Ignore the answers completely., 15 Jun 2008
Never before have I felt compelled to write a review, but this book annoyed me so much that it had to be done.

The book consists of several chapters teaching you skills such as ratios and percentages, this first part is absolutely fine and the answers that I checked were correct also.

However, the final part of the book, the section which should be the most useful, data interpretation. You are given quite a few different data interpretation questions to answer in the form of tables, bar graphs and pie charts, all good so far. But unbelievably so after you have racked your brain to figure out the answers, only to discover that the 'correct' answers written in the book are wrong. Needless to say this is indeed infuriating, especially as it takes you a while to realise this, at one point I thought I was making no progress at all.

Although the bulk of the book is useful I would avoid purchasing the book purely because of its blatant mistakes.

How to pass numerical reasoning tests: a step-by-step guide to learning key numeracy skills (how to pass), 06 Jun 2008
This book is rubbish it does not teach you a single thing and if I could give it 0 out of 5 I would. It's boring, confusing and doesnt explain anything clearly how it ever got printed is beyond me, don't waste your money.

Infuriating, 25 Jan 2008
It's not often I feel compelled to write a review of a book or anything else for that matter but, this book has infuriated me to such an extent that I feel I have to.

Are the questions representative of those you might find in a real numerical reasoning test? Yes.

Does the book have a reasonable number of practice questions? Yes.

Will this book help you pass a numerical reasoning test? No

Why??

The questions often try to catch you out which, ordinarily, is fine. However, the author over does this too such an extent that sometimes even they appear to be confused (as can be seen by their incorrect explanation of the answer). This is a problem because often in real tests you might only get 45 seconds or so per question and after reading this book you'll find yourself searching for things in real tests that simply don't exist. Another problem is the confusing way in which the questions are worded which, when combined with a smattering of incorrect answers and the aforementioned will have you screaming in no time!

I ran this book by a couple of my friends who both have masters' degrees in maths from Imperial College. They struggled even more than I did!! Could they do the maths? Yes. Could they make sense of this book? No. You've been warned.

Excellent book for reviewing your math skills., 22 Nov 2007
I have been studying in university for quite a while but in my current subject area, I didn't have to solve mathematical questions. However, I was applying for jobs which also involve case studies and numerical reasoning tests. This book was very helpful, it explains calculating with big numbers, percentages, ratios, etc. In addition, you got some practice questions, as well. I would definitely recommend this book if you wanna brush up your math skills.

Learning the trade, 04 Nov 2007
If you havent touched any maths for years and require to polish your basic maths skills, this is the book. You can oil all them rusty questions and grey areas with this book.

If your facing an SHL numeric test for the first time, you may want to have a look at this as it has all the basic numerical functions. THIS BOOK DOES NOT HAVE SHL TYPE QUESTIONS.

Do not rely on this book if you have a graduate level test. Its only for basic's which its very good at.

Ignore the answers completely., 15 Jun 2008
Never before have I felt compelled to write a review, but this book annoyed me so much that it had to be done.

The book consists of several chapters teaching you skills such as ratios and percentages, this first part is absolutely fine and the answers that I checked were correct also.

However, the final part of the book, the section which should be the most useful, data interpretation. You are given quite a few different data interpretation questions to answer in the form of tables, bar graphs and pie charts, all good so far. But unbelievably so after you have racked your brain to figure out the answers, only to discover that the 'correct' answers written in the book are wrong. Needless to say this is indeed infuriating, especially as it takes you a while to realise this, at one point I thought I was making no progress at all.

Although the bulk of the book is useful I would avoid purchasing the book purely because of its blatant mistakes.

How to pass numerical reasoning tests: a step-by-step guide to learning key numeracy skills (how to pass), 06 Jun 2008
This book is rubbish it does not teach you a single thing and if I could give it 0 out of 5 I would. It's boring, confusing and doesnt explain anything clearly how it ever got printed is beyond me, don't waste your money.

Infuriating, 25 Jan 2008
It's not often I feel compelled to write a review of a book or anything else for that matter but, this book has infuriated me to such an extent that I feel I have to.

Are the questions representative of those you might find in a real numerical reasoning test? Yes.

Does the book have a reasonable number of practice questions? Yes.

Will this book help you pass a numerical reasoning test? No

Why??

The questions often try to catch you out which, ordinarily, is fine. However, the author over does this too such an extent that sometimes even they appear to be confused (as can be seen by their incorrect explanation of the answer). This is a problem because often in real tests you might only get 45 seconds or so per question and after reading this book you'll find yourself searching for things in real tests that simply don't exist. Another problem is the confusing way in which the questions are worded which, when combined with a smattering of incorrect answers and the aforementioned will have you screaming in no time!

I ran this book by a couple of my friends who both have masters' degrees in maths from Imperial College. They struggled even more than I did!! Could they do the maths? Yes. Could they make sense of this book? No. You've been warned.

Excellent book for reviewing your math skills., 22 Nov 2007
I have been studying in university for quite a while but in my current subject area, I didn't have to solve mathematical questions. However, I was applying for jobs which also involve case studies and numerical reasoning tests. This book was very helpful, it explains calculating with big numbers, percentages, ratios, etc. In addition, you got some practice questions, as well. I would definitely recommend this book if you wanna brush up your math skills.

Learning the trade, 04 Nov 2007
If you havent touched any maths for years and require to polish your basic maths skills, this is the book. You can oil all them rusty questions and grey areas with this book.

If your facing an SHL numeric test for the first time, you may want to have a look at this as it has all the basic numerical functions. THIS BOOK DOES NOT HAVE SHL TYPE QUESTIONS.

Do not rely on this book if you have a graduate level test. Its only for basic's which its very good at.

This book is the one ...., 05 Mar 2008
I would recommend for everybody who has an interest in mathematics and the development of his mind, whatever his age or education. I've got a lot of mathematical books but this one is a very special one, because it is the only one that could hook me from page one till the end.
It is not a book for readers but a book for people who want to be actively involved with thinking and mathematics. And when I say mathematics I do not mean those high school mathematics books that are designed to torture every student. When you are going to study science at university i would recommend reading this book, because it develops your brain-solving capabilities.


Life changing, 09 Jul 2005
In my experience there are no books that could be termed "life changing". Except this one :)

My view of mathematics was as a dry, complete subject until I met the work of John Mason during my mathematics degree with the OU. This book completed what he started there - and changed me into a passionate mathematician, as opposed to someone who could simply do maths.

'Thinking Mathematically' helps teach you how to literally think like a mathematician, something that a lot of schools fail at. It uses a series of problems that are genuinely interesting and guides you through the process of solving them. For example; "How many squares are on a chessboard?" (It's not 64!).

The books only drawback is that time is not just spent on reading, but also really working on the problems, many of which do not have solutions, and thus I have never manged to finish it!

A wonderful book. Buy now!

A wonderful book for teachers and students alike, 05 Apr 2004
"Thinking Mathematically" is a wonderful book that I warmly recommend to anyone teaching mathematics, at any level, from primary school to university lecturer. I was recently involved in designing an undergraduate course incorporating mathematical writing and thinking, and problem solving. I have only subsequently discovered this book - and John Mason's "Learning and Doing Mathematics" - when I come to write the lectures for the course, these two books will be my main references. There are many excellent open-ended problems for investigation, and the thought processes involved in thinking mathematically are beautifully explained. The problems are at a sufficiently low level that they are likely to be useful for teachers at all levels. I shall encourage our library to buy copies of these books and will strongly recommend them to our students.

A unique and immensley practical book., 25 Apr 2002
This book requires no specialist maths knowledge (hardly any required) but almost from the first page will immerse you in the techniques and strategies which underly mathematical thinking.
I've used this book for many years and still keep coming back to it.
It is the only book I've ever seen which addresses the true emotional states a problem solver must go through AND shows you how to deal with them. Best of all, it will teach you to ask your own questions and find your own answers by the time you reach the end.
I'd suggest one takes one time to really absorb the tips presented in the book - well worth it.

Ignore the answers completely., 15 Jun 2008
Never before have I felt compelled to write a review, but this book annoyed me so much that it had to be done.

The book consists of several chapters teaching you skills such as ratios and percentages, this first part is absolutely fine and the answers that I checked were correct also.

However, the final part of the book, the section which should be the most useful, data interpretation. You are given quite a few different data interpretation questions to answer in the form of tables, bar graphs and pie charts, all good so far. But unbelievably so after you have racked your brain to figure out the answers, only to discover that the 'correct' answers written in the book are wrong. Needless to say this is indeed infuriating, especially as it takes you a while to realise this, at one point I thought I was making no progress at all.

