What Is Mathematics?: An Elementary Approach to Ideas and Methods 2nd Edition by Herbert Robbins (PDF)

Description

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant’s and Herbert Robbins’s classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat’s Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar–a matter of the correct application of local rules. Meaningful mathematics is like journalism–it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature–it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature–it opens a window onto the world of mathematics for anyone interested to view.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent read, I had always wondered; and now I know.It’s a total nerd book, if you love math at the conceptual level, enjoy history, and the engineering aspect of how things came to be- this is a great book. I’m a network engineer, wife turned me on to this book from her college days – she was a math major. Well written, decently paced given the subject matter, and enlightening.If none of the above interests you, the book may also be used as a soporific.

⭐Book contents are very good, but the diagrams are too small.

⭐This is like a mathematics bible!!! It touches on subjects that I have learned as a math major throughout my college career. It is also an easy read and I love how it contains exercises throughout the reading. If you are looking for a math book to refresh your mind on some content, then this is the book for you as well!!!

⭐I’m really excited to have gotten this book. I used to hate math, and as a college student, I got lucky enough to have a great teacher who helped me appreciate the subject. This book has everything! The basics all the way through calculus. It’s accessible to many levels too. When I finish school and begin teaching, I will be using this book to create lesson plans. Out toy like math at all, or want to learn, this is a great book.

⭐really love this book, hope i met this book earlier. this gives me a whole new view of math and the logic flows, maths becomes natural to explain!!

⭐It is a shame that this edition is low-quality photo-copy of previous edition on low-quality papers with low-quality binding. This classic deserves a much better treatment.

⭐After reading this:”It doesn’t matter what mathematical things are: it’s what they do that counts. Thus mathematics hovers uneasily between the real and the not real; its meaning does not reside in formal abstractions, but neither is it tangible. This may cause problems with philosophers who like tidy categories, but it is the great strength of mathematics — what I have elsewhere called its ‘unreal reality.’ Mathematics links the abstract world of mental concepts to the real world of physical things without being located completely in either.” – Ian Stewart, What is Mathematics?…I was hooked and after reading it several times, I still can’t put it down! Great job to all who contributed to creating this masterpiece.

⭐This is a great overview of many key areas of modern mathematics. The book is wonderful because it’s not a typical “For Dummies” book. It has some real mathematics in it, and many of the theorems and proofs are mathematical masterpieces that every Ph.D. student should know. If you want to master the basics, I would use this book along with your text books. This book gives a really good overview of many important areas of mathematics.

⭐Not quite what I wanted, but that’s my fault – caveat emptor. I’m wanted something on the philosophy of maths, but this is basically a maths textbook, although it is much more discursive than the ones I remember from school and is quite a good read. Early on, the authors put me in my place by remarking that the mathematical object “exhausts itself in the totality of its possible relations with the perceiver [and although] these relations must be co-ordinated with the thing in itself” further speculation on this point can be let to the philosophers. Nevertheless it is a beautiful book and I shall keep it as a handy reference to the subject. I have one criticism, which is that the text dates from 1941 but recent developments are set out in an appendix written by Ian Stewart in 1996. It would have been useful to have the main text marked-up to show where there is further matter in the appendix.

⭐This is a good book if you have a good level of mathematics knowledge already. The book is for university student, not for a high school student.

⭐This book is probably my all time favourite mathematics text for introducing undergraduate mathematics. The author is a prolific writer and very engaging. The breadth of topics covered is impressive.

⭐A classic – but still highly enjoyable introduction to basic concepts and ideas in Mathematics. This revised version includes interesting updates by I. Stewart.

⭐All ok

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