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16 of 17 people found the following review helpful
5.0 out of 5 stars An Excellent Introduction to Pure Mathematics, 17 Sept. 2006
By 
Mr. P. Bilokon "Paul Bilokon" (London, UK) - See all my reviews
(REAL NAME)   
This review is from: A Concise Introduction to Pure Mathematics, Second Edition (Chapman & Hall/CRC Mathematics) (Paperback)
I had a privilege of attending a first-year course at Imperial College, based on Prof. Martin Liebeck's book. The book, as well as the course (then taught by Prof. Kevin Buzzard), are superb. They are readily accessible to first-year university students and provide an easy transition from A-level to undergraduate mathematics. Moreover, the language is clear and concise, the examples instructive, and the book is generally fun to read. Liebeck selects some of the most interesting topics in elementary pure mathematics and stimulates the student's interest in the subject. Unfortunately, A-level mathematics is taught as a collection of algorithms, and the student may not be able to appreciate its depth and beauty. Whether you are a first-year mathematics undergraduate, or still at school, I would thoroughly recommend you to read this book so that you know what mathematics is really about.
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14 of 15 people found the following review helpful
4.0 out of 5 stars Nicely-written transition from secondary school to unuversity mathematics. Targeted more toward classroom use than self-study, 17 Aug. 2009
This review is from: A Concise Introduction to Pure Mathematics, Second Edition (Chapman & Hall/CRC Mathematics) (Paperback)
This is a review of the (2005) 2nd ed. The number of texts covering the transition from secondary school to college mathematics has grown considerably in recent years. This is one of the better-written and well-organized texts. Its greatest concentration is on important concepts from pure mathematics, such as sets and numbers, real and complex, and some interesting topics from number theory. Explanations are clear and the in-text examples and proofs are well chosen and explained. The emphasis here is primarily on proofs rather than on the solution of applied problems. The author uses only the minimum level of mathematical rigor required, and this is supplemented by clear discussions. I particularly appreciated the gentle introduction to set theory and the in-text questions, followed by solutions. The proofs of propositions are clear and complete.

The Forward says this book can "be read by a student on his or her own". The Preface restates this slightly differently, by saying that as "well as being designed for use in a first university course, the book is also suitable for self-study". However, debatably, this text does not serve both purposes equally well, as it seems less suitable for a self-study target audience.

A " Solutions Manual for a Concise Introduction to Pure Mathematics" is listed on-line. The Solutions Manual described is about 70 pages in length. If this is correct, it's contents could easily have been included with this text, while still keeping the text relatively concise at less than 300 pages. At the time of this review, this manual was not available from Amazon or other on-line sellers.

The lack of fully-worked solutions to exercises is typical of many books designed for classroom use. This allows faculty to assign problems that students must work out on their own, as solutions are not readily available. While this approach is, arguably, appropriate for a classroom environment, the lack of detailed exercise solutions considerably reduces the value of this text for self-study. For self-study, the opportunity to work through a considerable variety of problems and check results against detailed solutions is quite important. This is perhaps the key deficiency of this text. However, it is enjoyable to read, with explanations that are very well done. Thus, although not self-contained, it could be excellent for self-study if supplemented by a source of problems with fully worked solutions.

Conclusion: Excellent for self-study but not standalone, as it is best supplemented by problems book with solutions. For classroom use, this is clearly in the top tier of mathematics transition texts.
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8 of 9 people found the following review helpful
5.0 out of 5 stars A very useful book for anyone thinking of doing Mathematics at university., 31 Oct. 2006
This review is from: A Concise Introduction to Pure Mathematics, Second Edition (Chapman & Hall/CRC Mathematics) (Paperback)
I am a first year student at Imperial College (where Professor Liebeck lectures) and I have to say that this book has really helped me. It was on the reading list that the university gave to me, so over the summer I used he book as a study aid.

Liebeck writes clearly and concisely, presenting the mathematics in an easy to understand way. At the same time the material covered is more challenging than at A-Level (which I found to be a bit repetitive) and will stimulate all students, regardless of their ability.
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2 of 2 people found the following review helpful
4.0 out of 5 stars Maths wise, for clever people only!, 28 Jun. 2011
This review is from: A Concise Introduction to Pure Mathematics, Second Edition (Chapman & Hall/CRC Mathematics) (Paperback)
This very quickly gets beyond a light read and into hard maths. NOT a bedtime read! But if you have the time and mental ability, it does lead you from a basic beginning to a better understanding.
I'm not sufficiently qualified to say much more, except that I WILL come back to it when life allows more time.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Good introduction., 11 Feb. 2009
By 
T. H. A. Teng (London) - See all my reviews
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This review is from: A Concise Introduction to Pure Mathematics, Second Edition (Chapman & Hall/CRC Mathematics) (Paperback)
A very good introduction to people who wonder what Maths looks like in University. This book is actually a textbook for Foundation of Analysis course in Imperial College London (and the author is one of my lecturer too). Recommend to bright students in high school. If you can do those questions in the book then you ace the first term of mathematics in Uni.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Excellent., 18 Nov. 2010
This review is from: A Concise Introduction to Pure Mathematics, Second Edition (Chapman & Hall/CRC Mathematics) (Paperback)
Everything is explained extremely clearly which makes it a brilliant learning tool. Definitely the book I always refer to when notes don't seem to make much sense!
Prof. Liebeck @ Imperial College London = Immense!!
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