For one, your time would be better spent reading Heath's translation of Euclid. I'll see how it compares. This book has risen to the top to be one of my favorite math books. The other is David Foster Wallace's book on Infinity. What makes them fun are these are prose books on math. The rigor is there but you do not need to work through the actual with a pencil and paper. Instead the author walks you through the logic. You will find this book very difficult at times.
But that's the point. It's fun to be challenged. You don't need any knowledge of advanced math to read this book. What makes it fun is t This book has risen to the top to be one of my favorite math books. What makes it fun is that the author walks you through the most famous proofs in all of mathematics simplifying them to simple equations that you can solve in your head.
Some of these are difficult and you will need to pull out paper and pencil. But there is a lot of joy in understanding, for example, how the proof of Fermat's Last Theorem works or what is an algebraic expression. Feb 13, Phil Filippak rated it did not like it Shelves: maths , dropped.
I am strongly disappointed with this book. I think it only delayed my progress in mathematics. And here's why: written supposedly for non-mathematicians it contains so many abstract concepts and strict reasoning that it's virtually impossible to apprehend it being a person with a non-technical background put aside that I work as a software developer for almost 5 years now. For me, the book is more like Wikipedia than like a guide for newcomers.
My point is that for a novice, a tour into somethi I am strongly disappointed with this book. My point is that for a novice, a tour into something new should contain hooks tying new ideas to the person's previous experience.
And this book doesn't provide such approach at all. Oct 24, Ankush Rajput rated it really liked it. Passed a lot of math courses but failed to make any sense out of them? If your answer is yes, this book is for you. As Albert Einstein said this book is a lucid representation of fundamental concepts and methods of whole field of mathematics. But, it is not a casual mathematics history book which you can flip through at leisure. It is a serious read involving actual mathematics and should be treated as a reference book and should be refrenced from time to time, specially if you are in high schoo Passed a lot of math courses but failed to make any sense out of them?
It is a serious read involving actual mathematics and should be treated as a reference book and should be refrenced from time to time, specially if you are in high school or college. Dec 22, Ron Banister rated it really liked it.
One of my favorite books on mathematics. Also, one of Einstein's favorites. Apr 15, Alan Chan rated it it was amazing. Everyone who's interested in Math should read this book.
Jun 20, CM rated it it was ok Shelves: didnt-finish , sci-n-maths. So I returned the book after page The premise is promising: bridging high school and college mathematics by going through all major areas of mathematics from scratch and showing everything in proof with exercise problems.
While one can learn a lot of the actual rationale behind the mathematical principles we study with rote learning like why we get a positive number from multiplying two negative numbers , the explanation ,for this reader, is often too technical and requires multiple reading So I returned the book after page While one can learn a lot of the actual rationale behind the mathematical principles we study with rote learning like why we get a positive number from multiplying two negative numbers , the explanation ,for this reader, is often too technical and requires multiple reading to follow its logic Yet, there are times when this reader spent the whole evening to get through 2 pages The lack of any tip for the exercise here is not helping either.
As a book to bring expertise knowledge to the public, it's hard to see why the author decided to convey his content in this dry, technical tone. The author did suggest readers to skip all the harder parts and enjoy the journey but, argh, just so frustrating. Sep 25, Noureldin rated it it was amazing Shelves: pop-science. Jul 01, Parsa rated it really liked it. As a first approximation, here are the abridged contents of the book more on all of these later : Chapter 1 : natural numbers intuitive "definition" of integers, representations of integers in non-decimal bases.
Elementary number theory congruence, divisibility etc. Chapter 2: number systems definitions of Q and R not formal definitions, but reasonably well-exp Q. Chapter 2: number systems definitions of Q and R not formal definitions, but reasonably well-explained , cardinality of reals. Chapter 3 : geometrical constructions limits of ruler and compass constructions, proofs of the impossibility of two of the three famous Greek construction problems trisecting and angle and all that Chapter 4: mainly projective geometry, remarks on non-euclidean geometries, discussion of the axiomatic method.
Chapter 5: Basics of Topology. Chapter 6: functions and limits Chapter 7: Maximum and minimum problems Chapter 8 : Differential and integral calculus Q.