Although the bulk of the book is useful I would avoid purchasing the book purely because of its blatant mistakes.

How to pass numerical reasoning tests: a step-by-step guide to learning key numeracy skills (how to pass), 06 Jun 2008
This book is rubbish it does not teach you a single thing and if I could give it 0 out of 5 I would. It's boring, confusing and doesnt explain anything clearly how it ever got printed is beyond me, don't waste your money.

Infuriating, 25 Jan 2008
It's not often I feel compelled to write a review of a book or anything else for that matter but, this book has infuriated me to such an extent that I feel I have to.

Are the questions representative of those you might find in a real numerical reasoning test? Yes.

Does the book have a reasonable number of practice questions? Yes.

Will this book help you pass a numerical reasoning test? No

Why??

The questions often try to catch you out which, ordinarily, is fine. However, the author over does this too such an extent that sometimes even they appear to be confused (as can be seen by their incorrect explanation of the answer). This is a problem because often in real tests you might only get 45 seconds or so per question and after reading this book you'll find yourself searching for things in real tests that simply don't exist. Another problem is the confusing way in which the questions are worded which, when combined with a smattering of incorrect answers and the aforementioned will have you screaming in no time!

I ran this book by a couple of my friends who both have masters' degrees in maths from Imperial College. They struggled even more than I did!! Could they do the maths? Yes. Could they make sense of this book? No. You've been warned.

Excellent book for reviewing your math skills., 22 Nov 2007
I have been studying in university for quite a while but in my current subject area, I didn't have to solve mathematical questions. However, I was applying for jobs which also involve case studies and numerical reasoning tests. This book was very helpful, it explains calculating with big numbers, percentages, ratios, etc. In addition, you got some practice questions, as well. I would definitely recommend this book if you wanna brush up your math skills.

Learning the trade, 04 Nov 2007
If you havent touched any maths for years and require to polish your basic maths skills, this is the book. You can oil all them rusty questions and grey areas with this book.

If your facing an SHL numeric test for the first time, you may want to have a look at this as it has all the basic numerical functions. THIS BOOK DOES NOT HAVE SHL TYPE QUESTIONS.

Do not rely on this book if you have a graduate level test. Its only for basic's which its very good at.

This book is the one ...., 05 Mar 2008
I would recommend for everybody who has an interest in mathematics and the development of his mind, whatever his age or education. I've got a lot of mathematical books but this one is a very special one, because it is the only one that could hook me from page one till the end.
It is not a book for readers but a book for people who want to be actively involved with thinking and mathematics. And when I say mathematics I do not mean those high school mathematics books that are designed to torture every student. When you are going to study science at university i would recommend reading this book, because it develops your brain-solving capabilities.


Life changing, 09 Jul 2005
In my experience there are no books that could be termed "life changing". Except this one :)

My view of mathematics was as a dry, complete subject until I met the work of John Mason during my mathematics degree with the OU. This book completed what he started there - and changed me into a passionate mathematician, as opposed to someone who could simply do maths.

'Thinking Mathematically' helps teach you how to literally think like a mathematician, something that a lot of schools fail at. It uses a series of problems that are genuinely interesting and guides you through the process of solving them. For example; "How many squares are on a chessboard?" (It's not 64!).

The books only drawback is that time is not just spent on reading, but also really working on the problems, many of which do not have solutions, and thus I have never manged to finish it!

A wonderful book. Buy now!

A wonderful book for teachers and students alike, 05 Apr 2004
"Thinking Mathematically" is a wonderful book that I warmly recommend to anyone teaching mathematics, at any level, from primary school to university lecturer. I was recently involved in designing an undergraduate course incorporating mathematical writing and thinking, and problem solving. I have only subsequently discovered this book - and John Mason's "Learning and Doing Mathematics" - when I come to write the lectures for the course, these two books will be my main references. There are many excellent open-ended problems for investigation, and the thought processes involved in thinking mathematically are beautifully explained. The problems are at a sufficiently low level that they are likely to be useful for teachers at all levels. I shall encourage our library to buy copies of these books and will strongly recommend them to our students.

A unique and immensley practical book., 25 Apr 2002
This book requires no specialist maths knowledge (hardly any required) but almost from the first page will immerse you in the techniques and strategies which underly mathematical thinking.
I've used this book for many years and still keep coming back to it.
It is the only book I've ever seen which addresses the true emotional states a problem solver must go through AND shows you how to deal with them. Best of all, it will teach you to ask your own questions and find your own answers by the time you reach the end.
I'd suggest one takes one time to really absorb the tips presented in the book - well worth it.

Mr Spock would like this, 17 Nov 2008
I have always had a fairly logical mind having studied subjects such as mathematics, physics and accounting to a high level and I have always enjoyed doing crossword puzzles and other puzzles including IQ tests.

Some people can obviously think logically more easily than others since computer firms used to (and maybe still do) give one a sort of IQ test to see if one can learn to programme a computer.

Logic is also something that can be studied and it is treated like a science. It is a branch of philosophy and until the nineteenth century there hadn't been many advances on Aristotle's system. Attempts in the late nineteenth century and early twentieth century to reduce mathematics to logic by Bertand Russell and others were unsuccesful but Russell and many other scientists, mathematicians and philosophers greatly expanded the scope and range of logic introducing symbols and a wider range of techniques.

This is a compelling albeit basic introduction by an author who knows his stuff.

Not a course in logic, but a briliant taster., 07 Nov 2008
This book will not teach you logic.

What it will do, and it will do it well, is give you a high-speed tour of logic - including some background information, how logical arguments become symbolised, show the main areas of the subject, along with some existing puzzles in the field.

While you won't really learn logic from it, it will certainly make you want to learn logic!

A logical choice..., 24 Nov 2005
Graham Priest is author of several books on logic, including 'An Introduction to Non-Classical Logic' and 'Towards Non-Being: The Logic And Metaphysics Of Intentionality'. He has experience as a professor of logic at the University of Queensland in helping to determine the needs of those who are in need of logic help. This book, part of the Very Short Introductions series of Oxford University, is both an introduction and a refresher for those who have had logic before. Because of its brevity, it might be a bit too condensed for those looking for a logic course; however, used together with a larger text (Copi's logic book is the one I used in my early logic days), this VSI book provides good supplemental information and helps clarify key points.

This book provides an introduction both to symbolic logic as well as linguistic logic. Issues such as probability, truth and fact statements, conditional statements, decision theory and validity are all presented in clear, concise ways. There are fourteen chapters (a lot of chapters for book with barely over 100 pages of text), and each chapter deals with a few key points summarised in a pull-quote box at the end of each chapter. There are diagrams, sentences and equations to illustrate the points in visual as well as language terms.

The final chapter, 'A Little History and Some Further Reading', is a good short review of key figures and historical issues that underpin the material presented in the previous chapters. There is a helpful glossary of terms, and Priest also provides a page of logic puzzles and problems to be worked by the students, keyed to an Oxford University Press website that has the solutions to the questions.

This is a good book for review of logic prior to taking tests (such as the LSAT) or graduate courses that require understanding of logical thought processes (systematic theology or philosophy). As some reviewers have noted, this is not a lock-step presentation of standard analytic logic (indeed, many of Priest's other writings have a more non-standard approach), but does provide some good insights in the overall way in which logic is structured and done.

Not suitable for beginners, 05 Jun 2003
This book is really not an introductory text.
It does delve too deep for someone not acquainted with formal logic.
The Icon Series Introducig Logic is a much easier read and gives a more comprehensive overview of the subject.
This book is probably better read by someone who has a background in the subject.

A very good introduction, 18 Oct 2002
..this book is a very good introduction to logic, a fundamental aspect of philosohpy and mathematics. For example, logical propositions are constructed as a so called fraction with the premiss as the "numerator" and the conclusion as the "denominator", and this is explained clearly on page 7 out of 109.

The book condenses a wide range of loigcal topics into 109 pages very well, and as it says on the back cover 'it does not attempt to be a text-book' but rather provides a basic introduction to logic.

Any one with a difficulty, perhaps, to mathemtics and symbols might find this book slighlty challenging, but even then the symbols are explained so well it should be no problem. Besides, one cannot hope to be introduced to a technical subject, similar but not the same as mathematics, without the use of symbols.

The whole text is very thought provoking and mentally stimulating, and further questions for consideration are provided a the back, as well as a further reading list.

