This well written book by Professor Hamkins has a variety of interesting elementary mathematics And has many nuggets of wisdom eg the number 1 and prime factorization the usemention distinction with fractions and rational numbers and vacuous truth It s an excellent choice for aspiring mathematicians The author of the book is a world class set theorist who probably than anyone else has promoted a multiverse realism in set theory This argument somewhat crudely advances the point that the independence results obtained from the method of forcing suggest a multiplicity of set theory universes similar to that of non Euclidian geometries In

set * theory universes similar to that of non Euclidian geometries In he also *universes similar to of non Euclidian geometries In he has also the idea that the phenomenon of independence can even be found at the level of arithmetic I think he is wrong and my particular philosophical inch is better satisfied by the work of Hugh Woodin However the point remains that Joel David Hamkins is an exceptional philosophically astute mathematician whose work I have enjoyed immensely So I was disappointed when I discovered severe errors early in the book I even e mailed the author and have received no replyDear SirOn page 3 you define the natural numbers as 0 1 2 3 In doing so by distinguishing natural number from 1 2 3 a definition which is common in many mathematical texts especially undergraduate textbooks in elementary number theory In addition you also explain that subtraction between two natural numbers does not always result in another natural number and use this as a ustification for the integers Of course we could define subtraction in the natural numbers as cut off subtraction which would allow subtraction between any two natural numbers however you make no mention of this mathema. An introduction to writing proofs presented through compelling mathematical statements with interesting elementary proofsThis book offers an introduction to the art and craft of proof writing The author.

## Joel David Hamkins Á 5 Read & Download

Are beautifully illustrated and described in accessible butrigorous termsMy 7 year old daughter looks over my shoulder when I m reading this book and askstermsMy 7 year old daughter looks over my shoulder when I m reading this book and asks of curious uestions This book has been a great introduction to the beauty and wonder of mathematics for this budding mathematician Excellent purchase Especially Like The Mathematical like the mathematical sections which will surely cause a moment of reflection and will serve as conversation starters Proof and the Art of Mathematics is a wonderful book for multiple reasons first of all it really does what it says on the cover namely to introduce aspiring mathematicians to the art of writing proofsThis is achieved through a combination of being walked through various elegant proofs selected by Prof Hamkins being asked to critiue mistaken proofs which contain some subtle errors but most importantly by being provided with many carefully chosen exercises so that you can practise what you learn any craft reuires some personal effort At the very end of the book the author provides answers to some selected exercises where the you can compare your own proof attempts with model proofsOne big plus for me is the variety of mathematical areas covered you ll find sections on topics such as the mathematics of the infinite number theory combinatorics real analysis and many a total of 15 topics Each section is sprinkled with bits of mathematical wisdom which are bound to improve the mathematical skills of anyone willing to attempt the exercises with them in mind The book also contains some very helpful coloured illustrations Also I ve had a positive experience with the delivery I received this book on my doorstep only one day after its release despite not living in the UK. Ory combinatorics graph theory the theory of games geometry infinity order theory and real analysis The goal is to show students and aspiring mathematicians how to write proofs with elegance and precisi. Tical operation in the text

*page 10 you give Theorem 6 For any natural number n the number n2 is even Clearly this is true and defined in the natural*

On page 10 you give Theorem 6 For any natural number n the number n2

numbers as n2 is always eual or greater than nThe problem is in proof 2 byas n2 is always eual or greater than nThe problem is in proof 2 by school algebra in which you prove this theorem by rewriting n2 n as nn 1 n 1 Is Not Always A not always a number take n0 as your previous comments on page 3 point out uite naturally some may consider this a minor uibble however as the text has made the definitions of natural number and subtraction although informal at least conceptually clear The proof as it stands fails in the natural numbersThis does not seem to be a misprint and this is my point as he makes a similar mistake on page 12 In short very disappointed and so cannot recommend the book I will not continue with the book and will be returning my copy The author demonstrates his ability to write proofs and his inability to explain how to write them I cannot believe that anyone would find this helpful Even if you already have substantial training in mathematics this book is worth reading Functional Occlusion in Restorative Dentistry and Prosthodontics E-Book - Kindle edition by Iven Klineberg, Steven Eckert. Professional Technical Kindle eBooks @ Amazon.com. just for the elegance of the proofs Great book I recommend it for anyone who is interested in math Whether you are a beginner or advanced you will surely find something in the book that catches your attention I was really blown away by this book Besides the uality of the diagrams and illustrations which go far beyond any popular mathematics book I ve ever purchased the variety and depth of examples of proof techniues is really impressive All my old favorites like tiling a checkerboard and the mxn chocolate bar problem and many that I ve never seen before a proof that the number of different infinities is not any of the infinities. A leading research mathematician presents a series of engaging and compelling mathematical statements with interesting elementary proofs These proofs capture a wide range of topics including number the.