Generally, the proofs are provided, but they are not absolutely rigorous. Sometimes, the proofs are merely hinted at, this can be seen particularly on the chapter on Topology.
Again, varies chapter by chapter. But this is mainly a consequence of the changes in mathematics education since the book was published. I think that the chapters on geometry, especially chapter 4, were quite difficult, but I think that this is partly because of the lack of proper education in geometry in current school curricula.
Some other chapters, by contrast, were easy. Indeed, I only skimmed chapters 6 and 8 because I felt I was already familiar with most of the content. One might think that this is a book that talks about mathematics, without any actual mathematics being done.
This is not the case. This can mostly be thought of as an ordinary textbook on elementary mathematics.
Now, by this I don't mean that the contents are easy or shallow, they are not. You could say that the book is a response to the question : " What happens if you start thinking more deeply about certain areas of high-school mathematics? My main problem with the book was the over-emphasis on classical geometry. Although it is a beautiful subject, and I learnt many things that I'm certain I would not have known about in a standard undergraduate curriculum say, projective geometry , It is far-removed from most of the modern undergraduate mathematics curriculum, and seems to me to be almost a dead subject.
This is not, by itself, a problem. But I was reading this book mostly to prepare for university mathematics, and I Don't think that it did a very good job in that. However, in some ways, This was a type of book I had always wished to have read.
I always had the suspicion that my knowledge of elementary mathematics was woefully incomplete, and there are certainly many deep theorems and beautiful results to be found there. Indeed, there are, and you can find them in this book.
View 1 comment. Apr 26, Isaac Lambert rated it really liked it. I most enjoyed the problems I haven't worked rigorously before- see e. Jun 11, Erickson rated it it was amazing Shelves: mathematics. Skimmed through and it is quite useful, very similar to one of Felix Klein's books in terms of style. A little too mathematics for my purposes which is more towards physics, some insights are good nonetheless. Sep 04, Maria rated it liked it.
Chapter 2: numbe el review compiado de otra persona en goodreads pero tiene casi todo lo que yo diria Q. Indeed, there are, and you can find them in this book This is a good book to read in your first years in the maths degree, even for prospective mathematics students who wants an advance of how university mathematics are.
I think this is a high school level extension, but a very strong extension. Besides, Courant and Robbins give their opinion about the necessity of the mathematical concepts and ideas, just as their location in Mathematics, understanding these as an interconnected discipline. The edition I read is a revision by Ian Stewart, who added This is a good book to read in your first years in the maths degree, even for prospective mathematics students who wants an advance of how university mathematics are.
The edition I read is a revision by Ian Stewart, who added some commentaries and wrote extensions to several of the chapters in the light of recent progress well, recent in when this edition was published.
The chapters are almost entirely independent of one another, each one about a different mathematical topic, like natural numbers, ruler and compass contructions, projective geometry, topology, calculus or the number system.
Often the beginning is easier to understand, and then the path leads gradually upward. A reader who wants only a general vision may be content with a selection of material, avoiding the more detailed discussions. It's a book not to read in a day. It requires time and patience.
You will need paper and pencil near you. And to really enjoying it you have to have certain previous knowledge in issues like trigonometry or calculus. If not, you can be a little lost sometimes The book includes many exercises proposed to the advanced reader, some are easier and some a bit more difficult. The authors come out with them between discussiones, and Ian Stewarts add a bunch of them at the end of the book.
Aug 09, Michael Cayley rated it really liked it Shelves: maths. The book covers a broad range of topics in mainly pure maths. It should be comprehensible to anyone who has done the equivalent of UK "A" Level maths. To get the most out of it, you need to be willing to concentrate hard - explanations are clear but sometimes at a breathless pace - and to tackle some of the exercises.
The most technical parts are clearly flagged up as optional reading. For anyone wanting to go beyond school maths, or about to embark on a maths course at university, the book wi The book covers a broad range of topics in mainly pure maths.
For anyone wanting to go beyond school maths, or about to embark on a maths course at university, the book will be invaluable. If I have a quibble, it is that the exercises and some parts of the book are printed in smallish type which my ageing eyes had difficulty coping with, especially when it came to subscripts and superscripts, some of which I could not decipher. In places the notation - for instance some symbols used in relation to sets - is outmoded, but this is not a significant problem.