So, this book is a good introduction for anyone interested in formal logic, mathematics, computers etc., irrespective of previous knowledge.

Ignore the answers completely., 15 Jun 2008
Never before have I felt compelled to write a review, but this book annoyed me so much that it had to be done.

The book consists of several chapters teaching you skills such as ratios and percentages, this first part is absolutely fine and the answers that I checked were correct also.

However, the final part of the book, the section which should be the most useful, data interpretation. You are given quite a few different data interpretation questions to answer in the form of tables, bar graphs and pie charts, all good so far. But unbelievably so after you have racked your brain to figure out the answers, only to discover that the 'correct' answers written in the book are wrong. Needless to say this is indeed infuriating, especially as it takes you a while to realise this, at one point I thought I was making no progress at all.

Although the bulk of the book is useful I would avoid purchasing the book purely because of its blatant mistakes.

How to pass numerical reasoning tests: a step-by-step guide to learning key numeracy skills (how to pass), 06 Jun 2008
This book is rubbish it does not teach you a single thing and if I could give it 0 out of 5 I would. It's boring, confusing and doesnt explain anything clearly how it ever got printed is beyond me, don't waste your money.

Infuriating, 25 Jan 2008
It's not often I feel compelled to write a review of a book or anything else for that matter but, this book has infuriated me to such an extent that I feel I have to.

Are the questions representative of those you might find in a real numerical reasoning test? Yes.

Does the book have a reasonable number of practice questions? Yes.

Will this book help you pass a numerical reasoning test? No

Why??

The questions often try to catch you out which, ordinarily, is fine. However, the author over does this too such an extent that sometimes even they appear to be confused (as can be seen by their incorrect explanation of the answer). This is a problem because often in real tests you might only get 45 seconds or so per question and after reading this book you'll find yourself searching for things in real tests that simply don't exist. Another problem is the confusing way in which the questions are worded which, when combined with a smattering of incorrect answers and the aforementioned will have you screaming in no time!

I ran this book by a couple of my friends who both have masters' degrees in maths from Imperial College. They struggled even more than I did!! Could they do the maths? Yes. Could they make sense of this book? No. You've been warned.

Excellent book for reviewing your math skills., 22 Nov 2007
I have been studying in university for quite a while but in my current subject area, I didn't have to solve mathematical questions. However, I was applying for jobs which also involve case studies and numerical reasoning tests. This book was very helpful, it explains calculating with big numbers, percentages, ratios, etc. In addition, you got some practice questions, as well. I would definitely recommend this book if you wanna brush up your math skills.

Learning the trade, 04 Nov 2007
If you havent touched any maths for years and require to polish your basic maths skills, this is the book. You can oil all them rusty questions and grey areas with this book.

If your facing an SHL numeric test for the first time, you may want to have a look at this as it has all the basic numerical functions. THIS BOOK DOES NOT HAVE SHL TYPE QUESTIONS.

Do not rely on this book if you have a graduate level test. Its only for basic's which its very good at.

This book is the one ...., 05 Mar 2008
I would recommend for everybody who has an interest in mathematics and the development of his mind, whatever his age or education. I've got a lot of mathematical books but this one is a very special one, because it is the only one that could hook me from page one till the end.
It is not a book for readers but a book for people who want to be actively involved with thinking and mathematics. And when I say mathematics I do not mean those high school mathematics books that are designed to torture every student. When you are going to study science at university i would recommend reading this book, because it develops your brain-solving capabilities.


Life changing, 09 Jul 2005
In my experience there are no books that could be termed "life changing". Except this one :)

My view of mathematics was as a dry, complete subject until I met the work of John Mason during my mathematics degree with the OU. This book completed what he started there - and changed me into a passionate mathematician, as opposed to someone who could simply do maths.

'Thinking Mathematically' helps teach you how to literally think like a mathematician, something that a lot of schools fail at. It uses a series of problems that are genuinely interesting and guides you through the process of solving them. For example; "How many squares are on a chessboard?" (It's not 64!).

The books only drawback is that time is not just spent on reading, but also really working on the problems, many of which do not have solutions, and thus I have never manged to finish it!

A wonderful book. Buy now!

A wonderful book for teachers and students alike, 05 Apr 2004
"Thinking Mathematically" is a wonderful book that I warmly recommend to anyone teaching mathematics, at any level, from primary school to university lecturer. I was recently involved in designing an undergraduate course incorporating mathematical writing and thinking, and problem solving. I have only subsequently discovered this book - and John Mason's "Learning and Doing Mathematics" - when I come to write the lectures for the course, these two books will be my main references. There are many excellent open-ended problems for investigation, and the thought processes involved in thinking mathematically are beautifully explained. The problems are at a sufficiently low level that they are likely to be useful for teachers at all levels. I shall encourage our library to buy copies of these books and will strongly recommend them to our students.

A unique and immensley practical book., 25 Apr 2002
This book requires no specialist maths knowledge (hardly any required) but almost from the first page will immerse you in the techniques and strategies which underly mathematical thinking.
I've used this book for many years and still keep coming back to it.
It is the only book I've ever seen which addresses the true emotional states a problem solver must go through AND shows you how to deal with them. Best of all, it will teach you to ask your own questions and find your own answers by the time you reach the end.
I'd suggest one takes one time to really absorb the tips presented in the book - well worth it.

Mr Spock would like this, 17 Nov 2008
I have always had a fairly logical mind having studied subjects such as mathematics, physics and accounting to a high level and I have always enjoyed doing crossword puzzles and other puzzles including IQ tests.

Some people can obviously think logically more easily than others since computer firms used to (and maybe still do) give one a sort of IQ test to see if one can learn to programme a computer.

Logic is also something that can be studied and it is treated like a science. It is a branch of philosophy and until the nineteenth century there hadn't been many advances on Aristotle's system. Attempts in the late nineteenth century and early twentieth century to reduce mathematics to logic by Bertand Russell and others were unsuccesful but Russell and many other scientists, mathematicians and philosophers greatly expanded the scope and range of logic introducing symbols and a wider range of techniques.

This is a compelling albeit basic introduction by an author who knows his stuff.

Not a course in logic, but a briliant taster., 07 Nov 2008
This book will not teach you logic.

What it will do, and it will do it well, is give you a high-speed tour of logic - including some background information, how logical arguments become symbolised, show the main areas of the subject, along with some existing puzzles in the field.

While you won't really learn logic from it, it will certainly make you want to learn logic!

A logical choice..., 24 Nov 2005
Graham Priest is author of several books on logic, including 'An Introduction to Non-Classical Logic' and 'Towards Non-Being: The Logic And Metaphysics Of Intentionality'. He has experience as a professor of logic at the University of Queensland in helping to determine the needs of those who are in need of logic help. This book, part of the Very Short Introductions series of Oxford University, is both an introduction and a refresher for those who have had logic before. Because of its brevity, it might be a bit too condensed for those looking for a logic course; however, used together with a larger text (Copi's logic book is the one I used in my early logic days), this VSI book provides good supplemental information and helps clarify key points.

This book provides an introduction both to symbolic logic as well as linguistic logic. Issues such as probability, truth and fact statements, conditional statements, decision theory and validity are all presented in clear, concise ways. There are fourteen chapters (a lot of chapters for book with barely over 100 pages of text), and each chapter deals with a few key points summarised in a pull-quote box at the end of each chapter. There are diagrams, sentences and equations to illustrate the points in visual as well as language terms.

The final chapter, 'A Little History and Some Further Reading', is a good short review of key figures and historical issues that underpin the material presented in the previous chapters. There is a helpful glossary of terms, and Priest also provides a page of logic puzzles and problems to be worked by the students, keyed to an Oxford University Press website that has the solutions to the questions.

This is a good book for review of logic prior to taking tests (such as the LSAT) or graduate courses that require understanding of logical thought processes (systematic theology or philosophy). As some reviewers have noted, this is not a lock-step presentation of standard analytic logic (indeed, many of Priest's other writings have a more non-standard approach), but does provide some good insights in the overall way in which logic is structured and done.

Not suitable for beginners, 05 Jun 2003
This book is really not an introductory text.
It does delve too deep for someone not acquainted with formal logic.
The Icon Series Introducig Logic is a much easier read and gives a more comprehensive overview of the subject.
This book is probably better read by someone who has a background in the subject.

