- Hardcover: 680 pages
- Publisher: Publish or Perish; fourth edition (July 9, 2008)
- Language: English
- ISBN-10: 0914098918
- ISBN-13: 978-0914098911
- Product Dimensions: 10 x 9.2 x 1.5 inches
- Shipping Weight: 3.8 pounds (View shipping rates and policies)
- Average Customer Review: 4.4 out of 5 stars See all reviews (130 customer reviews)
- Amazon Best Sellers Rank: #47,056 in Books (See Top 100 in Books)
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Calculus, 4th edition fourth Edition
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Top Customer Reviews
Furthermore, I do not believe it is possible to truly understand what a limit is if you don't read something like this. I am appalled at calculus curricula at colleges and universities that just expect you to memorize rules and drill problems over and over; I prefer knowing exactly why something is true before doing any problems. I also prefer fully 100% understanding every single reason a theory works, so this book is perfect for me, though it doesn't construct the real numbers from the rationals. This is a prerequisite to understanding limits because if you don't understand what irrational numbers are first, then you'll never understand what is meant by "infinitely close," period. So I recommend you buy "Understanding Analysis" by Stephen Abbott with this book, and read ch1 of Abbott before this. That way you'll know what a real number actually is, by the way, it's the limit of a sequence of rational numbers, but don't worry, Abbott ch 1 is incredibly well written and you'll get it if you just read it and think about why it makes sense. If you want a little deeper of an understanding than Abbott (which is splitting hairs, and few could pull it off, but the man I'm about to name is one of the few who can) then take a look at "Analysis 1" by Terrance Tao. I'd read either of these analysis books before or concurrently with Spivak, and I might also suggest grabbing a copy of "Single Variable Calculus: Concepts and Contexts" 4th edition, by James Stewart in order to see the applications of things like the integral and in order to get a better idea of how modern courses have a working understanding of the subject in general. Sometimes it's just good to be up to date with things.
Even though I love this book, there are a few things I would like to tell people who are looking at potentially buying this book
1), This will most likely be your first encounter with real mathematics. This book tests an entirely new skill-set that isn't developed in high schools today, so there will naturally be a steep learning curve. Take heart! Chapters 1, 2 and 5 are the worst; all the others are not as bad.
2). Know what you want! This book is mathematically rigorous (aka proofs). If you are an engineer or anything other than a student of pure mathematics, this will not be your cup of tea.
3). You will never again solve a problem in under 5 minutes! Many people who claim to be "good at math" have only seen the routine exercises that comprise high school mathematics today. Please be aware that this book contains PROBLEMS that force you to think long and hard and actually learn something. There are several reviews that claim that the questions are completely separate from the text, and that this book does not sufficiently prepare you for attacking the problems sets. I would like to say that, yes, the problems sets can easily become the problem sets from hell. However, everything you need to tackle them is there. Many reviewers are used to the "Oh look, I'm given a formula, and now I punch in numbers to solve these twenty exercises. Look how good I am at math mom!" type of math book. This book is staggeringly different.
However, if you knew all of this and still wish to buy this, or if these three cautions only excited you more, you may have what it takes to get through and love this book. This is a great first exposure to mathematics, and it truly prepares you to tackle the likes of Walter Rudin's Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics).
Most Recent Customer Reviews
The material is written with extreme clarity and the organization of the material...Read more
Very reader-friendly book.
If you cannot understand epsilon - delta proofs, then you must read this book.Read more