Numbers & Proofs (Modular Mathematics Series)

This book is very approachable and spans the school to university mathematics. It presents in the first chapter 18 "test" statements that can be proved mathematically. The rest of the book takes the statements progressively and by explanation, further examples and student exercises it helps the reader to first clearly understand what each statement is saying then working through the proof.Different wording of statements requires different approaches. For example:Statement 4: IF 2^67 - 1 is prime then 2^67 + 1 is divisible by 3.andStatement 15: There exists a unique positive integer t such that t + 2 and t + 4 are all primes.Most of the examples are from (simple) number theory since these are the most accessible and familiar to most readers.I particularly like the discussion before the working of a proof that tries to work through the thinking that leads to the choice of a particular approach that is valid. Also it helps you read a mathematical statement so you can understand what is (are) the given(s) and what result you have to establish. I like example 1:"300 000 067 110 605 737 is not a perfect square"What are you being asked to prove? Is this statement actually true? The book clearly tackles such uncomfortable questions.The exercises help to clarify and reinforce the approach in the worked example. The book is finished off by a discussion of fallacies and mistakes in proofs.That's what the book contains and I think it does that job well. Beyond that, I think this is an important book because it introduces and develops skill in proof, a skill that is much neglected in school maths which focusses on applying methods without questioning if the approach is valid. If ever you are slightly bothered as to whether the mathematics you are writing is actually valid or are not clear as to what a mathematical question is asking you to show, then this may be the book for you.

* PhysicalThe book is printed on b&w quality paper, and a good size of font.* Target audience; A-level, H.N.D. undergraduate, postgraduate?This book is pitched at around A-level, H.N.D.(2). or perhaps first year degree?* What is the best about this book?The book is pitched at a wide - level, with enough information to illuminate the introductory bits of this topic. It covering basic logic, AND, OR and NOT in conditional 'if' true or false forms often in words, Mathematical induction, math sets of numbers ( integers, reals , quotients,real and rational numbers, prime numbers, and also complex numbers in a helpful way.The great thing is it assumes little as required prerequisites, it describes enough to help, and not enough to leave you hanging lost. There is also answers and help file supplied at the back of this volume.* SummaryThis is a lovely introductory book, a good starting point in truths and proofs. The price is great too. Its given me confidence to try a deeper book in the same topic area. What's better than this in a math book?

Handy for my first year on a maths degree, easier to read and follow than most textbooks I've seen so far too. Clear equations and explanations.

This book is outstanding. There is a growing recognition that in teaching mathematics we are not just imparting knowledge but teaching students to think as mathematicians think. A corollary of this is that it is often helpful to say something about the historical individuals who discovered the major theorems. Allenby achieves both of these aims with flying colours. By expressing the chains of thought that might pass through a mathematician's head as he grapples with a wide range of carefully selected problems, often in a light-hearted vein, he encourages us to think for ourselves. By interspersing these with biographical sketches of some of the giants of mathematical history he reminds us that maths is an activity carried out by people. The result is a book which meets a need in a way that is well nigh unique and will attract and instruct many.

Excellent print quality like 1960s newspaper. Low resolution font such that it won't hurt your eyes.Book dimension is much larger than the specification. What a big surprisedThe book is printed in Poland. I can't help liking the quality of Poland.Amazon service is excellent too to provide guides to teach me how to write only a good review.I hope you can read into my review and feel the happiness of the excellent quality ..

This book is good for readers that do not have too much mathematical background or those who need to brush up on some mathematical ideas of logic and rigorous mathematical thinking. Number Theory is used here only for illustration and because it's so familiar to all of us.

Super book! Covers the transition ideas from school to Uni with both humour and rigour. Really good for 'dipping-in'.

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.

Good