Math Major Struggles With Apostol's Calculus

[bonfire09]

Ive taken calculus 1-3 and differential equations and didnt think they were hard at all. I like math quite a bit so I decided to open Apostol's Single Variable Calculus Book and decided to attempt the problems. I was only able to do 30% of them and figured that Apostol's calculus is way too hard for me. I'm a math major and I know that I'll need to have done Apostols or spviak's books on Calculus for real analysis, but not being able to do Apostol's calculus is really frustrating me. Is there another way I can go? like maybe read an intro to proofs book and afterwards try doing apostols?

 

[micromass]

The exercises in Apostol can be quite tricky and difficult. You certainly don't need to be able to solve all of them before taking real analysis.

Can you give us a reason why you can't solve those exercises?? Can you give us an example??

 

[bonfire09]

here is an example of a problem in the very first section. I've hardly encountered a proof by induction

 

[intwo]

here is an example of a problem in the very first section. I've hardly encountered a proof by induction

I recommend skipping that section and starting from I 2.1 (Introduction to set theory). You can return to it after you finish the sections on induction (I 4.1 - I 4.10) or skip it entirely.

 

[mathwonk]

go right now and learn proofs by induction. do not pass go until you do, indeed you will not be able to pass go until you do. this is absolutely fundamental. i thought this was still taught in high school. here is a free set of notes on the topic.

 

[bonfire09]

i haven't had much exposure on proofs in a long time. Last time I had to do proofs were in geometry. I became good at it but after a while I forget about it.