At other times he mysteriously drops terms from equations with no explanations, which seem more like typos.

If you are a mathematical "layman," so to speak, or things like this bother you a lot, I might suggest you look for another book, to avoid confusion on the layman's part or annoyance on the part of the more knowledgable reader.