1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inability to solve problems

  1. Jun 21, 2008 #1
    Hi all. What do you do when you are reading a math book and there are multiple problems you can't solve in a chapter?

    For example, I am trying to learn from Apostol's book "Mathematical Analysis". In the problems at the end of the first chapter there are two that I haven't been able to figure out how to solve. It seems like the solution should be so simple but I'm just not seeing it. (There are two more I haven't attempted yet, but I think I can solve them.) Does this mean I'm not ready for the book and should get an easier one? Or is not being able to solve a couple problems in a chapter normal?

    In case anyone's wondering, here's one of the problems I haven't been able to figure out:

    Let [tex]w[/tex] be a given complex number. If [tex]w\not=\pm 1[/tex], show that there exist two values of [tex]z=x + iy[/tex] satisfying the conditions [tex]cos(z)=w[/tex] and [tex]-\pi<x\leq\pi[/tex].

    The identity [tex]cos(z) = cos(-z)[/tex] says that if there is one such [tex]z[/tex], there have to be two... Other than that I'm at a loss.
    Last edited: Jun 21, 2008
  2. jcsd
  3. Jun 21, 2008 #2
    I keep a set of notes per book with a section with problems that I can't solve.

    If you're able to solve all the problems in the book without trouble, I would say the book was too easy.

    Try to solve a more specific problem, say w = 0, w = i, or w = 1 + i. This should provide you with some insight.
  4. Jun 22, 2008 #3


    User Avatar
    Homework Helper

    Personally I don't know of anyone who is able to solve every single problem in a given textbook. Usually the authors would throw in a few difficult ones for every chapter's exercises. But that doesn't mean you shouldn't attempt to solve them.
  5. Jun 22, 2008 #4
    Thanks for the encouragement. The first chapter was starting to get boring (as "first chapters" tend to do) so I decided to move on and come back to try to solve those problems again later.

    One of the ones I didn't attempt was proving the Cauchy-Schwarz inequality for complex numbers (the book gives a hint that looks like it makes this reasonably easy although I haven't tried) which according to the book is an extremely important result in analysis... so I may have to come back to that sooner rather than later, lol.
  6. Jun 23, 2008 #5
    You can also try posting the questions and your attempt at solutions in the homework help section of this forum.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook