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2 of 3 people found the following review helpful
5.0 out of 5 stars well written and well planned course
It is many years since I did my engineering degree and I wanted to brush up my maths and learn the modern approach to the subject. This book is excellent and leads you into the subject in a gradual but rigorous way. It does get quite difficult so it will take me a while to work through. I would imagine that this book must be perfect for maths undergraduates in their first...
Published 12 months ago by MikeC

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2 of 4 people found the following review helpful
1.0 out of 5 stars A Confused Introduction to Pure Mathematics
This book will do little or nothing to enhance your understanding of Mathematics. It will just give you a superficial overview of a bunch of theories and theorems that you will encounter sooner or later, in better form, in your college years. Very superficial, no real "mathematical idea", and not in the least any insight about the levels of depth of mathematical...
Published 3 months ago by CriticalMathematician


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2 of 3 people found the following review helpful
5.0 out of 5 stars well written and well planned course, 23 April 2014
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This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
It is many years since I did my engineering degree and I wanted to brush up my maths and learn the modern approach to the subject. This book is excellent and leads you into the subject in a gradual but rigorous way. It does get quite difficult so it will take me a while to work through. I would imagine that this book must be perfect for maths undergraduates in their first year - or even in the summer before starting.
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4 of 6 people found the following review helpful
5.0 out of 5 stars M1F, 2 Dec. 2012
This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
This book is really helpful if you are doing the M1F course. The exercises are great (better still when you get them right!) and the layout is really clear (labelling each Proposition makes it easier to follow).
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2 of 3 people found the following review helpful
5.0 out of 5 stars Pure Mathematics Book, 9 April 2013
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This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
I bought this Maths book for my son to take with him to University as he is studing Maths. It has been helpful especially in his first term.
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5.0 out of 5 stars Five Stars, 7 Oct. 2014
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This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
Very interesting content and useful preparation for a university level Maths course.
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2 of 4 people found the following review helpful
1.0 out of 5 stars A Confused Introduction to Pure Mathematics, 25 Jan. 2015
This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
This book will do little or nothing to enhance your understanding of Mathematics. It will just give you a superficial overview of a bunch of theories and theorems that you will encounter sooner or later, in better form, in your college years. Very superficial, no real "mathematical idea", and not in the least any insight about the levels of depth of mathematical concepts, i.e., you will not learn absolutely nothing about how to think when you do Mathematics. Moreover, the book is confusing at times: concepts are often not precisely defined, and if you have the gift of critical thinking you will find lots of places where the logic standards of the book are less than acceptable.

Just to give you a couple of example, things start immediately pretty bad, as on p. 1 the author does not explain that the very first condition that a set should satisfy consists in giving a set through an expression which must be as unambiguous as possible. This is the very first brick of modern Mathematics and the author fails to explain it how and why. So he goes on giving as an example of a set the (nonexisting) "set of people who live in Denmark". Of course here the ambiguity reigns supreme, as it is not clear how to define the notion of "people living in Denmark" with precision, unless (and this should be specified when defining such a set) we add the sentence "according to a given population census".

As another example, the introduction of complex numbers is really confusing and logically inconsistent, much to the point that one cannot help but wonder what the rigor standards of the author are. The author introduces the absolutely unnecessary relation "i^2=-1" BEFORE he defines the multiplication of complex numbers and this makes no sense since the first is of course a consequence of the latter. The point is that this is an unnecessary/redundant axiom at this point. Moreover, you are left trying to figure out what in the world "taking the square of i" means, since at that point you haven't yet defined the multiplication of such symbols, i.e., you haven't defined what the square of a complex number should be! This is just bad logic, and the book is plenty of such examples of bad use of logic.

In conclusion, this is a book which completely fails to give a serious introduction to Mathematics and Mathematical thinking. If you really want some more serious book that achieves this goal, I suggest you turn to "Mathematics: its content, methods and meaning" by Aleksandrov, Kolmogorov and Lavrent'ev. This book is a masterpiece in the introduction of mathematical concepts and mathematical ideas, and was written by a real master of Mathematics like Kolmogorov. Avoid at all costs the confusing and confused bok I am reviewing here. PS: do not trust too much the enthusiastic reviews written before: reviews of three lines are clearly the proof that the reviewer didn't bother to carefully read the book.
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3 of 5 people found the following review helpful
5.0 out of 5 stars I love this book, 23 Oct. 2012
This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
This book claims to help bridge the gap from A-level Maths to 1st year Maths degree.
It does this well.
The only criticism is that the answers to the exercises isn't provided.
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1 of 2 people found the following review helpful
5.0 out of 5 stars Brilliant!!!, 2 July 2013
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This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
Brilliant book, a must have for uni. Liebeck explains things so concisely & clearly, it really helped me for my first year analysis courses.
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2 of 4 people found the following review helpful
5.0 out of 5 stars Very Good, 2 Jun. 2013
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This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
As expected I am very satisfied even though I have not read the book but a brief look indicates that it is well written and in a clear manner.
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5.0 out of 5 stars Five Stars, 23 Oct. 2014
This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
It's great!
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5.0 out of 5 stars great, 27 Aug. 2014
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Mr. P. G. Tomaney "paul" (durham) - See all my reviews
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This review is from: A Concise Introduction to Pure Mathematics, Third Edition (Chapman Hall/CRC Mathematics Series) (Paperback)
enjoyable
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