A very good introduction, 18 Oct 2002
..this book is a very good introduction to logic, a fundamental aspect of philosohpy and mathematics. For example, logical propositions are constructed as a so called fraction with the premiss as the "numerator" and the conclusion as the "denominator", and this is explained clearly on page 7 out of 109.

The book condenses a wide range of loigcal topics into 109 pages very well, and as it says on the back cover 'it does not attempt to be a text-book' but rather provides a basic introduction to logic.

Any one with a difficulty, perhaps, to mathemtics and symbols might find this book slighlty challenging, but even then the symbols are explained so well it should be no problem. Besides, one cannot hope to be introduced to a technical subject, similar but not the same as mathematics, without the use of symbols.

The whole text is very thought provoking and mentally stimulating, and further questions for consideration are provided a the back, as well as a further reading list.

So, this book is a good introduction for anyone interested in formal logic, mathematics, computers etc., irrespective of previous knowledge.

Very good book, 03 Dec 2008
The author seems to have been a classicist, theologian, philosopher and mathematician at various stages in his career. He has held a chair in mathematics and has written books on many subjects including history and psychology and has given lectures on music too.

This book is a paperback and has forty four chapters and is 292 pages long. It teaches various aspects of logic and makes use of symbols and diagrams.

This is not for expert logicians but is somewhat stronger than many critical thinking books. Would probably suit mathematics and philosophy students rather than general readers.


As a beginner..., 19 May 2006
...I had to start somewhere. There are plenty of examples throughout and exercises to do. More importantly the majority of the answers are in the back of the book for those of us who are more perplexed.

Admittingly some of the methods seem perhaps a bit dated but this is still a good book to have to start you off. Just enough to raise your game but easy enough for beginners to get a grasp of. Of course if you do get into logic properly though this only really scratches the surface.

One for the devoted fans and hard-working students of logic, 09 May 2004
This old-fashioned book is a more formal look at Logic, and its transcription into symbols and constituents in order to evaluate the truth and validity of paragraphs. Things get pretty messy towards the end, so avoid this if you're going for a lateral thinking type approach to the area.
This is a book to inform and educate, and does so very clearly, with simple excercises to do throughout (answers in the back), and plenty of info is given in each chapter - there's no dull waffle, all vital stuff for the next chapters.

Good luck with this taxing but effective look into the study of Logic.

An excellent introduction, 19 Dec 2002
Wilfrid Hodges' book is a comprehensive introduction to its subject, it's attractive presentation making the complexities and abstract qualities of his themes far more accessible. The book conveys something of the history of the subject through references to key names (e.g. Carnap and Russell) and suggests the relevance of logical thought to everyday activities. An excellent introduction to the Philosophy of Logic which invites the reader though clear explanations, rather than leaving them at a distance through what might otherwise be the daunting, mathematical-style appearance of numbers and symbols.

An excellent introduction to formal logic., 03 Dec 2002
Presuming no prior knowledge neither of philosophy nor logic, Hodges' book is an excellent, non technical, introduction to the subject. Although some sections of the book are mathematical, these are clearly indicated by the author and may be skipped if the reader wishes, without detriment to the rest of the book. This book presents the classical system of formal logic, introducing the reader to both propositonal and first order predicate calculi. Unlike most introductory texts, this book uses the semantic tree tableau method of deduction which some students find easier to understand than N.D.. Although I find this method a little cumbersome, it has the advantage of translating truth tables to deduction. Hodges the reader through some elementary meta-theory up to the interpolation theorem. The book concludes with a brief outline of some non-clasical logics such as modle logic and tense logic. I would recommend this book to anybody.

Ignore the answers completely., 15 Jun 2008
Never before have I felt compelled to write a review, but this book annoyed me so much that it had to be done.

The book consists of several chapters teaching you skills such as ratios and percentages, this first part is absolutely fine and the answers that I checked were correct also.

However, the final part of the book, the section which should be the most useful, data interpretation. You are given quite a few different data interpretation questions to answer in the form of tables, bar graphs and pie charts, all good so far. But unbelievably so after you have racked your brain to figure out the answers, only to discover that the 'correct' answers written in the book are wrong. Needless to say this is indeed infuriating, especially as it takes you a while to realise this, at one point I thought I was making no progress at all.

Although the bulk of the book is useful I would avoid purchasing the book purely because of its blatant mistakes.

How to pass numerical reasoning tests: a step-by-step guide to learning key numeracy skills (how to pass), 06 Jun 2008
This book is rubbish it does not teach you a single thing and if I could give it 0 out of 5 I would. It's boring, confusing and doesnt explain anything clearly how it ever got printed is beyond me, don't waste your money.

Infuriating, 25 Jan 2008
It's not often I feel compelled to write a review of a book or anything else for that matter but, this book has infuriated me to such an extent that I feel I have to.

Are the questions representative of those you might find in a real numerical reasoning test? Yes.

Does the book have a reasonable number of practice questions? Yes.

Will this book help you pass a numerical reasoning test? No

Why??

The questions often try to catch you out which, ordinarily, is fine. However, the author over does this too such an extent that sometimes even they appear to be confused (as can be seen by their incorrect explanation of the answer). This is a problem because often in real tests you might only get 45 seconds or so per question and after reading this book you'll find yourself searching for things in real tests that simply don't exist. Another problem is the confusing way in which the questions are worded which, when combined with a smattering of incorrect answers and the aforementioned will have you screaming in no time!

I ran this book by a couple of my friends who both have masters' degrees in maths from Imperial College. They struggled even more than I did!! Could they do the maths? Yes. Could they make sense of this book? No. You've been warned.

Excellent book for reviewing your math skills., 22 Nov 2007
I have been studying in university for quite a while but in my current subject area, I didn't have to solve mathematical questions. However, I was applying for jobs which also involve case studies and numerical reasoning tests. This book was very helpful, it explains calculating with big numbers, percentages, ratios, etc. In addition, you got some practice questions, as well. I would definitely recommend this book if you wanna brush up your math skills.

Learning the trade, 04 Nov 2007
If you havent touched any maths for years and require to polish your basic maths skills, this is the book. You can oil all them rusty questions and grey areas with this book.

If your facing an SHL numeric test for the first time, you may want to have a look at this as it has all the basic numerical functions. THIS BOOK DOES NOT HAVE SHL TYPE QUESTIONS.

Do not rely on this book if you have a graduate level test. Its only for basic's which its very good at.

This book is the one ...., 05 Mar 2008
I would recommend for everybody who has an interest in mathematics and the development of his mind, whatever his age or education. I've got a lot of mathematical books but this one is a very special one, because it is the only one that could hook me from page one till the end.
It is not a book for readers but a book for people who want to be actively involved with thinking and mathematics. And when I say mathematics I do not mean those high school mathematics books that are designed to torture every student. When you are going to study science at university i would recommend reading this book, because it develops your brain-solving capabilities.


Life changing, 09 Jul 2005
In my experience there are no books that could be termed "life changing". Except this one :)

My view of mathematics was as a dry, complete subject until I met the work of John Mason during my mathematics degree with the OU. This book completed what he started there - and changed me into a passionate mathematician, as opposed to someone who could simply do maths.

'Thinking Mathematically' helps teach you how to literally think like a mathematician, something that a lot of schools fail at. It uses a series of problems that are genuinely interesting and guides you through the process of solving them. For example; "How many squares are on a chessboard?" (It's not 64!).

The books only drawback is that time is not just spent on reading, but also really working on the problems, many of which do not have solutions, and thus I have never manged to finish it!

A wonderful book. Buy now!

A wonderful book for teachers and students alike, 05 Apr 2004
"Thinking Mathematically" is a wonderful book that I warmly recommend to anyone teaching mathematics, at any level, from primary school to university lecturer. I was recently involved in designing an undergraduate course incorporating mathematical writing and thinking, and problem solving. I have only subsequently discovered this book - and John Mason's "Learning and Doing Mathematics" - when I come to write the lectures for the course, these two books will be my main references. There are many excellent open-ended problems for investigation, and the thought processes involved in thinking mathematically are beautifully explained. The problems are at a sufficiently low level that they are likely to be useful for teachers at all levels. I shall encourage our library to buy copies of these books and will strongly recommend them to our students.

A unique and immensley practical book., 25 Apr 2002
This book requires no specialist maths knowledge (hardly any required) but almost from the first page will immerse you in the techniques and strategies which underly mathematical thinking.
I've used this book for many years and still keep coming back to it.
It is the only book I've ever seen which addresses the true emotional states a problem solver must go through AND shows you how to deal with them. Best of all, it will teach you to ask your own questions and find your own answers by the time you reach the end.
I'd suggest one takes one time to really absorb the tips presented in the book - well worth it.

