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Bridging the Gap to University Mathematics Paperback – Feb 2009

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Product details

  • Paperback: 358 pages
  • Publisher: Springer; 2009 edition (Feb 2009)
  • Language: English
  • ISBN-10: 1848002890
  • ISBN-13: 978-1848002890
  • Product Dimensions: 15.6 x 1.9 x 23.4 cm
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Bestsellers Rank: 22,400 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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From the reviews:

“This book has been ‘written by students for students’. … the quite talkative style makes this book a pleasant ‘arm chair reading’ for freshmen and event teachers. … it can be recommended as an additional source for students in their first year calculus or linear algebra course.” (Jürgen Appell, zbMATH, Vol. 1271, 2013)

“The authors of Bridging the Gap to University Mathematics, were students at a British university. … Their book consists of 20 independent chapters … including two on mechanics and two on differential equations. … Induction is done well, and there is material on logic and truth tables as well as on proof by contrapositive. … the book could be very useful to the beginning mathematics or engineering student–and even to the professor.” (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)

"The book can be used also by … undergraduate students, graduate students (in their first years), high-school teachers, even mathematics faculty (to get ideas on making their courses more accessible to students). The book covers an array of twenty topics, from simple inequalities to series, and is easy to read, which makes it ideal for self-study. … It is an easy and entertaining read. … a good book to have for any student taking mathematics courses, as well as for any teacher teaching mathematics courses." (Mihaela Poplicher, The Mathematical Association of America, April, 2009)

"Bridging the Gap to University Mathematics is intended to do exactly what the title suggests. Gould and Hurst were, at the time of writing, both students and one gets the feeling that their desire is to tell prospective students what they themselves wish someone had told them before they embarked on their own mathematical journey at university…The book covers a broad range of topics…Well written and easy to read, it divides the material into twenty chapters, which are broken down into manageable chunks. Every chapter begins with ten ’test yourself’ questions designed to help the student discover whether they really do understand a particular topic. As each one is written as a single entity, not depending on preceding content, it is a book that students can dip in and out of rather than read from cover to cover.

It is pleasantly laid out and contains numerous worked examples which clearly illustrate the more complicated concepts. Each subsection is followed by an exercise for the students to work through to test their understanding. All answers, to these and the starter questions, are provided at the back of the book enabling students to monitor their progress. Concluding each chapter is a very helpful section entitled ’where now?’ which explains how this area of mathematics might come into their university course and where it could lead to. Readers are helpfully referred to other texts for further, more in-depth, material or interest. Lastly, an appendix provides useful formulae and extension questions, this time with worked solutions...

The book is written in a fresh, conversational style that is neither patronising nor written in a format intended to solely appeal to the young. It is a book that one could quite easily use as the basis of an introductory or foundation course or to stretch the brightest sixth-formers with something interesting, possibly after they have taken their exams." (Noel-Ann Bradshaw, LMS, September 2010)

From the Back Cover

  • Full-worked solutions to all exercises available at www.springer.com

Written by students for students, Bridging the Gap to University Mathematics is a refreshing, new approach to making the transition into undergraduate-level mathematics or a similar numerate degree. Suitable for students of all backgrounds, whether A-level, Scottish Higher, International Baccalaureate or similar, the book helps readers to shape their existing knowledge and build upon current strengths in order to get the most out of their undergraduate studies.

The book can be used as a source of private study before embarking on a degree or as a textbook for an introductory course. Clear descriptions and a vast assortment of exercises – complete with solutions – enable the reader to develop and then practice new skills. Topics are delivered as twenty self-contained, manageable chapters, allowing students to dip in and out as they require, easily identifying those areas on which they need practice, whilst skimming over more familiar material. Important concepts are introduced in an easy-to-read manner with a sustained emphasis on worked examples and applications rather than abstract theory. Each chapter also includes an insight into where the reader’s new skills will be employed during the course of their studies, providing a springboard to further research where desired.



Inside This Book (Learn More)
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Customer Reviews

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Most Helpful Customer Reviews

19 of 20 people found the following review helpful By Nicholas Warren on 4 Aug 2010
Format: Paperback
This book delivers exactly what it promises. It is a very clear explanation of the mathematics that will used again and again at University in the first year. It assumes only a good understanding of High School mathematics.

