Question about Courant's Introduction to calculus and analysis

[Gravitational]

I am extremely interested in mathematics, and most probably plan to major in it. Do you guys feel as though this book would be accessible to a high-school student, willing to gain a more rigorous understanding of calculus? I have already completed calculus 1 and found it rather easy, and I am willing to take a step up in difficulty.

 

[deluks917]

It is accessible but it will not be easy. Go for it.

 

[Gravitational]

What is the level of difficulty like?

 

[deluks917]

Its hard to explain if you have never done math with proofs before. In my experience it is much harder (and more rewarding) to use a book like Courant than a regular calc book. I learned this stuff from Spivak (a lot of material overlap) and I remember it took me on average a little over two hours per problem. I remember not even knowing "what a proof was" when I started but the book really taught me a lot and made me appreciate math. I'm not sure how hard you will find it but if the going gets slow be aware in "higher math" the going usually is slow for everybody.

 

[Gravitational]

thanks for the input. I have had some experience with proofs before, as I have read several number theory texts, where the format is basically, theorem, proof, corollary, etc. Do you feel as though Courant or Spivak would be a better choice?

 

[mathwonk]

spivak is more user friendly, but aimed at the pure mathematician. courant has more applications to physics. I conjecture that spivak himself learned from courant then wrote his own book.

 

[deluks917]

Courant is probably better if you like physics. Can't really go wrong with either.

 

[sponsoredwalk]

http://archive.org/details/DifferentialIntegralCalculusVolI is a link to the original version of the book. Just read the first chapter, it's a litmus test - if you get through it without headaches then buy both volumes of the newer edition. When you get to the second volume(s) make sure you refer to the http://archive.org/details/DifferentialIntegralCalculusVol2 volume of the older edition simultaneously to get two pretty different perspectives on the same material.

 

[bda23]

Funny that you're asking the question because a few years ago when I was in high school I was in a similar situation and incidentally started off with Courant and John's Introduction to Calculus and Analysis. I must say, I greatly benefited from the book and didn't find it too difficult at all. It is very well written and introduces many concepts quite well. However, the book I used (which is, I think, not exactly the same as the one you're referring to, although similar) is very thick and it can be a bit frustrating trying to work through all of it as a beginner. It goes into great depth and in your situation it may be a good idea to go for a text that introduces a variety of concepts in analysis, but is a bit thinner and easier to work through. I've found "A first course in real analysis" by Protter and Morrey very good in that respect, as it introduces analysis in one and several dimensions, metric spaces, infinite series and many other concepts and gives a good overview. The explanations are very clear, the proofs make good sense and the exercises are very doable (Courant's exercises can be a bit more difficult at times, which is good, but in the beginning a more leisurely going speed may make it more fun). However, you can't really go wrong with Courant either, in my opinion, so whichever you choose it should be very doable.