Mr Spock would like this, 17 Nov 2008
I have always had a fairly logical mind having studied subjects such as mathematics, physics and accounting to a high level and I have always enjoyed doing crossword puzzles and other puzzles including IQ tests.

Some people can obviously think logically more easily than others since computer firms used to (and maybe still do) give one a sort of IQ test to see if one can learn to programme a computer.

Logic is also something that can be studied and it is treated like a science. It is a branch of philosophy and until the nineteenth century there hadn't been many advances on Aristotle's system. Attempts in the late nineteenth century and early twentieth century to reduce mathematics to logic by Bertand Russell and others were unsuccesful but Russell and many other scientists, mathematicians and philosophers greatly expanded the scope and range of logic introducing symbols and a wider range of techniques.

This is a compelling albeit basic introduction by an author who knows his stuff.

Not a course in logic, but a briliant taster., 07 Nov 2008
This book will not teach you logic.

What it will do, and it will do it well, is give you a high-speed tour of logic - including some background information, how logical arguments become symbolised, show the main areas of the subject, along with some existing puzzles in the field.

While you won't really learn logic from it, it will certainly make you want to learn logic!

A logical choice..., 24 Nov 2005
Graham Priest is author of several books on logic, including 'An Introduction to Non-Classical Logic' and 'Towards Non-Being: The Logic And Metaphysics Of Intentionality'. He has experience as a professor of logic at the University of Queensland in helping to determine the needs of those who are in need of logic help. This book, part of the Very Short Introductions series of Oxford University, is both an introduction and a refresher for those who have had logic before. Because of its brevity, it might be a bit too condensed for those looking for a logic course; however, used together with a larger text (Copi's logic book is the one I used in my early logic days), this VSI book provides good supplemental information and helps clarify key points.

This book provides an introduction both to symbolic logic as well as linguistic logic. Issues such as probability, truth and fact statements, conditional statements, decision theory and validity are all presented in clear, concise ways. There are fourteen chapters (a lot of chapters for book with barely over 100 pages of text), and each chapter deals with a few key points summarised in a pull-quote box at the end of each chapter. There are diagrams, sentences and equations to illustrate the points in visual as well as language terms.

The final chapter, 'A Little History and Some Further Reading', is a good short review of key figures and historical issues that underpin the material presented in the previous chapters. There is a helpful glossary of terms, and Priest also provides a page of logic puzzles and problems to be worked by the students, keyed to an Oxford University Press website that has the solutions to the questions.

This is a good book for review of logic prior to taking tests (such as the LSAT) or graduate courses that require understanding of logical thought processes (systematic theology or philosophy). As some reviewers have noted, this is not a lock-step presentation of standard analytic logic (indeed, many of Priest's other writings have a more non-standard approach), but does provide some good insights in the overall way in which logic is structured and done.

Not suitable for beginners, 05 Jun 2003
This book is really not an introductory text.
It does delve too deep for someone not acquainted with formal logic.
The Icon Series Introducig Logic is a much easier read and gives a more comprehensive overview of the subject.
This book is probably better read by someone who has a background in the subject.

A very good introduction, 18 Oct 2002
..this book is a very good introduction to logic, a fundamental aspect of philosohpy and mathematics. For example, logical propositions are constructed as a so called fraction with the premiss as the "numerator" and the conclusion as the "denominator", and this is explained clearly on page 7 out of 109.

The book condenses a wide range of loigcal topics into 109 pages very well, and as it says on the back cover 'it does not attempt to be a text-book' but rather provides a basic introduction to logic.

Any one with a difficulty, perhaps, to mathemtics and symbols might find this book slighlty challenging, but even then the symbols are explained so well it should be no problem. Besides, one cannot hope to be introduced to a technical subject, similar but not the same as mathematics, without the use of symbols.

The whole text is very thought provoking and mentally stimulating, and further questions for consideration are provided a the back, as well as a further reading list.

So, this book is a good introduction for anyone interested in formal logic, mathematics, computers etc., irrespective of previous knowledge.

Very good book, 03 Dec 2008
The author seems to have been a classicist, theologian, philosopher and mathematician at various stages in his career. He has held a chair in mathematics and has written books on many subjects including history and psychology and has given lectures on music too.

This book is a paperback and has forty four chapters and is 292 pages long. It teaches various aspects of logic and makes use of symbols and diagrams.

This is not for expert logicians but is somewhat stronger than many critical thinking books. Would probably suit mathematics and philosophy students rather than general readers.


As a beginner..., 19 May 2006
...I had to start somewhere. There are plenty of examples throughout and exercises to do. More importantly the majority of the answers are in the back of the book for those of us who are more perplexed.

Admittingly some of the methods seem perhaps a bit dated but this is still a good book to have to start you off. Just enough to raise your game but easy enough for beginners to get a grasp of. Of course if you do get into logic properly though this only really scratches the surface.

One for the devoted fans and hard-working students of logic, 09 May 2004
This old-fashioned book is a more formal look at Logic, and its transcription into symbols and constituents in order to evaluate the truth and validity of paragraphs. Things get pretty messy towards the end, so avoid this if you're going for a lateral thinking type approach to the area.
This is a book to inform and educate, and does so very clearly, with simple excercises to do throughout (answers in the back), and plenty of info is given in each chapter - there's no dull waffle, all vital stuff for the next chapters.

Good luck with this taxing but effective look into the study of Logic.

An excellent introduction, 19 Dec 2002
Wilfrid Hodges' book is a comprehensive introduction to its subject, it's attractive presentation making the complexities and abstract qualities of his themes far more accessible. The book conveys something of the history of the subject through references to key names (e.g. Carnap and Russell) and suggests the relevance of logical thought to everyday activities. An excellent introduction to the Philosophy of Logic which invites the reader though clear explanations, rather than leaving them at a distance through what might otherwise be the daunting, mathematical-style appearance of numbers and symbols.

An excellent introduction to formal logic., 03 Dec 2002
Presuming no prior knowledge neither of philosophy nor logic, Hodges' book is an excellent, non technical, introduction to the subject. Although some sections of the book are mathematical, these are clearly indicated by the author and may be skipped if the reader wishes, without detriment to the rest of the book. This book presents the classical system of formal logic, introducing the reader to both propositonal and first order predicate calculi. Unlike most introductory texts, this book uses the semantic tree tableau method of deduction which some students find easier to understand than N.D.. Although I find this method a little cumbersome, it has the advantage of translating truth tables to deduction. Hodges the reader through some elementary meta-theory up to the interpolation theorem. The book concludes with a brief outline of some non-clasical logics such as modle logic and tense logic. I would recommend this book to anybody.

Too tied to the software, 09 Oct 2008
This was a required reading piece for a degree course so I've been over this book in detail.

The explanations provided in the book are excellent and give you a good grasp of the material. However, the majority of the book is talking you through exercises in the software provided.

I felt like there was too much emphasis on the software and that there should have been more examples where you did not have to consult your computer.

Ignore the answers completely., 15 Jun 2008
Never before have I felt compelled to write a review, but this book annoyed me so much that it had to be done.

The book consists of several chapters teaching you skills such as ratios and percentages, this first part is absolutely fine and the answers that I checked were correct also.

However, the final part of the book, the section which should be the most useful, data interpretation. You are given quite a few different data interpretation questions to answer in the form of tables, bar graphs and pie charts, all good so far. But unbelievably so after you have racked your brain to figure out the answers, only to discover that the 'correct' answers written in the book are wrong. Needless to say this is indeed infuriating, especially as it takes you a while to realise this, at one point I thought I was making no progress at all.

Although the bulk of the book is useful I would avoid purchasing the book purely because of its blatant mistakes.

How to pass numerical reasoning tests: a step-by-step guide to learning key numeracy skills (how to pass), 06 Jun 2008
This book is rubbish it does not teach you a single thing and if I could give it 0 out of 5 I would. It's boring, confusing and doesnt explain anything clearly how it ever got printed is beyond me, don't waste your money.

Infuriating, 25 Jan 2008
It's not often I feel compelled to write a review of a book or anything else for that matter but, this book has infuriated me to such an extent that I feel I have to.

Are the questions representative of those you might find in a real numerical reasoning test? Yes.

Does the book have a reasonable number of practice questions? Yes.

Will this book help you pass a numerical reasoning test? No

Why??