It does not lead you much into the more rigorous approach to proof used at University, but makes sure you know the mathematics needed as tools in applications. As such, the book would be at least as valuable (if not more so) to a prospective physicist, chemist, economist or engineer as mathematician. There are many exercises and I have checked many of the given solutions at the back for accuracy. The topics are very well explained and can be used stand-alone for self-study. The book is also written in a lively fashion, as entertainingly as endless definition-theorem-proof in a standard mathematics textbook is not! There is also a good set of references to explore topics further.

If every student about to enter University for a quantitative degree carefully studied this book over the summer, he/she would be very well prepared.

I know nothing about the authors (other than I believe they come from the U.K.) but, congratulations for a job well done!
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7 of 7 people found the following review helpful By S Foster on 2 Nov 2011
Format: Paperback Verified Purchase
I found this text to be of great use to me.
The authors use of language was well balanced between using mathematical language whilst explaining concepts in everyday english.
Having passed MST121, the 1st level Open University maths course, I think the book will be a useful revision source for the next level courses.
I would recommend it as either a stepping stone or a revision guide to Uni maths course.
I'd say it does exactly what it says on the cover, it bridges the gap.
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12 of 13 people found the following review helpful By Matthew D. Crispin on 9 Jun 2011
Format: Paperback
I am prompted to write this review having seen that one Amazon reviewer scored the text with 1/5.
The authors admit that some of their contemporaries were familiar with many of the concepts they discuss, but the sad reality is that many were not. I have no reason to think that this situation has changed for the better. I think their approach is very accessible, clear, and suitably caveated when leaps of faith are being made. Their principle failure is with the title which fails to emphasise the suitability of the text to scientists. (This may have also deflected some of the 1/5 reviews from disappointed mathematicians).

My only minor gripe is that the Appendix is a bit disorganised and that there are examples of material being referred to from the main text which seems to be missing.

A very welcome book!

Dr M. Crispin
Oriel College,Oxford
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2 of 2 people found the following review helpful By Mrs. C. House on 21 July 2011
Format: Paperback
When I got this book I thought it would have lots of new stuff like analysis that is never covered at A-level Maths or Further Maths, but I found that most of it was work that if you are doing full further maths a level you will cover at school, although there are some chapters towards the end that cover new things in some detail like sequences, series, logic and set theory notation. The rest is eigenvectors, hyperbolic functions, polar coordinates stuff you will probably cover at school.

Although the book may not be perfectly fit for its purpose, it is still very good revision material for things at covered at school with short,clear and concise explanations lots of exercises (with answers)

If you are looking for something to actually bridge the gap to degree level, probably best just buy a book that is recommended by your no.1 choice university to guide you through one of the course covered in the first year of your degree. Cambridge University advises Algebra and Geometry by Alan F Beardon 2005 which covers groups, vectors and matrices etc. so thats probably a better idea to buy.
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2 of 2 people found the following review helpful By Madame Gourmand on 2 Nov 2011
Format: Paperback Verified Purchase
As a mature student returing to university after 12 years I really needed to brush up on my math skills and this book really helps with this.

Everything is explained in laymans terms, I'm studying a science based degree and the book covers everything I need to help me with my assignments, it really does bridge the gap to university maths.
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4 of 5 people found the following review helpful By DCC Gaster on 24 Nov 2010
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I have very little to say in criticism of this fascinating and beautifully presented book. It is this. Based upon graphical solutions to inequalities, I cannot always see why a solution takes a particular form. Looking for example at problems 1.2.7 and 1.2.8 which involve graphs of a similar form, why are the solutions written in a different way and could they be explained, especially 1.2.8.? Apart from this, I am enthralled to discover a mathematics book which describes with such clarity and economy the basic principles of undergraduate studies that someone like me, with only O Level maths taken over 40 years ago, can understand and even enjoy it. It has begun to assume the character of a crossword in my mind and it was a subject which presented a barrier to me until now. It must illuminate the interpretation of scientific results, but I have yet to reach this stage. For the moment, I restrict myself to a problem or two a day.
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