Jun 23, Erick Corona rated it really liked it. A nice book to get an overall understanding of the main fields of math. It's difficult to read sometimes, I read some sections without a full understanding, but it did help me have a better intuition of those topics. From this intuitive understanding now I will deepen my knowledge through other books and resources, this book is a good starting point.
I think more illustrations would make it easier to understand. The kindle edition has display issues. Math expressions are sometimes too small o blur A nice book to get an overall understanding of the main fields of math. Math expressions are sometimes too small o blurry. I recommend it to those who have many unknowns in math, those who got through school solving problems but lacking real understanding, or locking knowledge of how the different math areas relate.
Aug 16, Parham Hasani rated it it was amazing. I think it's good for Bachelor's students in Engineering or computer science. Aug 29, nika rated it really liked it Shelves: math. Nov 02, Abbas Moosajee rated it really liked it Shelves: math. An amazing introduction to mathematics, that not only discusses the methodology and logic taught in school but discusses the importance of maths to society, and how mathematical education can be revoltionized.
Oct 31, NuwAn rated it it was amazing. If this book didn't exist I would hate math with a passion. I would assume that it is just memorizing the way to reach certain solutions and applying the skelton framwork on test. But the logical break down of math in this book makes the subject so beautiful to learn about. Jul 22, Laura rated it really liked it. I liked it!
I could relate to much of the writing angst and decisions about stepping away from the novel writing. I loved this book. The book spends nearly all its time focusing on motivations and ideas, and much less on mechanical details. This is a sharp contrast to most under I loved this book.
This is a sharp contrast to most undergrad classes, where lack of time means the professor ends up working plenty of examples and hoping the quick tour of big ideas sticks.
It never does, but we always try. This book would be the perfect supplement for a mathematically-inclined undergrad who wanted a bit of context and history; I think it could be good for an eager and interested high-schooler, though it wouldn't hurt to have someone on hand to help talk things through.
Of course, a few bits didn't age as well as they could, eg the commentary about infinitesimals was a bit more awkward in light of the development of nonstandard analysis. Can't fault Courant and Robbins for not predicting the future, of course; the new final chapter does a great job of these sorts of updates. I'm sad it took me so long to read this book -- I'd seen it a zillion times, and I think my old roommate even had a copy in our dorm, but I'd never cracked it open.
I wish I had, both for my own enjoyment and to recommend to others. There are no discussion topics on this book yet. Be the first to start one ».
Readers also enjoyed. Goodreads is hiring! If you like books and love to build cool products, we may be looking for you. Learn more ». About Richard Courant. Richard Courant. He is best known by the general public for the book What is Mathematics? Books by Richard Courant. Some of the best stories take a few hundred years to tell. But if you're in the mood for uncanny connections, hoping back and forth through Read more Trivia About What Is Mathemati This book is a Masterpiece like no other.
It starts off with the most elementary ideas about numbers and before the reader realises, he is being introduced to advanced concepts. The transition is seamless and mentally unhindered -an worthy achievement in itself.
I only wish I had somet This should be a school text book with some chapters excluded of course. It is absolutely lovable and it makes math fun and simple. Great writing. Goutham V Certified Buyer. The Book is very informative.. I feel every Mathematics student should read this book. I have suggested to go through this book to my followers. R Rajendra Certified Buyer , Madikeri. Snehlata Dhanda Certified Buyer , Chandigarh.
The content of the book is very nice. The way the writer explain the matter is marvellous.. Those who really want to clear the concepts for mathematics Sagar Jadhav Certified Buyer , Pune. Genuine, precise, simple and clear. It doesn't let you bother about anything the way the other ordinary texts in maths do.
No ordinary explanation. The book deals with troubles in mathematics in an exact fashion of Feynman's classics in Physics. Maths is not an empty drill in problem solving but is much like a journalism with a divine taste. The book makes you feel exactly the same. An ordinary knowledge of high school mathematics is sufficient to understand this wo It is really an awesome book to learn new concepts in mathematics with ease.
Fatima Hussain Certified Buyer , Lakhimpur. Nice book and covers syallbus up to 12th class. Tge language is also simple as tgey give proof to Fermat's last theorem according to quadratic expression. Questions and Answers. Q: For which cass or level.
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