The questions often try to catch you out which, ordinarily, is fine. However, the author over does this too such an extent that sometimes even they appear to be confused (as can be seen by their incorrect explanation of the answer). This is a problem because often in real tests you might only get 45 seconds or so per question and after reading this book you'll find yourself searching for things in real tests that simply don't exist. Another problem is the confusing way in which the questions are worded which, when combined with a smattering of incorrect answers and the aforementioned will have you screaming in no time!

I ran this book by a couple of my friends who both have masters' degrees in maths from Imperial College. They struggled even more than I did!! Could they do the maths? Yes. Could they make sense of this book? No. You've been warned.

Excellent book for reviewing your math skills., 22 Nov 2007
I have been studying in university for quite a while but in my current subject area, I didn't have to solve mathematical questions. However, I was applying for jobs which also involve case studies and numerical reasoning tests. This book was very helpful, it explains calculating with big numbers, percentages, ratios, etc. In addition, you got some practice questions, as well. I would definitely recommend this book if you wanna brush up your math skills.

Learning the trade, 04 Nov 2007
If you havent touched any maths for years and require to polish your basic maths skills, this is the book. You can oil all them rusty questions and grey areas with this book.

If your facing an SHL numeric test for the first time, you may want to have a look at this as it has all the basic numerical functions. THIS BOOK DOES NOT HAVE SHL TYPE QUESTIONS.

Do not rely on this book if you have a graduate level test. Its only for basic's which its very good at.

This book is the one ...., 05 Mar 2008
I would recommend for everybody who has an interest in mathematics and the development of his mind, whatever his age or education. I've got a lot of mathematical books but this one is a very special one, because it is the only one that could hook me from page one till the end.
It is not a book for readers but a book for people who want to be actively involved with thinking and mathematics. And when I say mathematics I do not mean those high school mathematics books that are designed to torture every student. When you are going to study science at university i would recommend reading this book, because it develops your brain-solving capabilities.


Life changing, 09 Jul 2005
In my experience there are no books that could be termed "life changing". Except this one :)

My view of mathematics was as a dry, complete subject until I met the work of John Mason during my mathematics degree with the OU. This book completed what he started there - and changed me into a passionate mathematician, as opposed to someone who could simply do maths.

'Thinking Mathematically' helps teach you how to literally think like a mathematician, something that a lot of schools fail at. It uses a series of problems that are genuinely interesting and guides you through the process of solving them. For example; "How many squares are on a chessboard?" (It's not 64!).

The books only drawback is that time is not just spent on reading, but also really working on the problems, many of which do not have solutions, and thus I have never manged to finish it!

A wonderful book. Buy now!

A wonderful book for teachers and students alike, 05 Apr 2004
"Thinking Mathematically" is a wonderful book that I warmly recommend to anyone teaching mathematics, at any level, from primary school to university lecturer. I was recently involved in designing an undergraduate course incorporating mathematical writing and thinking, and problem solving. I have only subsequently discovered this book - and John Mason's "Learning and Doing Mathematics" - when I come to write the lectures for the course, these two books will be my main references. There are many excellent open-ended problems for investigation, and the thought processes involved in thinking mathematically are beautifully explained. The problems are at a sufficiently low level that they are likely to be useful for teachers at all levels. I shall encourage our library to buy copies of these books and will strongly recommend them to our students.

A unique and immensley practical book., 25 Apr 2002
This book requires no specialist maths knowledge (hardly any required) but almost from the first page will immerse you in the techniques and strategies which underly mathematical thinking.
I've used this book for many years and still keep coming back to it.
It is the only book I've ever seen which addresses the true emotional states a problem solver must go through AND shows you how to deal with them. Best of all, it will teach you to ask your own questions and find your own answers by the time you reach the end.
I'd suggest one takes one time to really absorb the tips presented in the book - well worth it.

Mr Spock would like this, 17 Nov 2008
I have always had a fairly logical mind having studied subjects such as mathematics, physics and accounting to a high level and I have always enjoyed doing crossword puzzles and other puzzles including IQ tests.

Some people can obviously think logically more easily than others since computer firms used to (and maybe still do) give one a sort of IQ test to see if one can learn to programme a computer.

Logic is also something that can be studied and it is treated like a science. It is a branch of philosophy and until the nineteenth century there hadn't been many advances on Aristotle's system. Attempts in the late nineteenth century and early twentieth century to reduce mathematics to logic by Bertand Russell and others were unsuccesful but Russell and many other scientists, mathematicians and philosophers greatly expanded the scope and range of logic introducing symbols and a wider range of techniques.

This is a compelling albeit basic introduction by an author who knows his stuff.

Not a course in logic, but a briliant taster., 07 Nov 2008
This book will not teach you logic.

What it will do, and it will do it well, is give you a high-speed tour of logic - including some background information, how logical arguments become symbolised, show the main areas of the subject, along with some existing puzzles in the field.

While you won't really learn logic from it, it will certainly make you want to learn logic!

A logical choice..., 24 Nov 2005
Graham Priest is author of several books on logic, including 'An Introduction to Non-Classical Logic' and 'Towards Non-Being: The Logic And Metaphysics Of Intentionality'. He has experience as a professor of logic at the University of Queensland in helping to determine the needs of those who are in need of logic help. This book, part of the Very Short Introductions series of Oxford University, is both an introduction and a refresher for those who have had logic before. Because of its brevity, it might be a bit too condensed for those looking for a logic course; however, used together with a larger text (Copi's logic book is the one I used in my early logic days), this VSI book provides good supplemental information and helps clarify key points.

This book provides an introduction both to symbolic logic as well as linguistic logic. Issues such as probability, truth and fact statements, conditional statements, decision theory and validity are all presented in clear, concise ways. There are fourteen chapters (a lot of chapters for book with barely over 100 pages of text), and each chapter deals with a few key points summarised in a pull-quote box at the end of each chapter. There are diagrams, sentences and equations to illustrate the points in visual as well as language terms.

The final chapter, 'A Little History and Some Further Reading', is a good short review of key figures and historical issues that underpin the material presented in the previous chapters. There is a helpful glossary of terms, and Priest also provides a page of logic puzzles and problems to be worked by the students, keyed to an Oxford University Press website that has the solutions to the questions.

This is a good book for review of logic prior to taking tests (such as the LSAT) or graduate courses that require understanding of logical thought processes (systematic theology or philosophy). As some reviewers have noted, this is not a lock-step presentation of standard analytic logic (indeed, many of Priest's other writings have a more non-standard approach), but does provide some good insights in the overall way in which logic is structured and done.

Not suitable for beginners, 05 Jun 2003
This book is really not an introductory text.
It does delve too deep for someone not acquainted with formal logic.
The Icon Series Introducig Logic is a much easier read and gives a more comprehensive overview of the subject.
This book is probably better read by someone who has a background in the subject.

A very good introduction, 18 Oct 2002
..this book is a very good introduction to logic, a fundamental aspect of philosohpy and mathematics. For example, logical propositions are constructed as a so called fraction with the premiss as the "numerator" and the conclusion as the "denominator", and this is explained clearly on page 7 out of 109.

The book condenses a wide range of loigcal topics into 109 pages very well, and as it says on the back cover 'it does not attempt to be a text-book' but rather provides a basic introduction to logic.

Any one with a difficulty, perhaps, to mathemtics and symbols might find this book slighlty challenging, but even then the symbols are explained so well it should be no problem. Besides, one cannot hope to be introduced to a technical subject, similar but not the same as mathematics, without the use of symbols.

The whole text is very thought provoking and mentally stimulating, and further questions for consideration are provided a the back, as well as a further reading list.

So, this book is a good introduction for anyone interested in formal logic, mathematics, computers etc., irrespective of previous knowledge.

Very good book, 03 Dec 2008
The author seems to have been a classicist, theologian, philosopher and mathematician at various stages in his career. He has held a chair in mathematics and has written books on many subjects including history and psychology and has given lectures on music too.

This book is a paperback and has forty four chapters and is 292 pages long. It teaches various aspects of logic and makes use of symbols and diagrams.

This is not for expert logicians but is somewhat stronger than many critical thinking books. Would probably suit mathematics and philosophy students rather than general readers.


As a beginner..., 19 May 2006
...I had to start somewhere. There are plenty of examples throughout and exercises to do. More importantly the majority of the answers are in the back of the book for those of us who are more perplexed.

Admittingly some of the methods seem perhaps a bit dated but this is still a good book to have to start you off. Just enough to raise your game but easy enough for beginners to get a grasp of. Of course if you do get into logic properly though this only really scratches the surface.

