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I can't do Spivak's exercises 
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#1
Mar1712, 09:40 PM

P: 38

For around 90% of Spivak's exercises, I need to look in the solutions manual. I'm on chapter 5, which covers limits, and the proofs just aren't coming to me. It's as if I just can't think like him. The question is: Should I come back later, or should I just trudge through until I have "mathematical maturity"?



#2
Mar1712, 09:46 PM

P: 1,072

What was your math background prior to forgoing Spivak?



#3
Mar1712, 09:48 PM

P: 38

I learned the properties of real numbers, proof by induction, by contradiction, and direct proof. Subjects were limits, sequences, series, vectors, logs and exps, functions and their inverses, and trigonometry. Perhaps this just has a steep learning curve and I'm adjusting. 


#4
Mar1712, 09:50 PM

P: 1,072

I can't do Spivak's exercises



#5
Mar1712, 09:52 PM

P: 38

It should be noted I understand the proofs after looking at them, but I can't think of them myself. 


#6
Mar1712, 09:54 PM

P: 1,072




#7
Mar1712, 10:49 PM

P: 1,583

It's probably a good idea to first go through the calculus material in a less rigorous setting, a conventional textbook like Stewart or Anton, and then study Spivak as a stepping stone to introductory analysis texts like Rudin (or my favorite, Carothers).



#8
Mar1712, 11:19 PM

P: 905

That's true. a lot of Spivak's problems become almost trivial once you already know the fact that you are trying to prove is true, and the general gist of why it should be true.



#9
Mar1812, 01:25 AM

P: 367

I could do about 65% of them eventually. I remember thinking it took about 2.5 hours an exercise on average (some took about 68 hours before I got them or gave up, some only about 30 min). How long are you giving yourself per question on average?



#10
Mar1812, 10:21 AM

P: 38




#11
Mar2212, 11:19 PM

P: 36




#12
Apr512, 02:19 AM

P: 832

Also, is the appendix on Spivak's book not just a rigorous precalculus course? 


#13
Apr512, 08:54 AM

P: 1,072




#14
Apr512, 09:24 AM

P: 832




#15
Apr1012, 10:57 PM

P: 52

I had to rely heavily on the solutions manual at first, as well. I would try to just look at it one line at a time to give me a bump in the right direction, but at first I almost completely relied on it. Specifically I had trouble seeing why things even needed to be proved in the first place, when intuition makes the truth of the statement appear obvious. Gradually, I needed it less and less. Possibly I didn't get as much out of the beginning as I would have if I was properly prepared, but that's life.
As long as you're working through every problem and making an honest effort without using the solutions manual, I think you will find that eventually you won't need it anymore. 


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