I have some proof experience (some velleman how to prove it, some cs courses) and have learned computational single variable calculus before. Right now I’m trying to tackle Spivak’s calculus (self study) and I’m struggling even at chapter 1’s exercises (25 total). My initial belief was that given my inexperience in proof based math it is going to be difficult and a steep learning curve but if I persevere I will eventually struggle less and less, but now I’m questioning that belief.

The first 15 or so exercises in chapter 1 were difficult at times but doable with effort. The more difficult ones took me multiple hours to complete but it always felt like I was close to a proof. 16-19 however gets really difficult for me in that I sometimes don’t even know where to start and I don’t really get closer to a solution (19 which concerns the Schwarz inequality has taken me 1 hour+ and I’m not even done with part a out of d) and some of 20-25 make my head hurt just looking at them.

So it’s looking like I may have to try for however long and then ultimately look for the solutions in the solutions book for each of the remaining exercises in chapter 1, or spend 4+ hours on each and solve it if I’m lucky.

My question is does this mean I’m not ready for the book? Should I continue? If I end up trying for let’s say 1 hour for each exercise then giving up and looking at the solutions for the each of them, would I still be learning enough that way? Would my lack of a strong foundation in chapter 1 result in me struggling in chapter 2 and thus 3, 4, and so on? My fear is that in the remaining chapters I will also have to try and then give up and look up the answers and ultimately I will have learned nothing and will be unable to solve any difficult exercises even after I’ve completed the entire book. Advice appreciated.