One for the devoted fans and hard-working students of logic, 09 May 2004
This old-fashioned book is a more formal look at Logic, and its transcription into symbols and constituents in order to evaluate the truth and validity of paragraphs. Things get pretty messy towards the end, so avoid this if you're going for a lateral thinking type approach to the area.
This is a book to inform and educate, and does so very clearly, with simple excercises to do throughout (answers in the back), and plenty of info is given in each chapter - there's no dull waffle, all vital stuff for the next chapters.

Good luck with this taxing but effective look into the study of Logic.

An excellent introduction, 19 Dec 2002
Wilfrid Hodges' book is a comprehensive introduction to its subject, it's attractive presentation making the complexities and abstract qualities of his themes far more accessible. The book conveys something of the history of the subject through references to key names (e.g. Carnap and Russell) and suggests the relevance of logical thought to everyday activities. An excellent introduction to the Philosophy of Logic which invites the reader though clear explanations, rather than leaving them at a distance through what might otherwise be the daunting, mathematical-style appearance of numbers and symbols.

An excellent introduction to formal logic., 03 Dec 2002
Presuming no prior knowledge neither of philosophy nor logic, Hodges' book is an excellent, non technical, introduction to the subject. Although some sections of the book are mathematical, these are clearly indicated by the author and may be skipped if the reader wishes, without detriment to the rest of the book. This book presents the classical system of formal logic, introducing the reader to both propositonal and first order predicate calculi. Unlike most introductory texts, this book uses the semantic tree tableau method of deduction which some students find easier to understand than N.D.. Although I find this method a little cumbersome, it has the advantage of translating truth tables to deduction. Hodges the reader through some elementary meta-theory up to the interpolation theorem. The book concludes with a brief outline of some non-clasical logics such as modle logic and tense logic. I would recommend this book to anybody.

Too tied to the software, 09 Oct 2008
This was a required reading piece for a degree course so I've been over this book in detail.

The explanations provided in the book are excellent and give you a good grasp of the material. However, the majority of the book is talking you through exercises in the software provided.

I felt like there was too much emphasis on the software and that there should have been more examples where you did not have to consult your computer.

Absolutely brilliant A **, 17 Apr 2006
The first time I've bothered to leave my thoughts on a book. But this one is well worth a recommendation. A must if you wanna recap or bridge knowledge from GCSE level onwards

Gives easily understood explanations, 31 Mar 2006
I've just started studying maths with the Open University and have found this book invaluable. I haven't really thought above maths since leaving school 30 years ago and so needed a refresher in the basics, algebra, fractions, etc. This book has been a great help!

Fantastic book to help bridge the gap, 12 Feb 2003
I was having real difficulty with the maths portion of my Computer Engineering degree having not done A level maths. This book goes over the concepts needed in everyday language and is easy to follow with helpful tips and assessment sections. A must for anyone who is having problems with maths.

Ignore the answers completely., 15 Jun 2008
Never before have I felt compelled to write a review, but this book annoyed me so much that it had to be done.

The book consists of several chapters teaching you skills such as ratios and percentages, this first part is absolutely fine and the answers that I checked were correct also.

However, the final part of the book, the section which should be the most useful, data interpretation. You are given quite a few different data interpretation questions to answer in the form of tables, bar graphs and pie charts, all good so far. But unbelievably so after you have racked your brain to figure out the answers, only to discover that the 'correct' answers written in the book are wrong. Needless to say this is indeed infuriating, especially as it takes you a while to realise this, at one point I thought I was making no progress at all.

Although the bulk of the book is useful I would avoid purchasing the book purely because of its blatant mistakes.

How to pass numerical reasoning tests: a step-by-step guide to learning key numeracy skills (how to pass), 06 Jun 2008
This book is rubbish it does not teach you a single thing and if I could give it 0 out of 5 I would. It's boring, confusing and doesnt explain anything clearly how it ever got printed is beyond me, don't waste your money.

Infuriating, 25 Jan 2008
It's not often I feel compelled to write a review of a book or anything else for that matter but, this book has infuriated me to such an extent that I feel I have to.

Are the questions representative of those you might find in a real numerical reasoning test? Yes.

Does the book have a reasonable number of practice questions? Yes.

Will this book help you pass a numerical reasoning test? No

Why??

The questions often try to catch you out which, ordinarily, is fine. However, the author over does this too such an extent that sometimes even they appear to be confused (as can be seen by their incorrect explanation of the answer). This is a problem because often in real tests you might only get 45 seconds or so per question and after reading this book you'll find yourself searching for things in real tests that simply don't exist. Another problem is the confusing way in which the questions are worded which, when combined with a smattering of incorrect answers and the aforementioned will have you screaming in no time!

I ran this book by a couple of my friends who both have masters' degrees in maths from Imperial College. They struggled even more than I did!! Could they do the maths? Yes. Could they make sense of this book? No. You've been warned.

Excellent book for reviewing your math skills., 22 Nov 2007
I have been studying in university for quite a while but in my current subject area, I didn't have to solve mathematical questions. However, I was applying for jobs which also involve case studies and numerical reasoning tests. This book was very helpful, it explains calculating with big numbers, percentages, ratios, etc. In addition, you got some practice questions, as well. I would definitely recommend this book if you wanna brush up your math skills.

Learning the trade, 04 Nov 2007
If you havent touched any maths for years and require to polish your basic maths skills, this is the book. You can oil all them rusty questions and grey areas with this book.

If your facing an SHL numeric test for the first time, you may want to have a look at this as it has all the basic numerical functions. THIS BOOK DOES NOT HAVE SHL TYPE QUESTIONS.

Do not rely on this book if you have a graduate level test. Its only for basic's which its very good at.

This book is the one ...., 05 Mar 2008
I would recommend for everybody who has an interest in mathematics and the development of his mind, whatever his age or education. I've got a lot of mathematical books but this one is a very special one, because it is the only one that could hook me from page one till the end.
It is not a book for readers but a book for people who want to be actively involved with thinking and mathematics. And when I say mathematics I do not mean those high school mathematics books that are designed to torture every student. When you are going to study science at university i would recommend reading this book, because it develops your brain-solving capabilities.


Life changing, 09 Jul 2005
In my experience there are no books that could be termed "life changing". Except this one :)

My view of mathematics was as a dry, complete subject until I met the work of John Mason during my mathematics degree with the OU. This book completed what he started there - and changed me into a passionate mathematician, as opposed to someone who could simply do maths.

'Thinking Mathematically' helps teach you how to literally think like a mathematician, something that a lot of schools fail at. It uses a series of problems that are genuinely interesting and guides you through the process of solving them. For example; "How many squares are on a chessboard?" (It's not 64!).

The books only drawback is that time is not just spent on reading, but also really working on the problems, many of which do not have solutions, and thus I have never manged to finish it!

A wonderful book. Buy now!

A wonderful book for teachers and students alike, 05 Apr 2004
"Thinking Mathematically" is a wonderful book that I warmly recommend to anyone teaching mathematics, at any level, from primary school to university lecturer. I was recently involved in designing an undergraduate course incorporating mathematical writing and thinking, and problem solving. I have only subsequently discovered this book - and John Mason's "Learning and Doing Mathematics" - when I come to write the lectures for the course, these two books will be my main references. There are many excellent open-ended problems for investigation, and the thought processes involved in thinking mathematically are beautifully explained. The problems are at a sufficiently low level that they are likely to be useful for teachers at all levels. I shall encourage our library to buy copies of these books and will strongly recommend them to our students.

A unique and immensley practical book., 25 Apr 2002
This book requires no specialist maths knowledge (hardly any required) but almost from the first page will immerse you in the techniques and strategies which underly mathematical thinking.
I've used this book for many years and still keep coming back to it.
It is the only book I've ever seen which addresses the true emotional states a problem solver must go through AND shows you how to deal with them. Best of all, it will teach you to ask your own questions and find your own answers by the time you reach the end.
I'd suggest one takes one time to really absorb the tips presented in the book - well worth it.

Mr Spock would like this, 17 Nov 2008
I have always had a fairly logical mind having studied subjects such as mathematics, physics and accounting to a high level and I have always enjoyed doing crossword puzzles and other puzzles including IQ tests.

Some people can obviously think logically more easily than others since computer firms used to (and maybe still do) give one a sort of IQ test to see if one can learn to programme a computer.

Logic is also something that can be studied and it is treated like a science. It is a branch of philosophy and until the nineteenth century there hadn't been many advances on Aristotle's system. Attempts in the late nineteenth century and early twentieth century to reduce mathematics to logic by Bertand Russell and others were unsuccesful but Russell and many other scientists, mathematicians and philosophers greatly expanded the scope and range of logic introducing symbols and a wider range of techniques.

This is a compelling albeit basic introduction by an author who knows his stuff.

Not a course in logic, but a briliant taster., 07 Nov 2008
This book will not teach you logic.

What it will do, and it will do it well, is give you a high-speed tour of logic - including some background information, how logical arguments become symbolised, show the main areas of the subject, along with some existing puzzles in the field.

While you won't really learn logic from it, it will certainly make you want to learn logic!

A logical choice..., 24 Nov 2005
Graham Priest is author of several books on logic, including 'An Introduction to Non-Classical Logic' and 'Towards Non-Being: The Logic And Metaphysics Of Intentionality'. He has experience as a professor of logic at the University of Queensland in helping to determine the needs of those who are in need of logic help. This book, part of the Very Short Introductions series of Oxford University, is both an introduction and a refresher for those who have had logic before. Because of its brevity, it might be a bit too condensed for those looking for a logic course; however, used together with a larger text (Copi's logic book is the one I used in my early logic days), this VSI book provides good supplemental information and helps clarify key points.

This book provides an introduction both to symbolic logic as well as linguistic logic. Issues such as probability, truth and fact statements, conditional statements, decision theory and validity are all presented in clear, concise ways. There are fourteen chapters (a lot of chapters for book with barely over 100 pages of text), and each chapter deals with a few key points summarised in a pull-quote box at the end of each chapter. There are diagrams, sentences and equations to illustrate the points in visual as well as language terms.

The final chapter, 'A Little History and Some Further Reading', is a good short review of key figures and historical issues that underpin the material presented in the previous chapters. There is a helpful glossary of terms, and Priest also provides a page of logic puzzles and problems to be worked by the students, keyed to an Oxford University Press website that has the solutions to the questions.

This is a good book for review of logic prior to taking tests (such as the LSAT) or graduate courses that require understanding of logical thought processes (systematic theology or philosophy). As some reviewers have noted, this is not a lock-step presentation of standard analytic logic (indeed, many of Priest's other writings have a more non-standard approach), but does provide some good insights in the overall way in which logic is structured and done.

Not suitable for beginners, 05 Jun 2003
This book is really not an introductory text.
It does delve too deep for someone not acquainted with formal logic.
The Icon Series Introducig Logic is a much easier read and gives a more comprehensive overview of the subject.
This book is probably better read by someone who has a background in the subject.

A very good introduction, 18 Oct 2002
..this book is a very good introduction to logic, a fundamental aspect of philosohpy and mathematics. For example, logical propositions are constructed as a so called fraction with the premiss as the "numerator" and the conclusion as the "denominator", and this is explained clearly on page 7 out of 109.

The book condenses a wide range of loigcal topics into 109 pages very well, and as it says on the back cover 'it does not attempt to be a text-book' but rather provides a basic introduction to logic.

Any one with a difficulty, perhaps, to mathemtics and symbols might find this book slighlty challenging, but even then the symbols are explained so well it should be no problem. Besides, one cannot hope to be introduced to a technical subject, similar but not the same as mathematics, without the use of symbols.

The whole text is very thought provoking and mentally stimulating, and further questions for consideration are provided a the back, as well as a further reading list.

So, this book is a good introduction for anyone interested in formal logic, mathematics, computers etc., irrespective of previous knowledge.

Very good book, 03 Dec 2008
The author seems to have been a classicist, theologian, philosopher and mathematician at various stages in his career. He has held a chair in mathematics and has written books on many subjects including history and psychology and has given lectures on music too.

This book is a paperback and has forty four chapters and is 292 pages long. It teaches various aspects of logic and makes use of symbols and diagrams.

This is not for expert logicians but is somewhat stronger than many critical thinking books. Would probably suit mathematics and philosophy students rather than general readers.


As a beginner..., 19 May 2006
...I had to start somewhere. There are plenty of examples throughout and exercises to do. More importantly the majority of the answers are in the back of the book for those of us who are more perplexed.

Admittingly some of the methods seem perhaps a bit dated but this is still a good book to have to start you off. Just enough to raise your game but easy enough for beginners to get a grasp of. Of course if you do get into logic properly though this only really scratches the surface.

One for the devoted fans and hard-working students of logic, 09 May 2004
This old-fashioned book is a more formal look at Logic, and its transcription into symbols and constituents in order to evaluate the truth and validity of paragraphs. Things get pretty messy towards the end, so avoid this if you're going for a lateral thinking type approach to the area.
This is a book to inform and educate, and does so very clearly, with simple excercises to do throughout (answers in the back), and plenty of info is given in each chapter - there's no dull waffle, all vital stuff for the next chapters.

Good luck with this taxing but effective look into the study of Logic.

An excellent introduction, 19 Dec 2002
Wilfrid Hodges' book is a comprehensive introduction to its subject, it's attractive presentation making the complexities and abstract qualities of his themes far more accessible. The book conveys something of the history of the subject through references to key names (e.g. Carnap and Russell) and suggests the relevance of logical thought to everyday activities. An excellent introduction to the Philosophy of Logic which invites the reader though clear explanations, rather than leaving them at a distance through what might otherwise be the daunting, mathematical-style appearance of numbers and symbols.

An excellent introduction to formal logic., 03 Dec 2002
Presuming no prior knowledge neither of philosophy nor logic, Hodges' book is an excellent, non technical, introduction to the subject. Although some sections of the book are mathematical, these are clearly indicated by the author and may be skipped if the reader wishes, without detriment to the rest of the book. This book presents the classical system of formal logic, introducing the reader to both propositonal and first order predicate calculi. Unlike most introductory texts, this book uses the semantic tree tableau method of deduction which some students find easier to understand than N.D.. Although I find this method a little cumbersome, it has the advantage of translating truth tables to deduction. Hodges the reader through some elementary meta-theory up to the interpolation theorem. The book concludes with a brief outline of some non-clasical logics such as modle logic and tense logic. I would recommend this book to anybody.

Too tied to the software, 09 Oct 2008
This was a required reading piece for a degree course so I've been over this book in detail.

The explanations provided in the book are excellent and give you a good grasp of the material. However, the majority of the book is talking you through exercises in the software provided.

I felt like there was too much emphasis on the software and that there should have been more examples where you did not have to consult your computer.

Absolutely brilliant A **, 17 Apr 2006
The first time I've bothered to leave my thoughts on a book. But this one is well worth a recommendation. A must if you wanna recap or bridge knowledge from GCSE level onwards

Gives easily understood explanations, 31 Mar 2006
I've just started studying maths with the Open University and have found this book invaluable. I haven't really thought above maths since leaving school 30 years ago and so needed a refresher in the basics, algebra, fractions, etc. This book has been a great help!

Fantastic book to help bridge the gap, 12 Feb 2003
I was having real difficulty with the maths portion of my Computer Engineering degree having not done A level maths. This book goes over the concepts needed in everyday language and is easy to follow with helpful tips and assessment sections. A must for anyone who is having problems with maths.

A very useful book for anyone thinking of doing Mathematics at university., 31 Oct 2006
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.

An Excellent Introduction to Pure Mathematics, 17 Sep 2006
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.

An excellent introduction to university mathematics, 27 Sep 2004
The gap between high school and university mathematics is
quite noticeable. I found this book to be an excellent book
to prep a smooth landing to university mathematics.
(The best one out of a long list of other similar books
I had a look at)

Starts of really easy and clear but still goes beyond the
"surface" when required.
The chapters are structured very short, which I thought
was a good thing.

It has a lot of worked examples.
However, the book does not have solutions to the
end-of-chapter exercises, which I thought was a long minus
since I was reading the book on my own as a self study..

But all in all, a very enjoyable book to read!

Very useful, 11 Sep 2004
This book is ideal for A-level students who are considering doing a numerate degree, particularly maths. It contains lots of useful methods and tricks, with full proofs of every theorem. It isn't highly technical, nor does it go into much depth, but it is an excellent primer and will make you realise some of the amazing things that can be proved quite simply with the right concepts.

Enjoyable and educational, 05 Sep 2000
A concise Introduction to Pure Mathematics is very legible, it is written so that it is absorbed easily, it intoduces many prime topics including a very extensive and clear section on Integration